Combinatorics and graph theory Books
Taylor & Francis Inc Handbook of Graph Theory
Book SynopsisIn the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second editionover 400 pages longer than its predecessorincorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation.With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick aTrade ReviewPraise for the First Edition:… a fine guide to various literatures, especially for topics like Ramsey theory … . Many first-rate mathematicians have contributed, making the exposition's quality high overall. …. Highly recommended.—CHOICE, January 2005, Vol. 42, No. 05Praise for the First Edition:… a fine guide to various literatures, especially for topics like Ramsey theory … . Many first-rate mathematicians have contributed, making the exposition's quality high overall. …. Highly recommended.—CHOICE, January 2005, Vol. 42, No. 05Table of ContentsIntroduction to Graphs. Graph Representation. Directed Graphs. Connectivity and Traversability. Colorings and Related Topics. Algebraic Graph Theory. Topological Graph Theory. Analytic Graph Theory. Graphical Measurement. Graphs in Computer Science. Networks and Flows. Communication Networks. Natural Science and Processes. Index.
£194.75
MP-AMM American Mathematical Asymptopia
Book SynopsisTrade ReviewThe style and the beauty make this book an excellent reading. Keep it on your coffee table or/and bed table and open it often, Asymptopia is a fascinating place." - Péter Hajnal, ACTA Sci. Math.Table of Contents An infinity of primes Stirling's formula Big Oh, little Oh and all that Integration in Asymptopia From integrals to sums Asymptotics of binomial coefficients (n k ) Unicyclic graphs Ramsey numbers Large deviations Primes Asymptotic geometry Algorithms Potpourri Really Big Numbers! Bibliography Index
£47.70
MP-AMM American Mathematical Combinatorial Reciprocity Theorems An Invitation
Book SynopsisUsing the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature.Table of Contents Four polynomials Partially ordered sets Polyhedral geometry Rational generating functions Subdivisions Partially ordered sets, geometrically Hyperplane arrangements Bibliography Notation index Index.
£108.00
MP-AMM American Mathematical Polynomial Methods in Combinatorics
Book SynopsisExplains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields. The author also discusses in detail various problems in incidence geometry associated to Paul Erdos's distinct distances problem in the plane from the 1940s.Trade ReviewSome of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accomplished using the polynomial method. Larry Guth gives a readable and timely exposition of this important topic, which is destined to influence a variety of critical developments in combinatorics, harmonic analysis and other areas for many years to come." - Alex Iosevich, University of Rochester, author of The Erdos Distance Problem and A View from the Top"It is extremely challenging to present a current (and still very active) research area in a manner that a good mathematics undergraduate would be able to grasp after a reasonable effort, but the author is quite successful in this task, and this would be a book of value to both undergraduates and graduates." - Terence Tao, University of California, Los Angeles, author of An Epsilon of Room I, II and Hilbert's Fifth Problem and Related Topics"In the 273 page long book, a huge number of concepts are presented, and many results concerning them are formulated and proved. The book is a perfect presentation of the theme." - Béla Uhrin, Mathematical Reviews "One of the strengths that combinatorial problems have is that they are understandable to non-experts in the field...One of the strengths that polynomials have is that they are well understood by mathematicians in general. Larry Guth manages to exploit both of those strengths in this book and provide an accessible and enlightening drive through a selection of combinatorial problems for which polynomials have been used to great effect." - Simeon Ball, Jahresbericht der Deutschen Mathematiker-VereinigungTable of Contents Introduction Fundamental examples of the polynomial method Why polynomials? The polynomial method in error-correcting codes On polynomials and linear algebra in combinatorics The Bezout theorem Incidence geometry Incidence geometry in three dimensions Partial symmetries Polynomial partitioning Combinatorial structure, algebraic structure, and geometric structure An incidence bound for lines in three dimensions Ruled surfaces and projection theory The polynomial method in differential geometry Harmonic analysis and the Kakeya problem The polynomial method in number theory Bibliography
£54.90
MP-AMM American Mathematical A Unified Approach to Structural Limits and Limits of Graphs with Bounded TreeDepth
Book SynopsisIntroduces a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases'' of a general theory.Table of Contents Introduction General theory Modelings for sparse structures Limits of graphs with bounded tree-depth Concluding remarks.
£67.50
MP-AMM American Mathematical The TriangleFree Process and the Ramsey Number
Book SynopsisIn 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that $R(3,k) = \Theta \big ( k^2 / \log k \big )$. In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.Table of Contents Introduction An overview of the proof Martingale bounds: the line of peril and the line of death Tracking everything else Tracking $Y_e$, and mixing in the $Y$-graph Whirlpools and Lyapunov functions Independent sets and maximum degrees in $G_n,\triangle $ Bibliography.
£72.20
MP-AMM American Mathematical Introduction to Analysis on Graphs
Book SynopsisExplores the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk on finite graphs.Table of Contents The Laplace operator on graphs Spectral properties of the Laplace operator Geometric bounds for the eigenvalues Eigenvalues on infinite graphs Estimates of the heat kernel The type problem Exercises Bibliography Index
£55.80
MP-AMM American Mathematical Graphs and Geometry
Book SynopsisGraphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool.Trade ReviewGeometric representations of graphs lead to significant insights in the study of graph properties and their algorithmic aspects. This book is a thorough study of the subject written by the pioneer of many of the results in the area. It is a fascinating manuscript written by a superb mathematician who is also a fantastic expositor." - Noga Alon, Princeton University and Tel Aviv University"A beautiful book, rich in intuition, insights, and examples, from one of the masters of combinatorics, geometry, and graph theory. This book presents old friends of graph theory in a new light and introduces more recent developments, providing connections to many areas in combinatorics, analysis, algorithms, and physics. Those of us who know graph theory still have much to learn from this presentation; for those who are new to the field, the book is a wonderful gift and invitation to participate." - Jennifer Chayes, Microsoft Research"Laszlo Lovasz is one of the most prominent experts in discrete mathematics. The book is unique and inspiring for students and researchers as well. The author succeeded to show the wealth and beauty of the subject." - Endre Szemeredi, Rutgers UniversityTable of Contents Why are geometric representations interesting? Planar graphs Rubber bands Discrete harmonic functions Coin representation Square tilings Discrete analytic functions Discrete analytic functions: Statistical physics Adjacency matrix and its square Orthogonal representations: Dimension Orthogonal representations: The smallest cone Orthogonal representations: Quantum physics Semidefinite optimization Stresses Rigidity and motions of frameworks The Colin de Verdiere number Metric representations Matching and covering in frameworks Combinatorics of subspaces Concluding thoughts Appendix A: Linear algebra Appendix B: Graphs Appendix C: Convex bodies Bibliography Author index Subject index
£78.30
American Mathematical Society Graph Theory
Book SynopsisPresents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems intended to be used as homework assignments.Trade ReviewThis work could be the basis for a very nice one-semester ""transition"" course in which students evolve from users of theorems to creators of proofs. With their intuitive appeal and pictorial representations, graphs may be a better basis than analysis and limits for such a transtion."" - Choice
£59.40
American Mathematical Society DavenportZannier Polynomials and Dessins dEnfants
Book SynopsisThe polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.Table of Contents Introduction. Dessins d'enfants: From polynomials through Belyi functions to weighted trees. Existence theorem. Recapitulation and perspective. Classification of unitrees. Computation of Davenport-Zannier pairs for unitrees. Primitive monodromy groups of weighted trees. Trees with primitive monodromy groups. A zoo of examples and constructions. Diophantine invariants. Enumeration. What remains to be done. Bibliography. Index.
£115.60
MP-AMM American Mathematical Conversational Problem Solving
Book SynopsisPresents a dialogue between a professor and eight students in a summer problem solving camp and allows for a conversational approach to the problems as well as some mathematical humour and a few non-mathematical digressions. The problems have been selected for their entertainment value, elegance, trickiness, and unexpectedness.Table of Contents The first day Polynomials Base mathematics A mysterious visitor Set theory Triangles Independence day Independence aftermath Amanda An aesthetical error Miraculous cancellation Probability theory Geometry Hodegepodge Self-referential mathematics All good things must come to an end Bibliography Index.
£39.56
MP-AMM American Mathematical The Mathematics of Shuffling Cards
Book SynopsisProvides a lively development of the mathematics needed to answer the question, ‘How many times should a deck of cards be shuffled to mix it up?’ The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table.Table of Contents Shuffling cards: An introduction Practice and history of shuffling cards Convergence rates for riffle shuffles Features Eigenvectors and Hopf algebras Shuffling and carries Different models for riffle shuffling Move to front shuffling and variations Shuffling and geometry Shuffling and algebraic topology Type B shuffles and shelf shuffling machines Descent algebras, $P$-partitions, and quasisymmetric functions Overhand shuffling ``Smoosh'' shuffle How to shuffle perfectly (randomly) Applications to magic tricks, traffic merging, and statistics Shuffling and multiple zeta values Bibliography Index
£66.50
MP-AMM American Mathematical An Introduction to Proof via InquiryBased
Book SynopsisA textbook for the transition to proof course for mathematics majors. Designed to promote active learning through inquiry, the book features a highly structured set of leading questions and explorations. The content ranges over topics traditionally included in transitions courses.Table of Contents Introduction Mathematics and logic Set theory Induction The real numbers Three famous theorems Relations and partitions Functions Cardinality Elements for syle for proofs Fancy mathematical terms Paradoxes Defintions in mathematics
£25.60
MP-AMM American Mathematical The Unity of Combinatorics
Book SynopsisTopics covered include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable.Table of Contents Introduction Blocks, sequences, bow ties, and worms Combinatorial games Fibonacci, Pascal, and Catalan Catwalks, sandsteps, and Pascal pyramids Unique rook circuits Sums, colorings, squared squares, and packings Difference sets and combinatorial designs Geometric connections The groups $PSL(2,7)$ and $GL(3,2)$ and why they are isomorphic Incidence matrices, codes, and sphere packings Kirkman's Schoolgirls, fields, spreads, and hats $(7,3,1)$ and combinatorics $(7,3,1)$ and normed algebras $(7,3,1)$ and matroids Coin turning games and Mock Turtles The $(11,5,2)$ biplane, codes, designs, and groups Rick's Tricky Six Puzzle: More than meets the eye $S(5,8,24)$ The miracle octad generator Bibliography Index
£51.30
MP-AMM American Mathematical Inverse Problems and Zero Forcing for Graphs
Book SynopsisProvides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to a rich set of deep problems in that area as well as a breadth of ‘ancillary’ problems in related areas.Table of Contents Introduction to the inverse eigenvalue problem of a graph and zero forcing: Introduction to an motivation for the IEP-$G$ Zero forcing and maximum eigenvalue multiplicity Strong properties, theory, and consequences: Implicit function theorem and strong properties Consequences of the strong properties Theoretical underpinnings of the strong properties Further discussion of ancillary problems: Ordered multiplicity lists of a graph Rigid linkages Minimum number of district eigenvalues Zero forcing, propagation time, and throttling: Zero forcing, variants, and related parameters Propagation time and capture time Throttling Appendix A. Graph terminology and notation Bibliography Index
£98.10
MP-AMM American Mathematical An Invitation to PursuitEvasion Games and Graph
Book SynopsisSurveys different areas in graph searching and highlights many fascinating topics intersecting classical graph theory, geometry, and combinatorial designs. Each chapter ends with approximately twenty exercises and five larger scale projects.
£46.80
MP-AMM American Mathematical An Introductory Course on Mathematical Game
Book SynopsisAn introductory and up-to-date course on game theory for mathematicians, economists and other scientists with a basic mathematical background. This self-contained book provides a formal description of classic game-theoretic concepts alongside rigorous proofs and illustrates the theory through abundant examples, applications, and exercises.Table of Contents Introduction to decision theory Strategic games Extensive games Games with incomplete information Fundamentals of cooperative games Applications of cooperative games Bibliography Notations Index Index of solution concepts Subject Index
£106.20
American Mathematical Society Topological and Ergodic Theory of Symbolic
Book SynopsisIntroduces symbolic dynamics from a perspective of topological dynamical systems. After introducing symbolic and topological dynamics, the core of the book consists of discussions of subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and the ergodic properties of these systems.Table of Contents First examples and general properties of subshifts Topological dynamics Subshifts of positive entropy Subshifts of zero entropy Further minimal Cantor systems Methods from ergodic theory Automata and linguistic complexity Miscellaneous background topics Solutions to exercises Bibliography Index
£98.80
American Mathematical Society Topological and Ergodic Theory of Symbolic
Book SynopsisIntroduces symbolic dynamics from a perspective of topological dynamical systems. After introducing symbolic and topological dynamics, the core of the book consists of discussions of subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and the ergodic properties of these systems.Table of Contents First examples and general properties of subshifts Topological dynamics Subshifts of positive entropy Subshifts of zero entropy Further minimal Cantor systems Methods from ergodic theory Automata and linguistic complexity Miscellaneous background topics Solutions to exercises Bibliography Index
£67.45
American Mathematical Society Numbers and Figures
Book SynopsisOne of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their connections to geometry, calculus, and real-life problems such as COVID-19 vaccines.Table of Contents Integer points, polygons, and polyhedra Simpson's paradox, Farey sequences, and Diophantine approximation A coin problem and generating functions Pythagorean triples and sums of squares Benford's law, uniform distribution and normal numbers Sums and integrals Index
£46.80
American Mathematical Society Proofs that Really Count
Book SynopsisMathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.Trade ReviewThis book is written in an engaging, conversational style, and this reviewer found it enjoyable to read through (besides learning a few new things). Along the way, there are a few surprises, like the 'world's fastest proof by induction' and a magic trick. As a resource for teaching, and a handy basic reference, it will be a great addition to the library of anyone who uses combinatorial identities in their work." —Society for Industrial and Applied Mathematics Review
£48.60
MP-AMM American Mathematical Combinatorics A Guided Tour
Book SynopsisCombinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Polya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.Trade ReviewThis is a well-written, reader-friendly, and self-contained undergraduate course on combinatorics, focusing on enumeration. The book includes plenty of exercises, and about half of them come with hints."" - M. Bona, Choice Magazine""The delineation of the topics is first rate-better than I have ever seen in any other book. ... CAGT has both good breadth and great presentation; it is in fact a new standard in presentation for combinatorics, essential as a resource for any instructor, including those teaching out of a different text. For the student: If you are just starting to build a library in combinatorics, this should be your first book."" - The UMAP Journal""... [This book] is an excellent candidate for a special topics course for mathematics majors; with the broad spectrum of applications that course can simultaneously be an advanced and a capstone course. This book would be an excellent selection for the textbook of such a course. ... This book is the best candidate for a textbook in combinatorics that I have encountered."" - Charles Ashbacher
£60.30
MP-AMM American Mathematical An Introductory Course on Mathematical Game
Book SynopsisPresents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field.Table of Contents Introduction to decision theory Strategic games Extensive games Games with incomplete information Fundamentals of cooperative games Applications of cooperative games Bibliography Notations Index Index of solution concepts Subject index.
£71.10
American Mathematical Society Combinatorial Game Theory
Book SynopsisIt is wonderful to see advanced combinatorial game theory made accessible. Siegel's expertise and enjoyable writing style make this book a perfect resource for anyone wanting to learn the latest developments and open problems in the field. --Erik Demaine, MIT Aaron Siegel has been the major contributor to Combinatorial Game Theory over the last decade or so. Now, in this authoritative work, he has made the latest results in the theory accessible, so that the subject will achieve the place in mathematics that it deserves. --Richard Guy, University of Calgary Combinatorial game theory is the study of two-player games with no hidden information and no chance elements. The theory assigns algebraic values to positions in such games and seeks to quantify the algebraic and combinatorial structure of their interactions. Its modern form was introduced thirty years ago, with the publication of the classic Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy, and interest has raTable of Contents Combinatorial games Short games The structure of $\mathbb{G}$ Impartial games Misere play Loopy games Temperature theory Transfinite games Open problems Mathematical prerequisites A finite loopfree history Bibliography Glossary of notation Author index Index of games Index.
£66.60
Taylor & Francis Inc Monomial Algebras
Book SynopsisMonomial Algebras, Second Edition presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including StanleyReisner rings, monomial subrings, Ehrhart rings, and blowup algebras. It emphasizes square-free monomials and the corresponding graphs, clutters, or hypergraphs. New to the Second Edition Four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs Two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs Full revisions of existing chapters to provide an up-to-date account of the subject Bringing together several areas of pure and applied mathematics, this book shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs. It Trade Review"… an introduction to algebraic, combinatorial, and computational aspects of monomial ideals. In the second edition, a full revision of all the chapters has been made."—Zentralblatt MATH 1325Table of ContentsPolyhedral Geometry and Linear Optimization. Commutative Algebra. Affine and Graded Algebras. Rees Algebras and Normality. Hilbert Series. Stanley–Reisner Rings and Edge Ideals of Clutters. Edge Ideals of Graphs. Toric Ideals and Affine Varieties. Monomial Subrings. Monomial Subrings of Graphs. Edge Subrings and Combinatorial Optimization. Normality of Rees Algebras of Monomial Ideals. Combinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters. Combinatorial Optimization and Blowup Algebras. Appendix. Bibliography. Notation Index. Index.
£175.75
CRC Press Introduction to Number Theory
Book SynopsisIntroduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbertâs tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Eulerâs theorem in RSA encryption, and quadratic residues in the construction of tournaments. Ideal for a one- or two-semester undergraduate-level course, this Second Edition: Features a more flexible structure that offers a greater range of options for course design Adds new sections on the representations of integTrade ReviewPraise for the Previous Edition "The authors succeed in presenting the topics of number theory in a very easy and natural way, and the presence of interesting anecdotes, applications, and recent problems alongside the obvious mathematical rigor makes the book even more appealing. … a valid and flexible textbook for any undergraduate number theory course."—International Association for Cryptologic Research Book Reviews, May 2011 "… a welcome addition to the stable of elementary number theory works for all good undergraduate libraries."—J. McCleary, Vassar College, Poughkeepsie, New York, USA, from CHOICE, Vol. 46, No. 1, August 2009 "… a reader-friendly text. … provides all of the tools to achieve a solid foundation in number theory."—L’Enseignement Mathématique, Vol. 54, No. 2, 2008 The theory of numbers is a core subject of mathematics. The authors have written a solid update to the first edition (CH, Aug'09, 46-6857) of this classic topic. There is no shortage of introductions to number theory, and this book does not offer significantly different information. Nonetheless, the authors manage to give the subject a fresh, new feel. The writing style is simple, clear, and easy to follow for standard readers. The book contains all the essential topics of a first-semester course and enough advanced topics to fill a second. In particular, it includes several modern aspects of number theory, which are often ignored in other texts, such as the use of factoring in computer security, searching for large prime numbers, and connections to other branches of mathematics. Each section contains supplementary homework exercises of various difficulties, a crucial ingredient of any good textbook. Finally, much emphasis is placed on calculating with computers, a staple of modern number theory. Overall, this title should be considered by any student or professor seeking an excellent text on the subject. --A. Misseldine, Southern Utah University, Choice magazine 2016 Praise for the Previous Edition "The authors succeed in presenting the topics of number theory in a very easy and natural way, and the presence of interesting anecdotes, applications, and recent problems alongside the obvious mathematical rigor makes the book even more appealing. … a valid and flexible textbook for any undergraduate number theory course."—International Association for Cryptologic Research Book Reviews, May 2011 "… a welcome addition to the stable of elementary number theory works for all good undergraduate libraries."—J. McCleary, Vassar College, Poughkeepsie, New York, USA, from CHOICE, Vol. 46, No. 1, August 2009 "… a reader-friendly text. … provides all of the tools to achieve a solid foundation in number theory."—L’Enseignement Mathématique, Vol. 54, No. 2, 2008 The theory of numbers is a core subject of mathematics. The authors have written a solid update to the first edition (CH, Aug'09, 46-6857) of this classic topic. There is no shortage of introductions to number theory, and this book does not offer significantly different information. Nonetheless, the authors manage to give the subject a fresh, new feel. The writing style is simple, clear, and easy to follow for standard readers. The book contains all the essential topics of a first-semester course and enough advanced topics to fill a second. In particular, it includes several modern aspects of number theory, which are often ignored in other texts, such as the use of factoring in computer security, searching for large prime numbers, and connections to other branches of mathematics. Each section contains supplementary homework exercises of various difficulties, a crucial ingredient of any good textbook. Finally, much emphasis is placed on calculating with computers, a staple of modern number theory. Overall, this title should be considered by any student or professor seeking an excellent text on the subject. --A. Misseldine, Southern Utah University, Choice magazine 2016 Table of ContentsIntroduction. Divisibility. Greatest Common Divisor. Primes. Congruences. Special Congruences. Primitive Roots. Cryptography. Quadratic Residues. Applications of Quadratic Residues. Sums of Squares. Further Topics in Diophantine Equations. Continued Fractions. Continued Fraction Expansions of Quadratic Irrationals. Arithmetic Functions. Large Primes. Analytic Number Theory. Elliptic Curves.
£92.14
Taylor & Francis Inc Handbook of Geometric Constraint Systems
Book SynopsisThe Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures CTrade ReviewBroadly speaking, a geometric constraint system (GCS) consists of basic geometric objects such as points, lines, or rigid bodies that satisfy some specified geometric relationships such as distances, angles, or incidences. Such systems arise in many prac-tical applications, including computer-aided design, molecular and materials modelling, robotics, sensor networks, and machine learning. This handbook is a wide-ranging reference work on the core principles, methods, and results in GCS research. It makes this topic fully accessible to nonspecialists as well as to experts who work in this area professionally, either as academics or as practitioners in fields such as engineering or robotics. The book is divided into four major parts. The first part (Chapters 2–7) deals with geometric reasoning techniques, with many of the approaches based on algebraic meth-ods. It starts with a discussion of techniques for automated geometry theorem proving. In particular, it introduces the bracket algebra and Grassmann-Cayley algebra in the context of proving theorems in projective and Euclidean geometry. These algebras are also discussed in relation to algebraic conditions (and their geometric interpretations) that make realisations of a GCS special. After a discussion of molecular distance geome-try and algebraic invariants in geometric reasoning, the first part of the book concludes with a description of various triangle-decomposable GCSs and algorithms for solving such systems via recursive decompositions and recombinations, as well as generalisations of this method to non-triangle-decomposable GCSs. The second part (Chapters 8–12) discusses techniques for understanding dependent constraints and certain types of rigidity (such as dimensional or universal rigidity) arising from the structure of the Euclidean distance cone. This is followed by a discussion of the structure of general metric cones. Additional topics include Cayley configuration spaces and constraint varieties of mechanisms. The second part of the book concludes with an introduction to real algebraic geometry for geometric constraints. The third part (Chapters 13–17) is dedicated to geometric results and techniques for analysing the rigidity and flexibility of GCSs, with a particular focus on bar-joint frameworks. It discusses the rigidity of polyhedra in 3-space, the rigidity of tensegrity frameworks (i.e., distance-constrained point configurations with equality and inequality constraints), geometric conditions of rigidity in nongeneric settings, methods and results for analysing global rigidity of generic bar-joint frameworks in general dimension, and transformations between metric spaces that preserve various types of rigidity. Finally, the fourth part of the book (Chapters 18–24) is concerned with methods and results in combinatorial rigidity theory, which looks for polynomial-time deterministic algorithms for testing the rigidity of GCSs that are in generic position. It gives detailed discussions of the generic rigidity and global rigidity of bar-joint frameworks (and related structures) in the Euclidean plane, and of frameworks in general dimension consisting of rigid bodies that are connected by bars or hinges. Moreover, it discusses the rigidity of generic point-line and body-and-cad frameworks, the rigidity of bar-joint frameworks where the underlying metric is governed by a polyhedral norm, and the rigidity of frameworks that are as generic as possible subject to certain symmetry or periodicity constraints. Many proofs in combinatorial rigidity are obtained via recursive graph constructions that preserve generic rigidity or global rigidity, and hence a whole chapter is dedicated to this topic. - Bernd Schulze - Mathematical Reviews Clippings - June 2019 Table of ContentsOverview and preliminaries. Computer-assisted Theorem Proving in Synthetic Geometry. Coordinate-Free Theorem Proving in Incidence Geometry. Special positions of frameworks and the Grassmann-Cayley Algebra. From Molecular Distance Geometry to Conformal Geometric Algebra. Tree-decomposable and Underconstrained Geometric Constraint Problems. Geometric Constraint Decomposition: The General Case. Dimensional and Universal Rigidities of Bar Frameworks. Computations of metric/cut polyhedra and their relatives. Cayley Configuration Spaces. Constraint Varieties in Mechanism Science. Real Algebraic Geometry for Geometric Constraints. Polyhedra in 3-Space. Tensegrity. Geometric Conditions of Rigidity in Nongeneric settings. Generic Global Rigidity in General Dimension. Change of Metrics in Rigidity Theory. Planar Rigidity. Inductive constructions for combinatorial local and global rigidity. Rigidity of Body-bar-hinge Frameworks. Global rigidity of two-dimensional frameworks. Point-line frameworks. Generic rigidity of body-and-cad frameworks. Rigidity with polyhedral norms. Combinatorial rigidity of symmetric and periodic frameworks.
£218.50
Taylor & Francis Inc An Invitation to the RogersRamanujan Identities
Book SynopsisThe Rogers--Ramanujan identities are a pair of infinite seriesinfinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the RogersRamanujan identities and will include related historical material that is unavailable elsewhere.Trade ReviewThis one-of-a-kind text, best suited for graduate level students and above, focuses exclusively on the Rogers-Ramanujan identities and their history. These two identities from number theory involve both infinite series and infinite products. The identities were independently discovered by Leonard James Rogers (1894 with proof), Srinivasa Ramanujan (before 1913 without proof), and Issai Schur (1917 with proof). The identities are relevant to the study of integer partitions, Lie algebras, statistical mechanics, computer science, and several other areas. Sills (Georgia Southern Univ.) begins with a review of partition theory and hypergeometric series. In the next two chapters, he moves on to prove the Rogers-Ramanujan identities and to explain their combinatorial aspects, as well as related identities and extensions. The final two chapters treat applications including continued fractions and knot theory. One appendix lists 236 related identities. A second appendix enhances the book's historical utility by providing transcriptions of letters between key researchers from 1943 to 1961. The book also includes more than 60 enlightening exercises.—D. P. Turner, Faulkner University, CHOICE Reviews"In recent years ¿-series have arisen in knot theory, and Sills discusses a few ¿-series that arise in the study of certain simple fundamental knots. While there have been systematic discussions of many of the topics mentioned above in various books, monographs, and survey articles, Sills’s book is the first comprehensive discussion of R-R type identities in all their forms, describing the state of the art. Since the subject is so vast, he does not provide proofs for most of the identities discussed, but he provides an interesting and illuminating historical context for each topic, gives good motivation, and describes the key ideas underlying the proofs. He also provides a substantial number of references that will lead both the studenTable of ContentsBackground and the Pre-History. The Golden Age and its Modern Legacy. Infinite Families...Everywhere! From Infinite to Finite. Motivated Proofs, Connections to Lie Algebras, and More Identities. But wait...there's more!
£99.75
Taylor & Francis Inc Buildings and Schubert Schemes
Book SynopsisThe first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck''s SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.Table of ContentsGrassmannians and Flag Varieties. Schubert Cell Decomposition of Grassmannians and Flag Varieties. Resolution of Singularities of a Schubert Variety. The Singular Locus of a Schubert Variety. The Flag Complex. Configurations and Galleries Varieties. Configurations Varieties as Galleries Varieties. The Coxeter Complex. Minimal Generalized Galleries in a Coxeter Complex. Minimal Generalized Galleries in a Reductive Group Building. Parabolic Subgroups in a Reductive Group Scheme. Associated Schemes to the Relative Building. Incidence Type Schemes of the Relative Building. Smooth Resolutions of Schubert Schemes. Contracted Products and Galleries Configurations Schemes. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes. About the Coxeter Complex. Generators and Relations and the Building of a Reductive Group.
£175.75
Taylor & Francis Inc Combinatorics
Book SynopsisCombinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorTable of ContentsPART 1: ENUMERATION. Chapter 1: Basic Counting; Chapter 2: Combinatorial Identities and Recursions; Chapter 3: Counting Problems in Graph Theory; Chapter 4: Inclusion-Exclusion and Related Techniques; New Chapter 5: Generating Functions; Chapter 6: Ranking, Unranking, and Successor Algorithms; PART 2: ALGEBRAIC COMBINATORICS; Chapter 7: Permutation Statistics and q-Analogues; Chapter 8: Permutations and Group Actions; Chapter 9: Tableaux and Symmetric Polynomials. Chapter 10: Abaci and Antisymmetric Polynomials; Chapter 11: Additional Topics. New Appendix: Background in Abstract Algebra.
£104.50
Charlesbridge Publishing,U.S. Show and Tell! Great Graphs and Smart Charts: An
Book SynopsisA visual-learning expert races up the charts and graphs math success with kid-friendly content sure to help with homework.Want to find the most popular meal in the cafeteria? Compare town sports enrollments? Or maybe you just want to know who burps the most in your family! Learn what line graphs, bar graphs, pie charts, and pictographs are and how and when to use them to represent data. Each project shows how to build a chart or graph and ties it all together with a creative infographic that really puts the A in STEAM (Science, Technology, Engineering, ARTS, and Mathematics). Whether used as an introductory aid or to underscore previous knowledge, the book prepares today''s visually savvy children to succeed in school and life by analyzing the world around them.
£15.29
Taylor & Francis Inc Handbook of Graph Drawing and Visualization
Book SynopsisGet an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and ApplicationsThe Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references.The first several chapters of the book deal with fundamental topological and geometric concepts and techniques used in graph drawing, such as planarity testing and embedding, crossings and planarization, symmetric drawings, and proximity drawings. The following chapters present a large collection of algorithms for constructing drawings of graphs, including tree, planar straight-line, planar orthogonal and polyline, spine and radial, circular, rectangular, hierarchical, and three-dimensional drawings as well as labeling algorithms, simultaneous embeddings, and force-directed methods. The book then introduces the GraphML language for representing graphs and their drawings and describes three software systems for constructing drawings of graphs: OGDF, GDToolkit, and PIGALE. The final chapters illustrate the use of graph drawing methods in visualization applications for biological networks, computer security, data analytics, education, computer networks, and social networks.Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.Trade Review"In the topological and geometric foundations to graph drawing, this collection goes beyond defining planarity or even minimizing edge crossings, discussing also spine, radial, circular, tree, and rectangular drawing definitions and algorithms. There is much content on formally defining and approaching such subjective and even aesthetic areas as legibility in name placement and labeling, as well as maximizing pleasing symmetries and other methods related to edge lengths and linearity that research has shown to impart information to humans effectively. Many chapters touch on history and open problems in this well-arranged compendium weighted toward content ripe for practical implementation."—Tom Schulte, MAA Reviews, February 2014"This handbook fills an important need. It is an impressive compendium of research in the booming field of graph drawing and visualization: algorithms, layout strategies, and software for diverse problem domains. It’s great to have all these resources in one place, showing the vibrant activity in graph drawing and visualization. The book lays a foundation for the next generation of research breakthroughs. Whether you drill down or go wide, you’ll learn something useful. You’ll see how effectively designed network visualizations can produce powerful insights in many fields."—Prof. Ben Shneiderman, University of Maryland"This handbook is the most comprehensive reference on graph drawing I have ever seen. It is an indispensable aid to programmers, engineers, students, teachers, and researchers who create or use algorithms and systems for visualizing networks and abstract graphs. It covers the theory and practice in core topics and related areas, such as labeling, programming frameworks, and applications in network analysis. It’s an amazing compendium of almost everything known about practical graph drawing."—Stephen North, Executive Director and Co-Founder of graphviz.org"After two decades of annual graph drawing conferences, the field is sufficiently developed to warrant this nearly 900-page Handbook. All constituencies are well-served. New researchers can become quickly oriented to the field through the opening foundational chapters. Practitioners can find algorithms to suit their needs in the heart of the handbook: ten chapters on a wealth of algorithms, usefully organized into intuitive categories: from planar algorithms to three-dimensional drawings, passing through the natural restrictions—radial, rectangular, circular, polyline—and from hierarchical to force-directed.Many algorithms are now incorporated into graph-drawing software packages, and all the major packages are described in chapters by their developers. The key application areas are surveyed, some to be expected—biological networks, social networks, cartography—and some less obvious but no less active, e.g., education and computer security. All chapters are authored by the leaders of the field and edited into a pleasing common style.The field of graph drawing remains dynamic, as testified by the many open problems collected in the chapters, from turning Mani’s theorem into an algorithm for 3-connected planar graphs, to deciding whether every degree-6 graph has a 2-bend orthogonal drawing in 3D. It is an achievement to so thoroughly cover the range from theory to algorithms to software to applications, and I expect the Handbook to serve as the key resource for researchers in the field."—Joseph O’Rourke, Smith CollegeTable of ContentsPlanarity Testing and Embedding. Crossings and Planarization. Symmetric Graph Drawing. Proximity Drawings. Tree Drawing Algorithms. Planar Straight-Line Drawing Algorithms. Planar Orthogonal and Polyline Drawing Algorithms. Spine and Radial Drawings. Circular Drawing Algorithms. Rectangular Drawing Algorithms. Simultaneous Embedding of Planar Graphs. Force-Directed Drawing Algorithms. Hierarchical Drawing Algorithms. Three-Dimensional Drawings. Labeling Algorithms. Graph Markup Language (GraphML). The Open Graph Drawing Framework (OGDF). GDToolkit. PIGALE. Biological Networks. Computer Security. Graph Drawing for Data Analytics. Graph Drawing and Cartography. Graph Drawing in Education. Computer Networks. Social Networks. Index.
£194.75
Taylor & Francis Inc Handbook of Finite Translation Planes
Book SynopsisThe Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems.From the methods of André to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences. In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes.As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane. It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known examples.Trade Review"The authors, who are the undisputed leaders in the subject, present the huge material in shorter but virtually independent chapters, each dedicated to a particular aspect, such as the connection between translation planes and quasifields... This book highly recommended for the very clear, rigorous and detailed expostion and cannot be missing in the library of any researcher in Geometry."-Bambina Larato, Zentralblatt MATH, 2008, 1136Table of ContentsPreface and Acknowledgments. An Overview. Translation Plane Structure Theory. Partial Spreads and Translation Nets. Partial Spreads and Generalizations. Quasifields. Derivation. Frequently Used Tools. Sharply Transitive Sets. SL(2, p) × SL(2, p)-Planes. Classical Semifields. Groups of Generalized Twisted Field Planes. Nuclear Fusion in Semifields. Cyclic Semifields. T-Cyclic GL(2, q)-Spreads. Cone Representation Theory. André Net Replacements and Ostrom-Wilke Generalizations. Foulser's ?-Planes. Regulus Lifts, Intersections over Extension Fields. Hyper-Reguli Arising from André Hyper-Reguli. Translation Planes with Large Homology Groups. Derived Generalized André Planes. The Classes of Generalized André Planes. C-System Nearfields. Subregular Spreads. Fano Configurations. Fano Configurations in Generalized André Planes. Planes with Many Elation Axes. Klein Quadric. Parallelisms. Transitive Parallelisms. Ovoids.Known Ovoids. Simple T-Extensions of Derivable Nets. Baer Groups on Parabolic Spreads. Algebraic Lifting. Semifield Planes of Orders q4, q6. Known Classes of Semifields. Methods of Oyama-Suetake Planes. Coupled Planes. Hyper-Reguli. Subgeometry Partitions. Groups on Multiple Hyper-Reguli. Hyper-Reguli of Dimension 3. Elation-Baer Incompatibility. Hering-Ostrom Elation Theorem. Baer-Elation Theory. Spreads Admitting Unimodular Sections-Foulser-Johnson Theorem. Spreads of Order q2-Groups of Order q2. Transversal Extensions. Indicator Sets. Geometries and Partitions. Maximal Partial Spreads. Sperner Spaces. Conical Flocks. Ostrom and Flock Derivation. Transitive Skeletons. BLT-Set Examples. Many Ostrom-Derivates. Infinite Classes of Flocks. Sporadic Flocks. Hyperbolic Fibrations. Spreads with Many Homologies. Nests of Reguli. Chains. Multiple Nests. A Few Remarks on Isomorphisms. Flag-Transitive Geometries. Quartic Groups in Translation Planes. Double Transitivity. Triangle Transitive Planes. Hiramine-Johnson-Draayer Theory. Bol Planes. 2/3-Transitive Axial Groups. Doubly Transitive Ovals and Unitals. Rank 3 Affine Planes. Transitive Extensions. Higher-Dimensional Flocks. j…j-Planes. Orthogonal Spreads. Symplectic Groups-The Basics. Symplectic Flag-Transitive Spreads. Symplectic Spreads. When Is a Spread Not Symplectic? When Is a Spread Symplectic? The Translation Dual of a Semifield. Unitals in Translation Planes. Hyperbolic Unital Groups. Transitive Parabolic Groups. Doubly Transitive Hyperbolic Unital Groups. Retraction. Multiple Spread Retraction. Transitive Baer Subgeometry Partitions. Geometric and Algebraic Lifting. Quasi-Subgeometry Partitions. Hyper-Regulus Partitions. Small-Order Translation Planes. Dual Translation Planes and Their Derivates. Affine Planes with Transitive Groups. Cartesian Group Planes-Coulter-Matthews. Planes Admitting PGL(3, q). Planes of Order = 25. Real Orthogonal Groups and Lattices. Aspects of Symplectic and Orthogonal Geometry. Fundamental Results on Groups. Atlas of Planes and Processes. Bibliography. Theorems. Models. General Index.
£54.14
Taylor & Francis Inc Handbook of Discrete and Combinatorial
Book SynopsisHandbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians.The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies.This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition. Table of ContentsFoundations. Counting Methods. Sequences. Number Theory. Algebraic Structures. Linear Algebra. Discrete Probability. Graph Theory. Trees. Networks and Flows. Partially Ordered Sets. Combinatorial Designs. Discrete and Computational Geometry. Coding Theory and Cryptology. Discrete Optimization. Theoretical Computer Science. Information Structures. Data Mining. Bioinformatics.
£209.00
Merchant Books Principia Mathematica - Volume Two
£27.97
Merchant Books Principia Mathematica - Volume Three
£24.42
Watchmaker Publishing Philosophiae Naturalis Principia Mathematica (Latin Edition)
£25.39
Society for Industrial & Applied Mathematics,U.S. An Introduction to Compressed Sensing
Book SynopsisCompressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing.An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate.The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.
£78.20
States Academic Press Foundations of Combinatorics
Book Synopsis
£108.80
States Academic Press Probabilistic and Combinatorial Techniques:
Book Synopsis
£106.69
World Scientific Europe Ltd Boolean Structures: Combinatorics, Codification,
Book SynopsisBoolean Structures: Combinatorics, Codification, Representation offers the first analytical and architectural approach to Boolean algebras based combinatorial calculus and codification with applications in IT, quantum information and classification of data.
£99.00
ISTE Ltd and John Wiley & Sons Inc Graphs and Networks: Multilevel Modeling
Book SynopsisA transport network is typically a network of roads, streets, pipes, aqueducts, power lines, or nearly any structure that permits either vehicular movement or the flow of some commodity. Transport network analysis, a field of transport engineering that typically employs the use of graph theory, is used to determine the flow of vehicles, commodities, or people through these networks. It may combine different modes of transport - for example, walking and driving - to model multi-modal journeys. This edition is completely updated and contains two new chapters covering spatial analysis and urban management through graph theory simulation. Highly practical, the simulation approach allows readers to solve classic problems, such as placement of high-speed roads, the capacity of a network, pollution emission control, and more.
£170.95
ISTE Ltd and John Wiley & Sons Inc Mathematics for Informatics and Computer Science
Book SynopsisHow many ways do exist to mix different ingredients, how many chances to win a gambling game, how many possible paths going from one place to another in a network ? To this kind of questions Mathematics applied to computer gives a stimulating and exhaustive answer. This text, presented in three parts (Combinatorics, Probability, Graphs) addresses all those who wish to acquire basic or advanced knowledge in combinatorial theories. It is actually also used as a textbook. Basic and advanced theoretical elements are presented through simple applications like the Sudoku game, search engine algorithm and other easy to grasp applications. Through the progression from simple to complex, the teacher acquires knowledge of the state of the art of combinatorial theory. The non conventional simultaneous presentation of algorithms, programs and theory permits a powerful mixture of theory and practice. All in all, the originality of this approach gives a refreshing view on combinatorial theory.Trade Review"On the other hand if you are looking for an approach to combinatorics that is routed in applications and with lots of exercises then this is the book for you. Yes, dare I say it, it's fun." (I Programmer, 21 January 2011)Table of ContentsGeneral Introduction xxiii Chapter 1. Some Historical Elements 1 PART 1. COMBINATORICS 17 Part 1. Introduction 19 Chapter 2. Arrangements and Combinations 21 Chapter 3. Enumerations in Alphabetical Order 43 Chapter 4. Enumeration by Tree Structures 63 Chapter 5. Languages, Generating Functions and Recurrences 85 Chapter 6. Routes in a Square Grid 105 Chapter 7. Arrangements and Combinations with Repetitions 119 Chapter 8. Sieve Formula 137 Chapter 9. Mountain Ranges or Parenthesis Words: Catalan Numbers 165 Chapter 10. Other Mountain Ranges 197 Chapter 11. Some Applications of Catalan Numbers and Parenthesis Words 215 Chapter 12. Burnside’s Formula 227 Chapter 13. Matrices and Circulation on a Graph 253 Chapter 14. Parts and Partitions of a Set 275 Chapter 15. Partitions of a Number 289 Chapter 16. Flags 305 Chapter 17. Walls and Stacks 315 Chapter 18. Tiling of Rectangular Surfaces using Simple Shapes 331 Chapter 19. Permutations 345 PART 2. PROBABILITY 387 Part 2. Introduction 389 Chapter 20. Reminders about Discrete Probabilities 395 Chapter 21. Chance and the Computer 427 Chapter 22. Discrete and Continuous 447 Chapter 23. Generating Function Associated with a Discrete Random Variable in a Game 469 Chapter 24. Graphs and Matrices for Dealing with Probability Problems 497 Chapter 25. Repeated Games of Heads or Tails 509 Chapter 26. Random Routes on a Graph 535 Chapter 27. Repetitive Draws until the Outcome of a Certain Pattern 565 Chapter 28. Probability Exercises 597 PART 3. GRAPHS 637 Part 3. Introduction 639 Chapter 29. Graphs and Routes 643 Chapter 30. Explorations in Graphs 661 Chapter 31. Trees with Numbered Nodes, Cayley’s Theorem and Prüfer Code 705 Chapter 32. Binary Trees 723 Chapter 33. Weighted Graphs: Shortest Paths and Minimum Spanning Tree 737 Chapter 34. Eulerian Paths and Cycles, Spanning Trees of a Graph 759 Chapter 35. Enumeration of Spanning Trees of an Undirected Graph 779 Chapter 36. Enumeration of Eulerian Paths in Undirected Graphs 799 Chapter 37. Hamiltonian Paths and Circuits 835 APPENDICES 867 Appendix 1. Matrices 869 Appendix 2. Determinants and Route Combinatorics 885 Bibliography 907 Index 911
£132.00
ISTE Ltd and John Wiley & Sons Inc Graph Partitioning
Book SynopsisGraph partitioning is a theoretical subject with applications in many areas, principally: numerical analysis, programs mapping onto parallel architectures, image segmentation, VLSI design. During the last 40 years, the literature has strongly increased and big improvements have been made. This book brings together the knowledge accumulated during many years to extract both theoretical foundations of graph partitioning and its main applications.Table of ContentsIntroduction xiii Charles-Edmond Bichot, Patrick Siarry Chapter 1. General Introduction to Graph Partitioning 1 Charles-Edmond Bichot 1.1. Partitioning 1 1.2. Mathematical notions 2 1.3. Graphs 4 1.4. Formal description of the graph partitioning problem 8 1.5. Objective functions for graph partitioning 11 1.6. Constrained graph partitioning 13 1.7. Unconstrained graph partitioning 14 1.8. Differences between constrained and unconstrained partitioning 16 1.9. From bisection to k-partitioning: the recursive bisection method 17 1.10. NP-hardness of graph partitioning optimization problems 19 1.11. Conclusion 22 1.12. Bibliography 22 Part 1: Graph Partitioning for Numerical Analysis 27 Chapter 2. A Partitioning Requiring Rapidity and Quality: The Multilevel Method and Partitions Refinement Algorithms 29 Charles-Edmond Bichot 2.1. Introduction 29 2.2. Principles of the multilevel method 30 2.3. Graph coarsening 33 2.4. Partitioning of the coarsened graph 37 2.5. Uncoarsening and partitions refinement 40 2.6. The spectral method 52 2.7. Conclusion 59 2.8. Bibliography 60 Chapter 3. Hypergraph Partitioning 65 Cédric Chevalier 3.1. Definitions and metrics 65 3.2. Connections between graphs, hypergraphs, and matrices 67 3.3. Algorithms for hypergraph partitioning 68 3.4. Purpose 72 3.5. Conclusion 77 3.6. Software references 78 3.7. Bibliography 78 Chapter 4. Parallelization of Graph Partitioning 81 François Pellegrini 4.1. Introduction 81 4.2. Distributed data structures 84 4.3. Parallelization of the coarsening phase 87 4.4. Folding 93 4.5. Centralization 95 4.6. Parallelization of the refinement phase 96 4.7. Experimental results 107 4.8. Conclusion 111 4.9. Bibliography 111 Chapter 5. Static Mapping of Process Graphs 115 François Pellegrini 5.1. Introduction 115 5.2. Static mapping models 116 5.3. Exact algorithms 121 5.4. Approximation algorithms 123 5.5. Conclusion 133 5.6. Bibliography 134 Part 2: Optimization Methods for Graph Partitioning 137 Chapter 6. Local Metaheuristics and Graph Partitioning 139 Charles-Edmond Bichot 6.1. General introduction to metaheuristics 140 6.2. Simulated annealing 141 6.3. Iterated local search 149 6.4. Other local search metaheuristics 158 6.5. Conclusion 159 6.6. Bibliography 159 Chapter 7. Population-based Metaheuristics, Fusion-Fission and Graph Partitioning Optimization 163 Charles-Edmond Bichot 7.1. Ant colony algorithms 163 7.2. Evolutionary algorithms 165 7.3. The fusion-fission method 182 7.4. Conclusion 195 7.5. Acknowledgments 196 7.6. Bibliography 196 Chapter 8. Partitioning Mobile Networks into Tariff Zones 201 Mustapha Oughdi, Sid Lamrous, Alexandre Caminada 8.1. Introduction 201 8.2. Spatial division of the network 208 8.3. Experimental results 220 8.4. Conclusion 222 8.5. Bibliography 223 Chapter 9. Air Traffic Control Graph Partitioning Application 225 Charles-Edmond Bichot, Nicolas Durand 9.1. Introduction 225 9.2. The problem of dividing up the airspace 227 9.3. Modeling the problem 231 9.4. Airspace partitioning: towards a new optimization metaheuristic 237 9.5. Division of the central European airspace 240 9.6. Conclusion 246 9.7. Acknowledgments 247 9.8. Bibliography 247 Part 3: Other Approaches to Graph Partitioning 249 Chapter 10. Application of Graph Partitioning to Image Segmentation 251 Amir Nakib, Laurent Najman, Hugues Talbot, Patrick Siarry 10.1. Introduction 251 10.2. The image viewed in graph form 251 10.3. Principle of image segmentation using graphs 254 10.4. Image segmentation via maximum flows 257 10.5. Unification of segmentation methods via graph theory 265 10.6. Conclusions and perspectives 269 10.7. Bibliography 271 Chapter 11. Distances in Graph Partitioning 275 Alain Guénoche 11.1. Introduction 275 11.2. The Dice distance 276 11.3. Pons-Latapy distance 281 11.4. A partitioning method for distance arrays 283 11.5. A simulation protocol 286 11.6. Conclusions 292 11.7. Acknowledgments 293 11.8. Bibliography 293 Chapter 12. Detection of Disjoint or Overlapping Communities in Networks 297 Jean-Baptiste Angelelli, Alain Guénoche, Laurence Reboul 12.1. Introduction 297 12.2. Modularity of partitions and coverings 299 12.3. Partitioning method 301 12.4. Overlapping partitioning methods 307 12.5. Conclusion 311 12.6. Acknowledgments 312 12.7. Bibliography 312 Chapter 13. Multilevel Local Optimization of Modularity 315 Thomas Aynaud, Vincent D. Blondel, Jean-Loup Guillaume and Renaud Lambiotte 13.1. Introduction 315 13.2. Basics of modularity 317 13.3. Modularity optimization 319 13.4. Validation on empirical and artificial graphs 327 13.5. Discussion 333 13.6. Conclusion 341 13.7. Acknowledgments 342 13.8. Bibliography 342 Appendix. The Main Tools and Test Benches for Graph Partitioning 347 Charles-Edmond Bichot A.1. Tools for constrained graph partitioning optimization 348 A.2. Tools for unconstrained graph partitioning optimization 350 A.3. Graph partitioning test benches 351 A.4. Bibliography 354 Glossary 357 List of Authors 361 Index 365
£132.00
ISTE Ltd and John Wiley & Sons Inc Advanced Graph Theory and Combinatorics
Book SynopsisAdvanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.Table of ContentsForeword ix Introduction xi Chapter 1. A First Encounter with Graphs 1 1.1. A few definitions 1 1.1.1. Directed graphs 1 1.1.2. Unoriented graphs 9 1.2. Paths and connected components 14 1.2.1. Connected components 16 1.2.2. Stronger notions of connectivity 18 1.3. Eulerian graphs 23 1.4. Defining Hamiltonian graphs 25 1.5. Distance and shortest path 27 1.6. A few applications 30 1.7. Comments 35 1.8. Exercises 37 Chapter 2. A Glimpse at Complexity Theory 43 2.1. Some complexity classes 43 2.2. Polynomial reductions 46 2.3. More hard problems in graph theory 49 Chapter 3. Hamiltonian Graphs 53 3.1. A necessary condition 53 3.2. A theorem of Dirac 55 3.3. A theorem of Ore and the closure of a graph 56 3.4. Chvátal’s condition on degrees 59 3.5. Partition of Kn into Hamiltonian circuits 62 3.6. De Bruijn graphs and magic tricks 65 3.7. Exercises 68 Chapter 4. Topological Sort and Graph Traversals 69 4.1. Trees 69 4.2. Acyclic graphs 79 4.3. Exercises 82 Chapter 5. Building New Graphs from Old Ones 85 5.1. Some natural transformations 85 5.2. Products 90 5.3. Quotients 92 5.4. Counting spanning trees 93 5.5. Unraveling 94 5.6. Exercises 96 Chapter 6. Planar Graphs 99 6.1. Formal definitions 99 6.2. Euler’s formula 104 6.3. Steinitz’ theorem 109 6.4. About the four-color theorem 113 6.5. The five-color theorem 115 6.6. From Kuratowski’s theorem to minors 120 6.7. Exercises 123 Chapter 7. Colorings 127 7.1. Homomorphisms of graphs 127 7.2. A digression: isomorphisms and labeled vertices 131 7.3. Link with colorings 134 7.4. Chromatic number and chromatic polynomial 136 7.5. Ramsey numbers 140 7.6. Exercises 147 Chapter 8. Algebraic Graph Theory 151 8.1. Prerequisites 151 8.2. Adjacency matrix 154 8.3. Playing with linear recurrences 160 8.4. Interpretation of the coefficients 168 8.5. A theorem of Hoffman 169 8.6. Counting directed spanning trees 172 8.7. Comments 177 8.8. Exercises 178 Chapter 9. Perron–Frobenius Theory 183 9.1. Primitive graphs and Perron’s theorem 183 9.2. Irreducible graphs 188 9.3. Applications 190 9.4. Asymptotic properties 195 9.4.1. Canonical form 196 9.4.2. Graphs with primitive components 197 9.4.3. Structure of connected graphs 206 9.4.4. Period and the Perron–Frobenius theorem 214 9.4.5. Concluding examples 218 9.5. The case of polynomial growth 224 9.6. Exercises 231 Chapter 10. Google’s Page Rank 233 10.1. Defining the Google matrix 238 10.2. Harvesting the primitivity of the Google matrix 241 10.3. Computation 246 10.4. Probabilistic interpretation 246 10.5. Dependence on the parameter α 247 10.6. Comments 248 Bibliography 249 Index 263
£125.06
ISTE Ltd and John Wiley & Sons Inc Graphs and Networks: Multilevel Modeling
Book SynopsisThis book concerns the use of graphs for the simulation and representation of transport networks. Its aim is to cover networks in both spatial analysis and urban management, together with the simulation by graph theory, a tool that makes it possible to solve various classic problems such as high-speed roads between one or more origins and destinations, the capacity of a network, etc. It will also be possible to apply these results to other applications such as personal networks and communications networks, making this book a useful reference tool for those involved in this area.Table of ContentsPreface. Introduction. Part 1. Graph Theory and Network Modeling. Chapter 1. The Space-time Variability of Road Base Accessibility: Application to London (Manuel Appert, Laurent Chapelon). Chapter 2. Journey Simluation of a Movement on a Double Scale (Fabrice Decoupigny). Chapter 3. Determination of Optimal Paths in a Time Delay Graph (Hervé Baptiste). Chapter 4. Modeling the Evolution of a Transport System and its Impacts on a French Urban System (Hervé Baptiste). Part 2. Graph Theory and Network Representation. Chapter 5. Dynamic Simulation of the Urban Reorganization of the City of Tours (Philippe Mathis). Chapter 6. From Social Networks to the Sociograph for the Analysis of the Actors' Games (Sébastien Larribe). Chapter 7. RESCOM: Towards Multiagent Modeling of Urban Communication Spaces (Ossama Khaddour). Chapter 8. Traffic Lanes and Emissions of Pollutants (Christophe Decoupigny). Part 3. Towards a Multilevel Graph Theory. Chapter 9. Graph Theory and Representation of Distances: Chronomaps and other Representations (Alain L'Hostis). Chapter 10. Evaluation of Covisibility of Planning and Housing Projects (Kamal Serrhini). Chapter 11. Dynamics and von Thünen’s Model: Duality and Multiple Levels (Philippe Mathis). Chapter 12. The Representation of Graphs: A Specific Domain of Graph Theory (Philippe Mathis). Chapter 13. Practical Examples (Philippe Mathis). List of Authors. Index.
£184.46
ISTE Ltd and John Wiley & Sons Inc Probabilistic Combinatorial Optimization on
Book SynopsisThis title provides a comprehensive survey over the subject of probabilistic combinatorial optimization, discussing probabilistic versions of some of the most paradigmatic combinatorial problems on graphs, such as the maximum independent set, the minimum vertex covering, the longest path and the minimum coloring. Those who possess a sound knowledge of the subject mater will find the title of great interest, but those who have only some mathematical familiarity and knowledge about complexity and approximation theory will also find it an accessible and informative read.Table of ContentsPreface 11 Chapter 1. A Short Insight into Probabilistic Combinatorial Optimization 15 1.1. Motivations and applications 15 1.2. A formalism for probabilistic combinatorial optimization 19 1.3. The main methodological issues dealing with probabilistic combinatorial optimization 24 1.3.1. Complexity issues 24 1.3.1.1. Membership in NPO is not always obvious 24 1.3.1.2. Complexity of deterministic vs. complexity of probabilistic optimization problems 24 1.3.2. Solution issues 26 1.3.2.1. Characterization of optimal a priori solutions 26 1.3.2.2. Polynomial subcases 28 1.3.2.3. Exact solutions and polynomial approximation issues 29 1.4. Miscellaneous and bibliographic notes 31 FIRST PART. PROBABILISTIC GRAPH-PROBLEMS 35 Chapter 2. The Probabilistic Maximum Independent Set 37 2.1. The modification strategies and a preliminary result 39 2.1.1. Strategy M1 39 2.1.2. Strategies M2 and M3 39 2.1.3. Strategy M4 41 2.1.4. Strategy M5 41 2.1.5. A general mathematical formulation for the five functionals 42 2.2. PROBABILISTIC MAX INDEPENDENT SET1 44 2.2.1. Computing optimal a priori solutions 44 2.2.2. Approximating optimal solutions 45 2.2.3. Dealing with bipartite graphs 46 2.3. PROBABILISTIC MAX INDEPENDENT SET2 and 3 47 2.3.1. Expressions for E(G, S, M2) and E(G, S, M3) 47 2.3.2. An upper bound for the complexity of E(G, S, M2) 48 2.3.3. Bounds for E(G, S, M2) 49 2.3.4. Approximating optimal solutions 51 2.3.4.1. Using argmax{_vi∈S pi} as an a priori solution 51 2.3.4.2. Using approximations of MAX INDEPENDENT SET 53 2.3.5. Dealing with bipartite graphs 53 2.4. PROBABILISTIC MAX INDEPENDENT SET4 55 2.4.1. An expression for E(G, S, M4) 55 2.4.2. Using S∗ or argmax{_vi∈S pi} as an a priori solution 56 2.4.3. Dealing with bipartite graphs 57 2.5. PROBABILISTIC MAX INDEPENDENT SET5 58 2.5.1. In general graphs 58 2.5.2. In bipartite graphs 60 2.6. Summary of the results 61 2.7. Methodological questions 63 2.7.1. Maximizing a criterion associated with gain 65 2.7.1.1. The minimum gain criterion 65 2.7.1.2. The maximum gain criterion 66 2.7.2. Minimizing a criterion associated with regret 68 2.7.2.1. The maximum regret criterion 68 2.7.3. Optimizing expectation 70 2.8. Proofs of the results 71 2.8.1. Proof of Proposition 2.1 71 2.8.2. Proof of Theorem 2.6 74 2.8.3. Proof of Proposition 2.3 77 2.8.4. Proof of Theorem 2.13 78 Chapter 3. The Probabilistic Minimum Vertex Cover 81 3.1. The strategies M1, M2 and M3 and a general preliminary result 82 3.1.1. Specification of M1, M2 and M3 82 3.1.1.1. Strategy M1 82 3.1.1.2. Strategy M2 83 3.1.1.3. Strategy M3 83 3.1.2. A first expression for the functionals 84 3.2. PROBABILISTIC MIN VERTEX COVER1 84 3.3. PROBABILISTIC MIN VERTEX COVER2 86 3.4. PROBABILISTIC MIN VERTEX COVER3 87 3.4.1. Building E(G, C, M3) 87 3.4.2. Bounds for E(G, C, M3) 88 3.5. Some methodological questions 89 3.6. Proofs of the results 91 3.6.1. Proof of Theorem 3.3 91 3.6.2. On the the bounds obtained in Theorem 3.3 93 Chapter 4. The Probabilistic Longest Path 99 4.1. Probabilistic longest path in terms of vertices 100 4.2. Probabilistic longest path in terms of arcs 102 4.2.1. An interesting algebraic expression 104 4.2.2. Metric PROBABILISTIC ARC WEIGHTED LONGEST PATH 105 4.3. Why the strategies used are pertinent 109 4.4. Proofs of the results 110 4.4.1. Proof of Theorem 4.1 110 4.4.2. Proof of Theorem 4.2 112 4.4.3. An algebraic proof for Theorem 4.3 114 4.4.4. Proof of Lemma 4.1 116 4.4.5. Proof of Lemma 4.2 117 4.4.6. Proof of Theorem 4.4 117 Chapter 5. Probabilistic Minimum Coloring 125 5.1. The functional E(G,C) 127 5.2. Basic properties of probabilistic coloring 131 5.2.1. Properties under non-identical vertex-probabilities 131 5.2.2. Properties under identical vertex-probabilities 131 5.3. PROBABILISTIC MIN COLORING in general graphs 132 5.3.1. The complexity of probabilistic coloring 132 5.3.2. Approximation 132 5.3.2.1. The main result 132 5.3.2.2. Further approximation results 137 5.4. PROBABILISTIC MIN COLORING in bipartite graphs 139 5.4.1. A basic property 139 5.4.2. General bipartite graphs 141 5.4.3. Bipartite complements of bipartite matchings 147 5.4.4. Trees 151 5.4.5. Cycles 154 5.5. Complements of bipartite graphs 155 5.6. Split graphs 156 5.6.1. The complexity of PROBABILISTIC MIN COLORING 156 5.6.2. Approximation results 159 5.7. Determining the best k-coloring in k-colorable graphs 164 5.7.1. Bipartite graphs 164 5.7.1.1. PROBABILISTIC MIN 3-COLORING 164 5.7.1.2. PROBABILISTIC MIN k-COLORING fork > 3 168 5.7.1.3. Bipartite complements of bipartite matchings 171 5.7.2. The complements of bipartite graphs 171 5.7.3. Approximation in particular classes of graphs 174 5.8. Comments and open problems 175 5.9. Proofs of the different results 178 5.9.1. Proof of [5.5] 178 5.9.2. Proof of [5.4] 179 5.9.3. Proof of Property 5.1 180 5.9.4. Proof of Proposition 5.2 181 5.9.5. Proof of Lemma 5.11 183 SECOND PART. STRUCTURAL RESULTS 185 Chapter 6. Classification of Probabilistic Graph-problems 187 6.1. When MS is feasible 187 6.1.1. The a priori solution is a subset of the initial vertex-set 188 6.1.2. The a priori solution is a collection of subsets of the initial vertex-set 191 6.1.3. The a priori solution is a subset of the initial edge-set 193 6.2. When application of MS itself does not lead to feasible solutions 198 6.2.1. The functional associated with MSC 198 6.2.2. Applications 199 6.2.2.1. The a priori solution is a cycle 200 6.2.2.2. The a priori solution is a tree 201 6.3. Some comments 205 6.4. Proof of Theorem 6.4 206 Chapter 7. A Compendium of Probabilistic NPO Problems on Graphs 211 7.1. Covering and partitioning 214 7.1.1. MIN VERTEX COVER 214 7.1.2. MIN COLORING 214 7.1.3. MAX ACHROMATIC NUMBER 215 7.1.4. MIN DOMINATING SET 215 7.1.5. MAX DOMATIC PARTITION 216 7.1.6. MIN EDGE-DOMINATING SET 216 7.1.7. MIN INDEPENDENT DOMINATING SET 217 7.1.8. MIN CHROMATIC SUM 217 7.1.9. MIN EDGE COLORING 218 7.1.10. MIN FEEDBACK VERTEX-SET 219 7.1.11. MIN FEEDBACK ARC-SET 220 7.1.12. MAX MATCHING 220 7.1.13. MIN MAXIMAL MATCHING 220 7.1.14. MAX TRIANGLE PACKING 220 7.1.15. MAX H-MATCHING 221 7.1.16. MIN PARTITION INTO CLIQUES 222 7.1.17. MIN CLIQUE COVER 222 7.1.18. MIN k-CAPACITED TREE PARTITION 222 7.1.19. MAX BALANCED CONNECTED PARTITION 223 7.1.20. MIN COMPLETE BIPARTITE SUBGRAPH COVER 223 7.1.21. MIN VERTEX-DISJOINT CYCLE COVER 223 7.1.22. MIN CUT COVER 224 7.2. Subgraphs and supergraphs 224 7.2.1. MAX INDEPENDENT SET 224 7.2.2. MAX CLIQUE 224 7.2.3. MAX INDEPENDENT SEQUENCE 225 7.2.4. MAX INDUCED SUBGRAPH WITH PROPERTY π 225 7.2.5. MIN VERTEX DELETION TO OBTAIN SUBGRAPH WITH PROPERTY π 225 7.2.6. MIN EDGE DELETION TO OBTAIN SUBGRAPH WITH PROPERTY π 226 7.2.7. MAX CONNECTED SUBGRAPH WITH PROPERTY π 226 7.2.8. MIN VERTEX DELETION TO OBTAIN CONNECTED SUBGRAPH WITH PROPERTY π 226 7.2.9. MAX DEGREE-BOUNDED CONNECTED SUBGRAPH 226 7.2.10. MAX PLANAR SUBGRAPH 227 7.2.11. MIN EDGE DELETION k-PARTITION 227 7.2.12. MAX k-COLORABLE SUBGRAPH 227 7.2.13. MAX SUBFOREST 228 7.2.14. MAX EDGE SUBGRAPH or DENSE k-SUBGRAPH 228 7.2.15. MIN EDGE K-SPANNER 228 7.2.16. MAX k-COLORABLE INDUCED SUBGRAPH 229 7.2.17. MIN EQUIVALENT DIGRAPH 229 7.2.18. MIN CHORDAL GRAPH COMPLETION 229 7.3. Iso- and other morphisms 229 7.3.1. MAX COMMON SUBGRAPH 229 7.3.2. MAX COMMON INDUCED SUBGRAPH 230 7.3.3. MAX COMMON EMBEDDED SUBTREE 230 7.3.4. MIN GRAPH TRANSFORMATION 230 7.4. Cuts and connectivity 231 7.4.1. MAX CUT 231 7.4.2. MAX DIRECTED CUT 231 7.4.3. MIN CROSSING NUMBER 231 7.4.4. MAX k-CUT 232 7.4.5. MIN k-CUT 233 7.4.6. MIN NETWORK INHIBITION ON PLANAR GRAPHS 233 7.4.7. MIN VERTEX k-CUT 234 7.4.8. MIN MULTI-WAY CUT 234 7.4.9. MIN MULTI-CUT 234 7.4.10. MIN RATIO-CUT 235 7.4.11. MIN b-BALANCED CUT 236 7.4.12. MIN b-VERTEX SEPARATOR 236 7.4.13. MIN QUOTIENT CUT 236 7.4.14. MIN k-VERTEX CONNECTED SUBGRAPH 236 7.4.15. MIN k-EDGE CONNECTED SUBGRAPH 237 7.4.16. MIN BICONNECTIVITY AUGMENTATION 237 7.4.17. MIN STRONG CONNECTIVITY AUGMENTATION 237 7.4.18. MIN BOUNDED DIAMETER AUGMENTATION 237 Appendix A. Mathematical Preliminaries 239 A.1. Sets, relations and functions 239 A.2. Basic concepts from graph-theory 242 A.3. Elements from discrete probabilities 246 Appendix B. Elements of the Complexity and the Approximation Theory 249 B.1. Problem, algorithm, complexity 249 B.2. Some notorious complexity classes 250 B.3. Reductions and NP-completeness 251 B.4. Approximation of NP-hard problems 252 Bibliography 255 Index 261
£132.00
Wooden Books Useful Formulae
Book Synopsis
£8.13
