Discrete mathematics Books

271 products


  • Cambridge University Press Surveys in Combinatorics 2022

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    £52.25

  • Cambridge University Press Notes on Counting An Introduction to Enumerative Combinatorics

    15 in stock

    Book SynopsisEnumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years'' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the RedfieldPólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.Trade Review'It's indeed a very good introduction to enumerative combinatorics and has all the trappings of a pedagogically sound enterprise, in the old-fashioned sense: exercises, good explanations (not too terse, but certainly not too wordy), and mathematically serious (nothing namby-pamby here). It's an excellent book.' Michael Berg, MAA Reviews'Cameron's Notes on Counting is a clever introductory book on enumerative combinatorics … Overall, the text is well-written with a friendly tone and an aesthetic organization, and each chapter contains an ample number of quality exercises. Summing Up: Recommended.' A. Misseldine, CHOICETable of Contents1. Introduction; 2. Formal power series; 3. Subsets, partitions and permutations; 4. Recurrence relations; 5. The permanent; 6. q-analogues; 7. Group actions and cycle index; 8. Mobius inversion; 9. The Tutte polynomial; 10. Species; 11. Analytic methods: a first look; 12. Further topics; 13. Bibliography and further directions; Index.

    15 in stock

    £33.24

  • Graph Theory: New Research

    Nova Science Publishers Inc Graph Theory: New Research

    1 in stock

    Book Synopsis

    1 in stock

    £146.24

  • Theory of Computation Simplified: Simulate

    BPB Publications Theory of Computation Simplified: Simulate

    3 in stock

    Book Synopsis

    3 in stock

    £31.34

  • Springer Mathematical Problems and Proofs Combinatorics Number Theory and Geometry

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    £85.49

  • Springer Difference Equations

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    £82.83

  • Springer Difference Equations

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    £44.99

  • Springer New York Combinatorial Commutative Algebra

    15 in stock

    Book SynopsisRecent developments are covered Contains over 100 figures and 250 exercises Includes complete proofsTrade ReviewFrom the reviews: "The book under review constitutes a self-contained introduction to the use of combinatorial methods in commutative algebra. … Concrete calculations and examples are used to introduce and develop concepts. Numerous exercises provide the opportunity to work through the material and end of chapter notes comment on the history and development of the subject. The authors have provided us with a useful reference and an effective text book." (R. J. Shank, Zentralblatt MATH, Vol. 1090 (16), 2006)Table of ContentsMonomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.- Semigroup rings.- Multigraded polynomial rings.- Syzygies of lattice ideals.- Toric varieties.- Irreducible and injective resolutions.- Ehrhart polynomials.- Local cohomology.- Determinants.- Plücker coordinates.- Matrix Schubert varieties.- Antidiagonal initial ideals.- Minors in matrix products.- Hilbert schemes of points.

    15 in stock

    £64.99

  • Springer New York Convex Polytopes

    15 in stock

    Book Synopsis1 Notation and prerequisites.- 1.1 Algebra.- 1.2 Topology.- 1.3 Additional notes and comments.- 2 Convex sets.- 2.1 Definition and elementary properties.- 2.2 Support and separation.- 2.3 Convex hulls.- 2.4 Extreme and exposed points; faces and poonems.- 2.5 Unbounded convex sets.- 2.6 Polyhedral sets.- 2.7 Remarks.- 2.8 Additional notes and comments.- 3 Polytopes.- 3.1 Definition and fundamental properties.- 3.2 Combinatorial types of polytopes; complexes.- 3.3 Diagrams and Schlegel diagrams.- 3.4 Duality of polytopes.- 3.5 Remarks.- 3.6 Additional notes and comments.- 4 Examples.- 4.1 The d-simplex.- 4.2 Pyramids.- 4.3 Bipyramids.- 4.4 Prisms.- 4.5 Simplicial and simple polytopes.- 4.6 Cubical polytopes.- 4.7 Cyclic polytopes.- 4.8 Exercises.- 4.9 Additional notes and comments.- 5 Fundamental properties and constructions.- 5.1 Representations of polytopes as sections or projections.- 5.2 The inductive construction of polytopes.- 5.3 Lower semicontinuity of the functions fk(P).- 5.4 Gale-transforms and Gale-diagrams.- 5.5 Existence of combinatorial types.- 5.6 Additional notes and comments.- 6 Polytopes with few vertices.- 6.1 d-Polytopes with d + 2 vertices.- 6.2 d-Polytopes with d + 3 vertices.- 6.3 Gale diagrams of polytopes with few vertices.- 6.4 Centrally symmetric polytopes.- 6.5 Exercises.- 6.6 Remarks.- 6.7 Additional notes and comments.- 7 Neighborly polytopes.- 7.1 Definition and general properties.- 7.2 % MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadG% aGmUaaaeacaYOaiaiJigdaaeacaYOaiaiJikdaaaacbiGaiaiJ-rga% aiaawUfacaGLDbaaaaa!40CC!$$\left[ {\frac{1}{2}d} \right]$$-Neighborly d-polytopes.- 7.3 Exercises.- 7.4 Remarks.- 7.5 Additional notes and comments.- 8 Euler's relation.- 8.1 Euler's theorem.- 8.2 Proof of Euler's theorem.- 8.3 A generalization of Euler's relation.- 8.4 The Euler characteristic of complexes.- 8.5 Exercises.- 8.6 Remarks.- 8.7 Additional notes and comments.- 9 Analogues of Euler's relation.- 9.1 The incidence equation.- 9.2 The Dehn-Sommerville equations.- 9.3 Quasi-simplicial polytopes.- 9.4 Cubical polytopes.- 9.5 Solutions of the Dehn-Sommerville equations.- 9.6 The f-vectors of neighborly d-polytopes.- 9.7 Exercises.- 9.8 Remarks.- 9.9 Additional notes and comments.- 10 Extremal problems concerning numbers of faces.- 10.1 Upper bounds for fi, i ? 1, in terms of fo.- 10.2 Lower bounds for fi, i ? 1, in terms of fo.- 10.3 The sets f(P3) and f(PS3).- 10.4 The set fP4).- 10.5 Exercises.- 10.6 Additional notes and comments.- 11 Properties of boundary complexes.- 11.1 Skeletons of simplices contained in ?(P).- 11.2 A proof of the van Kampen-Flores theorem.- 11.3 d-Connectedness of the graphs of d-polytopes.- 11.4 Degree of total separability.- 11.5 d-Diagrams.- 11.6 Additional notes and comments.- 12 k-Equivalence of polytopes.- 12.1 k-Equivalence and ambiguity.- 12.2 Dimensional ambiguity.- 12.3 Strong and weak ambiguity.- 12.4 Additional notes and comments.- 13 3-Polytopes.- 13.1 Steinitz's theorem.- 13.2 Consequences and analogues of Steinitz's theorem.- 13.3 Eberhard's theorem.- 13.4 Additional results on 3-realizable sequences.- 13.5 3-Polytopes with circumspheres and circumcircles.- 13.6 Remarks.- 13.7 Additional notes and comments.- 14 Angle-sums relations; the Steiner point.- 14.1 Gram's relation for angle-sums.-14.2 Angle-sums relations for simplicial polytopes.- 14.3 The Steiner point of a polytope (by G. C. Shephard).- 14.4 Remarks.- 14.5 Additional notes and comments.- 15 Addition and decomposition of polytopes.- 15.1 Vector addition.- 15.2 Approximation of polytopes by vector sums.- 15.3 Blaschke addition.- 15.4 Remarks.- 15.5 Additional notes and comments.- 16 Diameters of polytopes (by Victor Klee).- 16.1 Extremal diameters of d-polytopes.- 16.2 The functions ? and ?b.- 16.3 Wv Paths.- 16.4 Additional notes and comments.- 17 Long paths and circuits on polytopes.- 17.1 Hamiltonian paths and circuits.- 17.2 Extremal path-lengths of polytopes.- 17.3 Heights of polytopes.- 17.4 Circuit codes.- 17.5 Additional notes and comments.- 18 Arrangements of hyperplanes.- 18.1 d-Arrangements.- 18.2 2-Arrangements.- 18.3 Generalizations.- 18.4 Additional notes and comments.- 19 Concluding remarks.- 19.1 Regular polytopes and related notions.- 19.2 k-Content of polytopes.- 19.3 Antipodality and related notions.- 19.4 Additional notes and comments.- Tables.- Addendum.- Errata for the 1967 edition.- Additional Bibliography.- Index of Terms.- Index of Symbols.Trade Review"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London) From the reviews of the second edition: "Branko Grünbaum’s book is a classical monograph on convex polytopes … . As was noted by many researchers, for many years the book provided a central reference for work in the field and inspired a whole generation of specialists in polytope theory. … Every chapter of the book is supplied with a section entitled ‘Additional notes and comments’ … these notes summarize the most important developments with respect to the topics treated by Grünbaum. … The new edition … is an excellent gift for all geometry lovers." (Alexander Zvonkin, Mathematical Reviews, 2004b)Table of Contents1 Notation and prerequisites.- 1.1 Algebra.- 1.2 Topology.- 1.3 Additional notes and comments.- 2 Convex sets.- 2.1 Definition and elementary properties.- 2.2 Support and separation.- 2.3 Convex hulls.- 2.4 Extreme and exposed points; faces and poonems.- 2.5 Unbounded convex sets.- 2.6 Polyhedral sets.- 2.7 Remarks.- 2.8 Additional notes and comments.- 3 Polytopes.- 3.1 Definition and fundamental properties.- 3.2 Combinatorial types of polytopes; complexes.- 3.3 Diagrams and Schlegel diagrams.- 3.4 Duality of polytopes.- 3.5 Remarks.- 3.6 Additional notes and comments.- 4 Examples.- 4.1 The d-simplex.- 4.2 Pyramids.- 4.3 Bipyramids.- 4.4 Prisms.- 4.5 Simplicial and simple polytopes.- 4.6 Cubical polytopes.- 4.7 Cyclic polytopes.- 4.8 Exercises.- 4.9 Additional notes and comments.- 5 Fundamental properties and constructions.- 5.1 Representations of polytopes as sections or projections.- 5.2 The inductive construction of polytopes.- 5.3 Lower semicontinuity of the functions fk(P).- 5.4 Gale-transforms and Gale-diagrams.- 5.5 Existence of combinatorial types.- 5.6 Additional notes and comments.- 6 Polytopes with few vertices.- 6.1 d-Polytopes with d + 2 vertices.- 6.2 d-Polytopes with d + 3 vertices.- 6.3 Gale diagrams of polytopes with few vertices.- 6.4 Centrally symmetric polytopes.- 6.5 Exercises.- 6.6 Remarks.- 6.7 Additional notes and comments.- 7 Neighborly polytopes.- 7.1 Definition and general properties.- 7.2 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadG % aGmUaaaeacaYOaiaiJigdaaeacaYOaiaiJikdaaaacbiGaiaiJ-rga % aiaawUfacaGLDbaaaaa!40CC! $$ \left[ {\frac{1} {2}d} \right] $$-Neighborly d-polytopes.- 7.3 Exercises.- 7.4 Remarks.- 7.5 Additional notes and comments.- 8 Euler’s relation.- 8.1 Euler’s theorem.- 8.2 Proof of Euler’s theorem.- 8.3 A generalization of Euler’s relation.- 8.4 The Euler characteristic of complexes.- 8.5 Exercises.- 8.6 Remarks.- 8.7 Additional notes and comments.- 9 Analogues of Euler’s relation.- 9.1 The incidence equation.- 9.2 The Dehn-Sommerville equations.- 9.3 Quasi-simplicial polytopes.- 9.4 Cubical polytopes.- 9.5 Solutions of the Dehn-Sommerville equations.- 9.6 The f-vectors of neighborly d-polytopes.- 9.7 Exercises.- 9.8 Remarks.- 9.9 Additional notes and comments.- 10 Extremal problems concerning numbers of faces.- 10.1 Upper bounds for fi, i ? 1, in terms of fo.- 10.2 Lower bounds for fi, i ? 1, in terms of fo.- 10.3 The sets f(P3) and f(PS3).- 10.4 The set fP4).- 10.5 Exercises.- 10.6 Additional notes and comments.- 11 Properties of boundary complexes.- 11.1 Skeletons of simplices contained in ?(P).- 11.2 A proof of the van Kampen-Flores theorem.- 11.3 d-Connectedness of the graphs of d-polytopes.- 11.4 Degree of total separability.- 11.5 d-Diagrams.- 11.6 Additional notes and comments.- 12 k-Equivalence of polytopes.- 12.1 k-Equivalence and ambiguity.- 12.2 Dimensional ambiguity.- 12.3 Strong and weak ambiguity.- 12.4 Additional notes and comments.- 13 3-Polytopes.- 13.1 Steinitz’s theorem.- 13.2 Consequences and analogues of Steinitz’s theorem.- 13.3 Eberhard’s theorem.- 13.4 Additional results on 3-realizable sequences.- 13.5 3-Polytopes with circumspheres and circumcircles.- 13.6 Remarks.- 13.7 Additional notes and comments.- 14 Angle-sums relations; the Steiner point.- 14.1 Gram’s relation for angle-sums.- 14.2 Angle-sums relations for simplicial polytopes.- 14.3 The Steiner point of a polytope (by G. C. Shephard).- 14.4 Remarks.- 14.5 Additional notes and comments.- 15 Addition and decomposition of polytopes.- 15.1 Vector addition.- 15.2 Approximation of polytopes by vector sums.- 15.3 Blaschke addition.- 15.4 Remarks.- 15.5 Additional notes and comments.- 16 Diameters of polytopes (by Victor Klee).- 16.1 Extremal diameters of d-polytopes.- 16.2 The functions ? and ?b.- 16.3 Wv Paths.- 16.4 Additional notes and comments.- 17 Long paths and circuits on polytopes.- 17.1 Hamiltonian paths and circuits.- 17.2 Extremal path-lengths of polytopes.- 17.3 Heights of polytopes.- 17.4 Circuit codes.- 17.5 Additional notes and comments.- 18 Arrangements of hyperplanes.- 18.1 d-Arrangements.- 18.2 2-Arrangements.- 18.3 Generalizations.- 18.4 Additional notes and comments.- 19 Concluding remarks.- 19.1 Regular polytopes and related notions.- 19.2 k-Content of polytopes.- 19.3 Antipodality and related notions.- 19.4 Additional notes and comments.- Tables.- Addendum.- Errata for the 1967 edition.- Additional Bibliography.- Index of Terms.- Index of Symbols.

    15 in stock

    £59.99

  • Springer New York Combinatorial Computational Biology of RNA Pseudoknots and Neutral Networks

    15 in stock

    Book SynopsisIn this monograph, new combinatorial and computational approaches in the study of RNA structures are presented which enhance both mathematics and computational biology.Trade ReviewFrom the reviews:“This book is devoted to the study of the structure of combinatorial models of the ribonucleic acid (RNA). … This book can serve as an introduction to the study of combinatorial computational biology as well as a reference of known results and state of the art in this topic.” (Ludovit Niepel, Zentralblatt MATH, Vol. 1207, 2011)Table of ContentsIntroduction.- Secondary Structures, Pseudoknot RNA and Beyond.- Folding Sequences into Structures.- Evolution of RNA Sequences.- Methods.- References.- Index.

    15 in stock

    £49.49

  • Springer The New Book of Prime Number Records

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    £85.49

  • Springer New York Algebraic Graph Theory

    15 in stock

    Book SynopsisThis book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.Trade ReviewC. Godsil and G.F. Royle Algebraic Graph Theory "A welcome addition to the literature . . . beautifully written and wide-ranging in its coverage."—MATHEMATICAL REVIEWS "An accessible introduction to the research literature and to important open questions in modern algebraic graph theory"—L'ENSEIGNEMENT MATHEMATIQUETable of Contents* Graphs * Groups * Transitive Graphs * Arc-Transitive Graphs * Generalized Polygons and Moore Graphs * Homomorphisms * Kneser Graphs * Matrix Theory * Interlacing * Strongly Regular Graphs * Two-Graphs * Line Graphs and Eigenvalues * The Laplacian of a Graph * Cuts and Flows * The Rank Polynomial * Knots * Knots and Eulerian Cycles * Glossary of Symbols * Index

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    £36.99

  • Springer Counting The Art of Enumerative Combinatorics

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  • Springer Constructive Combinatorics

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  • Springer Binary Quadratic Forms Classical Theory and Modern Computations

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    Book Synopsis1 Elementary Concepts.- 2 Reduction of Positive Definite Forms.- 3 Indefinite Forms.- 3.1 Reduction, Cycles.- 3.2 Automorphs, Pell's Equation.- 3.3 Continued Fractions and Indefinite Forms.- 4 The Class Group.- 4.1 Representation and Genera.- 4.2 Composition Algorithms.- 4.3 Generic Characters Revisited.- 4.4 Representation of Integers.- 5 Miscellaneous Facts.- 5.1 Class Number Computations.- 5.2 Extreme Cases and Asymptotic Results.- 6 Quadratic Number Fields.- 6.1 Basic Algebraic Definitions.- 6.2 Algebraic Numbers and Quadratic Fields.- 6.3 Ideals in Quadratic Fields.- 6.4 Binary Quadratic Forms and Classes of Ideals.- 6.5 History.- 7 Composition of Forms.- 7.1 Nonfundamental Discriminants.- 7.2 The General Problem of Composition.- 7.3 Composition in Different Orders.- 8 Miscellaneous Facts II.- 8.1 The Cohen-Lenstra Heuristics.- 8.2 Decomposing Class Groups.- 8.3 Specifying Subgroups of Class Groups.- 9 The 2-Sylow Subgroup.- 9.1 Classical Results on the Pell Equation.- 9.2 ModernRTable of Contents1 Elementary Concepts.- 2 Reduction of Positive Definite Forms.- 3 Indefinite Forms.- 3.1 Reduction, Cycles.- 3.2 Automorphs, Pell’s Equation.- 3.3 Continued Fractions and Indefinite Forms.- 4 The Class Group.- 4.1 Representation and Genera.- 4.2 Composition Algorithms.- 4.3 Generic Characters Revisited.- 4.4 Representation of Integers.- 5 Miscellaneous Facts.- 5.1 Class Number Computations.- 5.2 Extreme Cases and Asymptotic Results.- 6 Quadratic Number Fields.- 6.1 Basic Algebraic Definitions.- 6.2 Algebraic Numbers and Quadratic Fields.- 6.3 Ideals in Quadratic Fields.- 6.4 Binary Quadratic Forms and Classes of Ideals.- 6.5 History.- 7 Composition of Forms.- 7.1 Nonfundamental Discriminants.- 7.2 The General Problem of Composition.- 7.3 Composition in Different Orders.- 8 Miscellaneous Facts II.- 8.1 The Cohen-Lenstra Heuristics.- 8.2 Decomposing Class Groups.- 8.3 Specifying Subgroups of Class Groups.- 8.3.1 Congruence Conditions.- 8.3.2 Exact and Exotic Groups.- 9 The 2-Sylow Subgroup.- 9.1 Classical Results on the Pell Equation.- 9.2 Modern Results.- 9.3 Reciprocity Laws.- 9.4 Special References for Chapter 9.- 10 Factoring with Binary Quadratic Forms.- 10.1 Classical Methods.- 10.2 SQUFOF.- 10.3 CLASNO.- 10.4 SPAR.- 10.4.1 Pollard p — 1.- 10.4.2 SPAR.- 10.5 CFRAC.- 10.6 A General Analysis.- Appendix 1:Tables, Negative Discriminants.- Appendix 2:Tables, Positive Discriminants.

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  • Springer Easy as p

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  • Why Machines Learn

    Penguin Publishing Group Why Machines Learn

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    2 in stock

    £15.86

  • Springer Algorithms and Order 255 Nato Science Series C

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  • Springer Gibbs Random Fields Cluster Expansions 44 Mathematics and its Applications

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  • Springer Neural and Automata Networks Dynamical Behavior and Applications 58 Mathematics and Its Applications

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  • Springer Integer Programming 46 Mathematics and its Applications

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  • Springer Cycles and Bridges in Graphs 49 Mathematics and its Applications

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  • Springer Topics in Computational Algebra

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  • Springer Graph Theoretical Approaches to Chemical Reactivity 9 Understanding Chemical Reactivity

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  • Springer Polytopes Abstract Convex and Computational 440 Nato Science Series C

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  • Springer Extremal Combinatorial Problems and Their Applications 335 Mathematics and Its Applications

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  • Springer Embeddability in Graphs 338 Mathematics and Its Applications

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  • Springer Discrete Analysis and Operations Research 355 Mathematics and Its Applications

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  • Springer Total Positivity and Its Applications 359 Mathematics and Its Applications

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  • Springer Operations Research and Discrete Analysis 391 Mathematics and Its Applications

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  • Springer ConflictControlled Processes 405 Mathematics and Its Applications

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  • Springer Graph Symmetry Algebraic Methods and Applications 497 Nato Science Series C

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  • Springer Exercises in Graph Theory 19 Texts in the Mathematical Sciences

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  • Springer Applications of Fibonacci Numbers Volume 7

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  • Springer Introduction to Vertex Operator Superalgebras and Their Modules Mathematics and Its Applications 456

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  • Springer Continuous Selections of Multivalued Mappings 455 Mathematics and Its Applications

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  • Springer Differential and Difference Dimension Polynomials 461 Mathematics and Its Applications

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  • Springer A Study of Braids 484 Mathematics and Its Applications

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  • Springer Fundamentals of Integrated Coastal Management 49 GeoJournal Library

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  • Springer Fuzzy Sets Logics and Reasoning about Knowledge

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  • Springer A Set of Examples of Global and Discrete Optimization

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