Discrete mathematics Books

Book SynopsisGenerating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.Trade Review" ""Wilf's writing is clear and friendly; his exorcises are instructive and plentiful... This book is valuable reading for even the best of specialists..."" -E. Rodney Canfield, The Mathematical Intelligencer , March 1993 ""This is a first rate, carefully planned and executed book written by a 'black belt gereratingfunctionologist.' I'll be using it the next time I teach..."" -George Andrews, SIAM News, October 1994 ""Wilf's book is very well-written and easy to read by any serious mathematics student. Scientists in other disciplines often encounter the need to study sequences that naturally arise in their own discipline. The book is well-suited fo them, too."" -Short Book Reviews, January 2006"Table of ContentsIntroductory Ideas and Examples. Series. Cards, Decks and Hands: The Exponential Formula. Applications of Generating Functions. Analytic and Asymptotic Models. Appendix: Using Maple and Mathematica Solutions. References.

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Book SynopsisThe model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.Table of Contents1. Introduction to the Model Theory of Fields 2. Model Theory of Differential Fields 3. Differential Algebraic Groups and the Number of Countable Differentially Closed Fields 4. Some Model Theory of Separably Closed Fields

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Book SynopsisAgent-based models (ABM) and computational models simulate the actions and interactions of autonomous agents (both individual or collective entities such as organisations or groups) with a view to assessing their effects on the system as a whole. They combine elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming. In this book, the authors discuss the modelling, simulation and optimisation of resources management in hospital emergency departments using the agent-based approach; computational modelling in male reproduction; consumer-centric agent-based marketing models; Lattice-Boltzmann simulation of transport phenomena in agroindustrial biosystems; agent-based models in cancer prevention research; model-based approaches to diagnosis of multi-agent plans; and modelling behaviour of web users as agents with reason and sentiment.

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Book SynopsisA practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data scienceKey Features Apply the math of countable objects to practical problems in computer science Explore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematics Learn complex statistical and mathematical concepts with the help of hands-on examples and expert guidance Book DescriptionDiscrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.What you will learn Understand the terminology and methods in discrete math and their usage in algorithms and data problems Use Boolean algebra in formal logic and elementary control structures Implement combinatorics to measure computational complexity and manage memory allocation Use random variables, calculate descriptive statistics, and find average-case computational complexity Solve graph problems involved in routing, pathfinding, and graph searches, such as depth-first search Perform ML tasks such as data visualization, regression, and dimensionality reduction Who this book is forThis book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.Table of ContentsTable of Contents Key Concepts, Notation, Set Theory, Relations, and Functions Formal Logic and Constructing Mathematical Proofs Computing with Base-n Numbers Combinatorics Using SciPy Elements of Discrete Probability Computational Algorithms in Linear Algebra Computational Requirements for Algorithms Storage and Feature Extraction of Graphs, Trees, and Networks Searching Data Structures and Finding Shortest Paths Regression Analysis with NumPy and Scikit-Learn Web Searches with PageRank Principal Component Analysis with Scikit-Learn

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Book SynopsisThe primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.Trade Reviewdeveloped by Paul Seymour and Neil Robertson and followers), which certainly now deserves a monographic treatment of its own. Summing up: Recommended. Lower-division undergraduate through professional collections. CHOICE This book is a follow-on to the authors' 1976 text, Graphs with Applications. What began as a revision has evolved into a modern, first-class, graduate-level textbook reflecting changes in the discipline over the past thirty years... This text hits the mark by appearing in Springer’s Graduate Texts in Mathematics series, as it is a very rigorous treatment, compactly presented, with an assumption of a very complete undergraduate preparation in all of the standard topics. While the book could ably serve as a reference for many of the most important topics in graph theory, it fulfills the promise of being an effective textbook. The plentiful exercises in each subsection are divided into two groups, with the second group deemed "more challenging". Any exercises necessary for a complete understanding of the text have also been marked as such. There is plenty here to keep a graduate student busy, and any student would learn much in tackling a selection of the exercises... Not only is the content of this book exceptional, so too is its production. The high quality of its manufacture, the crisp and detailed illustrations, and the uncluttered design complement the attention to the typography and layout. Even in simple black and white with line art, it is a beautiful book. SIAM Book Reviews "A text which is designed to be usable both for a basic graph theory course … but also to be usable as an introduction to research in graph theory, by including more advanced topics in each chapter. There are a large number of exercises in the book … . The text contains drawings of many standard interesting graphs, which are listed at the end." (David B. Penman, Zentralblatt MATH, Vol. 1134 (12), 2008) MathSciNet Reviews "The present volume is intended to serve as a text for "advanced undergraduate and beginning graduate students in mathematics and computer science" (p. viii). It is well suited for this purpose. The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging… Even a complete listing of the chapters does not fully convey the breadth of this book… For researchers in graph theory, this book offers features which parallel the first Bondy and Murty book: it provides well-chosen terminology and notation, a multitude of especially interesting graphs, and a substantial unsolved problems section…One-hundred unsolved problems are listed in Appendix A, a treasure trove of problems worthy of study… (In short) this rewrite of a classic in graph theory stands a good chance of becoming a classic itself." "The present volume is intended to serve as a text for ‘advanced undergraduate and beginning graduate students in mathematics and computer science’ … . The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging. The book has many exercise sets, each containing problems … ." (Arthur M. Hobbs, Mathematical Reviews, Issue 2009 C) "A couple of fantastic features: Proof techniques: I love these nutshelled essences highlighted in bordered frames. They look like pictures on the wall and grab the view of the reader. Exercises: Their style, depth and logic remind me of Lovász’ classical exercise book. Also the fact that the name of the author is bracketed after the exercise…Figures: Extremely precise and high-tech…The book contains very recent results and ideas. It is clearly an up-to-date collection of fundamental results of graph theory…All-in-all, it is a marvelous book." (János Barát, Acta Scientiarum Mathematicarum, Vol. 75, 2009)Table of ContentsGraphs.- Subgraphs.- Connected Graphs.- Trees.- Nonseparable Graphs.- Tree-Search Algorithms.- Flows in Networks.- Complexity of Algorithms.- Connectivity.- Planar Graphs.- The Four-Colour Problem.- Stable Sets and Cliques.- The Probabilistic Method.- Vertex Colourings.- Colourings of Maps.- Matchings.- Edge Colourings.- Hamilton Cycles.- Coverings and Packings in Directed Graphs.- Electrical Networks.- Integer Flows and Coverings.

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Book SynopsisThis book aims to help engineers, Masters students and young researchers to understand and gain a general knowledge of logistic systems optimization problems and techniques, such as system design, layout, stock management, quality management, lot-sizing or scheduling. It summarizes the evaluation and optimization methods used to solve the most frequent problems. In particular, the authors also emphasize some recent and interesting scientific developments, as well as presenting some industrial applications and some solved instances from real-life cases.Performance evaluation tools (Petri nets, the Markov process, discrete event simulation, etc.) and optimization techniques (branch-and-bound, dynamic programming, genetic algorithms, ant colony optimization, etc.) are presented first. Then, new optimization methods are presented to solve systems design problems, layout problems and buffer-sizing optimization. Forecasting methods, inventory optimization, packing problems, lot-sizing quality management and scheduling are presented with examples in the final chapters.Trade Review“On the other hand, this book constitutes a valuable guide and convenient introduction to the fied of operations research applications for professionals, which deal with real production and logistic system design and management. It can be also recommended as a textbook for students of production management.” (Zentralblatt Math, 1 May 2013) Table of ContentsIntroduction xiii Chapter 1. Modeling and Performance Evaluation 1 1.1. Introduction 1 1.2. Markovian processes 2 1.2.1. Overview of stochastic processes 2 1.2.2. Markov processes 3 1.2.2.1. Basics 3 1.2.2.2. Chapman–Kolmogorov equations 4 1.2.2.3. Steady-state probabilities 5 1.2.2.4. Graph associated with a Markov process 6 1.2.2.5. Application to production systems 6 1.2.3. Markov chains 8 1.2.3.1. Basics 8 1.2.3.2. State probability vectors 9 1.2.3.3. Fundamental equation of a Markov chain 9 1.2.3.4. Graph associated with a Markov chain 10 1.2.3.5. Steady states of ergodic Markov chains 11 1.2.3.6. Application to production systems 12 1.3. Petri nets 14 1.3.1. Introduction to Petri nets 14 1.3.1.1. Basic definitions 14 1.3.1.2. Dynamics of Petri nets 15 1.3.1.3. Specific structures 16 1.3.1.4. Tools for Petri net analysis 18 1.3.1.5. Properties of Petri nets 19 1.3.2. Non-autonomous Petri nets 20 1.3.3. Timed Petri nets 20 vi Optimization of Logistics 1.3.4. Continuous Petri nets 23 1.3.4.1. Fundamental equation and performance analysis 24 1.3.4.2. Example 25 1.3.5. Colored Petri nets 27 1.3.6. Stochastic Petri nets 28 1.3.6.1. Firing time 29 1.3.6.2. Firing selection policy 29 1.3.6.3. Service policy 30 1.3.6.4. Memory policy 30 1.3.6.5. Petri net analysis 30 1.3.6.6. Marking graph 31 1.3.6.7. Generator of Markovian processes 31 1.3.6.8. Fundamental equation 32 1.3.6.9. Steady-state probabilities 32 1.3.6.10. Performance indices (steady state) 35 1.4. Discrete-event simulation 36 1.4.1. The role of simulation in logistics systems analysis 36 1.4.2. Components and dynamic evolution of systems 37 1.4.3. Representing chance and the Monte Carlo method 38 1.4.3.1. Uniform distribution U [0, 1] 38 1.4.3.2. The Monte Carlo method 39 1.4.4. Simulating probability distributions 41 1.4.4.1. Simulating random events 41 1.4.4.2. Simulating discrete random variables 44 1.4.4.3. Simulating continuous random variables 47 1.4.5. Discrete-event systems 52 1.4.5.1. Key aspects of simulation 52 1.5. Decomposition method 57 1.5.1. Presentation 57 1.5.2. Details of the method 58 Chapter 2. Optimization 61 2.1. Introduction 61 2.2. Polynomial problems and NP-hard problems 62 2.2.1. The complexity of an algorithm 62 2.2.2. Example of calculating the complexity of an algorithm 63 2.2.3. Some definitions 64 2.2.3.1. Polynomial-time algorithms 64 2.2.3.2. Pseudo-polynomial-time algorithms 64 2.2.3.3. Exponential-time algorithms 64 2.2.4. Complexity of a problem 64 2.2.4.1. Polynomial-time problems 64 2.2.4.2. NP-hard problems 64 2.3. Exact methods 64 2.3.1. Mathematical programming 64 2.3.2. Dynamic programming 65 2.3.3. Branch and bound algorithm 65 2.4. Approximate methods 66 2.4.1. Genetic algorithms 67 2.4.1.1. General principles 67 2.4.1.2. Encoding the solutions 67 2.4.1.3. Crossover operators 68 2.4.1.4. Mutation operators 70 2.4.1.5. Constructing the population in the next generation 70 2.4.1.6. Stopping condition 70 2.4.2. Ant colonies 70 2.4.2.1. General principle 70 2.4.2.2. Management of pheromones: example of the traveling salesman problem 71 2.4.3. Tabu search 72 2.4.3.1. Initial solution 73 2.4.3.2. Representing the solution 73 2.4.3.3. Creating the neighborhood 74 2.4.3.4. The tabu list 75 2.4.3.5. An illustrative example 76 2.4.4. Particle swarm algorithm 76 2.4.4.1. Description 76 2.4.4.2. An illustrative example 77 2.5. Multi-objective optimization 79 2.5.1. Definition 79 2.5.2. Resolution methods 80 2.5.3. Comparison criteria 81 2.5.3.1. The Riise distance 81 2.5.3.2. The Zitzler measure 82 2.5.4. Multi-objective optimization methods 82 2.5.4.1. Exact methods 82 2.5.4.2. Approximate methods 84 2.6. Simulation-based optimization 89 2.6.1. Dedicated tools 90 2.6.2. Specific methods 90 Chapter 3. Design and Layout 93 3.1. Introduction 93 3.2. The different types of production system 94 3.3. Equipment selection 97 viii Optimization of Logistics 3.3.1. General overview 97 3.3.2. Equipment selection with considerations of reliability 99 3.3.2.1. Introduction to reliability optimization 99 3.3.2.2. Design of a parallel-series system 100 3.4. Line balancing 110 3.4.1. The classification of line balancing problems 111 3.4.1.1. The simple assembly line balancing model (SALB) 111 3.4.1.2. The general assembly line balancing model (GALB) 112 3.4.2. Solution methods 112 3.4.2.1. Exact methods 112 3.4.2.2. Approximate methods 113 3.4.3. Literature review 113 3.4.4. Example 113 3.5. The problem of buffer sizing 114 3.5.1. General overview 116 3.5.2. Example of a multi-objective buffer sizing problem 116 3.5.3. Example of the use of genetic algorithms 117 3.5.3.1. Representation of the solutions 117 3.5.3.2. Calculation of the objective function 118 3.5.3.3. Selection of solutions for the archive 119 3.5.3.4. New population and stopping criterion 119 3.5.4. Example of the use of ant colony algorithms 119 3.5.4.1. Encoding 120 3.5.4.2. Construction of the ant trails 121 3.5.4.3. Calculation of the visibility 121 3.5.4.4. Global and local updates of the pheromones 122 3.5.5. Example of the use of simulation-based optimization 123 3.5.5.1. Simulation model 125 3.5.5.2. Optimization algorithms 129 3.5.5.3. The pairing of simulation and optimization 130 3.5.5.4. Results and comparison 130 3.6. Layout 132 3.6.1. Types of facility layout 132 3.6.1.1. Logical layout 132 3.6.1.2. Physical layout 133 3.6.2. Approach for treating a layout problem 133 3.6.2.1. Linear layout 134 3.6.2.2. Functional layout 135 3.6.2.3. Cellular layout 135 3.6.2.4. Fixed layout 135 3.6.3. The best-known methods 135 3.6.4. Example of arranging a maintenance facility 136 3.6.5. Example of laying out an automotive workshop 140 Chapter 4. Tactical Optimization 143 4.1. Introduction 143 4.2. Demand forecasting 143 4.2.1. Introduction 143 4.2.2. Categories and methods 144 4.2.3. Time series 145 4.2.4. Models and series analysis 146 4.2.4.1. Additive models 147 4.2.4.2. Multiplicative model 149 4.2.4.3. Exponential smoothing 150 4.3. Stock management 155 4.3.1. The different types of stocked products 156 4.3.2. The different types of stocks 157 4.3.3. Storage costs 157 4.3.4. Stock management 159 4.3.4.1. Functioning of a stock 159 4.3.4.2. Stock monitoring 161 4.3.4.3. Stock valuation 162 4.3.5. ABC classification method 163 4.3.6. Economic quantities 165 4.3.6.1. Economic quantity: the Wilson formula 166 4.3.6.2. Economic quantity with a discount threshold 167 4.3.6.3. Economic quantity with a uniform discount 168 4.3.6.4. Economic quantity with a progressive discount 169 4.3.6.5. Economic quantity with a variable ordering cost 170 4.3.6.6. Economic quantity with order consolidation 171 4.3.6.7. Economic quantity with a non-zero delivery time 172 4.3.6.8. Economic quantity with progressive input 172 4.3.6.9. Economic quantity with tolerated shortage 173 4.3.7. Replenishment methods 174 4.3.7.1. The (r, Q) replenishment method 175 4.3.7.2. The (T , S) replenishment method 175 4.3.7.3. The (s, S) replenishment method 175 4.3.7.4. The (T , r, S) replenishment method 176 4.3.7.5. The (T , r, Q) replenishment method 177 4.3.7.6. Security stock 177 4.4. Cutting and packing problems 178 4.4.1. Classifying cutting and packing problems 179 4.4.2. Packing problems in industrial systems 183 4.4.2.1. Model 183 4.4.2.2. Solution 185 4.5. Production and replenishment planning, lot-sizing methods 186 4.5.1. Introduction 186 x Optimization of Logistics 4.5.2. MRP and lot-sizing 186 4.5.3. Lot-sizing methods 187 4.5.3.1. The characteristic elements of the models 188 4.5.3.2. Lot-sizing in the scientific literature 189 4.5.4. Examples 190 4.5.4.1. The Wagner–Whitin method 191 4.5.4.2. The Florian and Klein method 193 4.6. Quality management 198 4.6.1. Evaluation, monitoring and improvement tools 198 4.6.1.1. The objective of metrology 198 4.6.1.2. Concepts of error and uncertainty 198 4.6.1.3. Statistical quality control 199 4.6.1.4. Stages of control 199 4.6.1.5. Tests of normality 200 4.6.2. Types of control 205 4.6.2.1. Reception or final control 205 4.6.2.2. Reception control by measurement 206 4.6.2.3. Manufacturing control 209 4.6.2.4. Control charts 214 Chapter 5. Scheduling 233 5.1. Introduction 233 5.2. Scheduling problems 234 5.2.1. Basic notions 234 5.2.2. Notation 234 5.2.3. Definition of the criteria and objective functions 234 5.2.3.1. Flow time 235 5.2.3.2. Lateness 235 5.2.3.3. Tardiness 235 5.2.3.4. The earliness 236 5.2.3.5. Objective functions 236 5.2.3.6. Properties of schedules 238 5.2.4. Project scheduling 239 5.2.4.1. Definition of a project 239 5.2.4.2. Projects with unlimited resources 240 5.2.4.3. Projects with consumable resources 247 5.2.4.4. Minimal-cost scheduling 252 5.2.5. Single-machine problems 254 5.2.5.1. Minimization of the mean flow time 5.2.5.2. Minimization of the mean weighted flow time 5.2.5.3. Minimization of the mean flow time 5.2.5.4. Minimization of the maximum tardiness Tmax, 1/ri = 0/Tmax 259 5.2.5.5. Minimization of the maximum tardiness when the jobs have different arrival dates, with pre-emption 1/ri, pmtn/Tmax 261 5.2.5.6. Minimization of the mean tardiness 1//T 261 5.2.5.7. Minimization of the flow time 1/ri/F 265 5.2.6. Scheduling a flow shop workshop 267 5.2.6.1. The two-machine problem 267 5.2.6.2. A particular case of the three-machine problem 268 5.2.6.3. The m-machine problem 268 5.2.7. Parallel-machine problems 270 5.2.7.1. Identical machines, ri = 0, M in F 270 5.2.7.2. Identical machines, ri = 0, M in Cmax interruptible jobs 271 Bibliography 273 Index 285

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Book SynopsisDrawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as well as proof of Hall's theorem. He concludes with the constructions of schedules and a brief introduction to block designs. Each chapter is backed by a number of examples, with straightforw ard applications of ideas and more challenging problems.Trade Review"Wie der Titel andeutet, handelt es sich bei diesem Buch um eine elementare Einführung in Denkweisen und Methoden der Diskreten Mathematik. Die fachlichen Voraussetzungen an den Leser sind minimal. Darauf aufbauend wird ein doch recht buntes Bild entwickelt, bestehend vor allem aus den wichtigsten Konzepten aus Kombinatorik und Graphentheorie sowie einigen spezielleren Themen wie Designs und Codes.... Der Vorteil besteht darin, dass auch dem mathematischen Laien auf knapp 200 Seiten ein durchaus einprägsames Bild von einem Zweig der Mathematik vermittelt wird, der in unserer Zeit u.a. durch die Allgegenwart der sogenannten Informationstechnologie extrem an Bedeutung gewonnen hat."Internationale Mathematische Nachrichten, Nr. 187, August 2001Table of Contents1. Counting and Binomial Coefficients.- 2. Recurrence.- 3. Introduction to Graphs.- 4. Travelling Round a Graph.- 5. Partitions and Colourings.- 6. The Inclusion Exclusion Principle.- 7. Latin Squares and Hall’s Theorem.- 8. Schedules and 1-Factorisations.- 9. Introduction to Designs.- Solutions.- Further Reading.

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Book SynopsisHighly technical monograph in which the authors, writing on the basis of their own recent research for the benefit of expert readers, describe a general theory of stochastic integration equations. First published in 1990.Table of ContentsIntroduction, Nonlinear Stochastic Integrators, Stochastic Calculus, Dependence on the initial Conditions and Flows.

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Book SynopsisThis book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the extension of Hilbert space.

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Book SynopsisThis book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more.As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.Table of Contents

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Book SynopsisThe goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.Table of Contents- Part I Preliminaries. - Ultrafilters. - Nonstandard Analysis. - Hyperfinite Generators of Ultrafilters. - Many Stars: Iterated Nonstandard Extensions. - LoebMeasure. - Part II Ramsey Theory. - Ramsey’s Theorem. - The Theorems of van der Waerden and Hales-Jewett. - From Hindman to Gowers. - Partition Regularity of Equations. - Part III Combinatorial Number Theory. - Densities and Structural Properties. - Working in the Remote Realm. - Jin’s Sumset Theorem. - Sumset Configurations in Sets of Positive Density. - Near Arithmetic Progressions in Sparse Sets. - The Interval Measure Property. - Part IV Other Topics. - Triangle Removal and Szemerédi Regularity. - Approximate Groups. - Foundations of Nonstandard Analysis.

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Book SynopsisThis easy-to-understand textbook introduces the mathematical language and problem-solving tools essential to anyone wishing to enter the world of computer and information sciences. Specifically designed for the student who is intimidated by mathematics, the book offers a concise treatment in an engaging style.The thoroughly revised third edition features a new chapter on relevance-sensitivity in logical reasoning and many additional explanations on points that students find puzzling, including the rationale for various shorthand ways of speaking and ‘abuses of language’ that are convenient but can give rise to misunderstandings. Solutions are now also provided for all exercises.Topics and features: presents an intuitive approach, emphasizing how finite mathematics supplies a valuable language for thinking about computation; discusses sets and the mathematical objects built with them, such as relations and functions, as well as recursion and induction; introduces core topics of mathematics, including combinatorics and finite probability, along with the structures known as trees; examines propositional and quantificational logic, how to build complex proofs from simple ones, and how to ensure relevance in logic; addresses questions that students find puzzling but may have difficulty articulating, through entertaining conversations between Alice and the Mad Hatter; provides an extensive set of solved exercises throughout the text.This clearly-written textbook offers invaluable guidance to students beginning an undergraduate degree in computer science. The coverage is also suitable for courses on formal methods offered to those studying mathematics, philosophy, linguistics, economics, and political science. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study.Table of ContentsPart I: Sets Collecting Things Together: Sets Comparing Things: Relations Associating One Item with Another: Functions Recycling Outputs as Inputs: Induction and Recursion Part II: Math Counting Things: Combinatorics Weighing the Odds: Probability Squirrel Math: Trees Part III: Logic Yea and Nay: Propositional Logic Something about Everything: Quantificational Logic Just Supposing: Proof and Consequence Sticking to the Point: Relevance in Logic

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Book SynopsisContinuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed. Table of Contents- Jean Bourgain: In Memoriam. - A Generalized Central Limit Conjecture for Convex Bodies. - The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding. - Two-Sided Estimates for Order Statistics of Log-Concave Random Vectors. - Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-Concave Densities. - Small Ball Probability for the Condition Number of Random Matrices. - Concentration of the Intrinsic Volumes of a Convex Body. - Two Remarks on Generalized Entropy Power Inequalities. - On the Geometry of Random Polytopes. - Reciprocals and Flowers in Convexity. - Moments of the Distance Between Independent Random Vectors. - The Alon–Milman Theorem for Non-symmetric Bodies. - An Interpolation Proof of Ehrhard’s Inequality. - Bounds on Dimension Reduction in the Nuclear Norm. - High-Dimensional Convex Sets Arising in Algebraic Geometry. - Polylog Dimensional Subspaces of lN/∞. - On a Formula for the Volume of Polytopes.

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Book SynopsisThis book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.Trade Review“‘Lectures on convex geometry’ is an excellent graduate book about convex geometry. … The book is very well-organized. … The presentation is clear, well-composed and illustrated. The problems at the end of each subchapter are carefully selected and revised. The whole text is readable, interesting and easy to learn from. … the book is excellent and it can serve the studies of the future generation students in convex geometry.” (Gergely Kiss, zbMATH 1487.52001, 2022)“The book is informative, very interesting, and mathematically accessible, and the authors have achieved the purpose that they outline above. As the title suggests, Lectures on convex geometry is well suited to be used as the prescribed textbook for graduate courses in convex geometry; this is because of its pedagogical style and the quality of the exercises. It will also be useful to students intending to pursue a research career in the area … .” (Daniel John Fresen, Mathematical Reviews, June, 2022)Table of ContentsPreface.- Preliminaries and Notation.- 1. Convex Sets.- 2. Convex Functions.- 3. Brunn-Minkowski Theory.- 4. From Area Measures to Valuations.- 5. Integral Geometric Formulas.-6. Solutions of Selected Exercises.- References.- Index.

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Book SynopsisThis book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.Trade Review“‘Lectures on convex geometry’ is an excellent graduate book about convex geometry. … The book is very well-organized. … The presentation is clear, well-composed and illustrated. The problems at the end of each subchapter are carefully selected and revised. The whole text is readable, interesting and easy to learn from. … the book is excellent and it can serve the studies of the future generation students in convex geometry.” (Gergely Kiss, zbMATH 1487.52001, 2022)“The book is informative, very interesting, and mathematically accessible, and the authors have achieved the purpose that they outline above. As the title suggests, Lectures on convex geometry is well suited to be used as the prescribed textbook for graduate courses in convex geometry; this is because of its pedagogical style and the quality of the exercises. It will also be useful to students intending to pursue a research career in the area … .” (Daniel John Fresen, Mathematical Reviews, June, 2022)Table of ContentsPreface.- Preliminaries and Notation.- 1. Convex Sets.- 2. Convex Functions.- 3. Brunn-Minkowski Theory.- 4. From Area Measures to Valuations.- 5. Integral Geometric Formulas.-6. Solutions of Selected Exercises.- References.- Index.

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Book SynopsisThis textbook can serve as a comprehensive manual of discrete mathematics and graph theory for non-Computer Science majors; as a reference and study aid for professionals and researchers who have not taken any discrete math course before. It can also be used as a reference book for a course on Discrete Mathematics in Computer Science or Mathematics curricula. The study of discrete mathematics is one of the first courses on curricula in various disciplines such as Computer Science, Mathematics and Engineering education practices. Graphs are key data structures used to represent networks, chemical structures, games etc. and are increasingly used more in various applications such as bioinformatics and the Internet. Graph theory has gone through an unprecedented growth in the last few decades both in terms of theory and implementations; hence it deserves a thorough treatment which is not adequately found in any other contemporary books on discrete mathematics, whereas about 40% of this textbook is devoted to graph theory. The text follows an algorithmic approach for discrete mathematics and graph problems where applicable, to reinforce learning and to show how to implement the concepts in real-world applications.Trade Review“This accessible reference book should be well received by undergraduate-level CS, engineering, and mathematics students.” (Soubhik Chakraborty, Computing Reviews, July 12, 2022)“The book under review is an elementary introduction to mathematical logic, set theory, discrete mathematics, number theory, probability theory and graph theory. Its undoubted advantage is its good algorithmic support. … I would recommend this book to students studying computer science at the bachelor’s level.” (I. M. Erusalimskiy, zbMATH 1477.68004, 2022)Table of ContentsPreface.- Part I: Fundamentals of Discrete Mathematics.- Logic.- Proofs.- Algorithms.- Set Theory.- Relations and Functions.- Sequences, Induction and Recursion.- Introduction to Number Theory.- Counting and Probability.- Boolean Algebra and Combinational Circuits.- Introduction to the Theory of Computation.- Part II: Graph Theory.- Introduction to Graphs.- Trees and Traversals.- Subgraphs.- Connectivity, Network Flows and Shortest Paths.- Graph Applications.- A:.- Pseudocode Conventions.- Index.

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Book SynopsisMany believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something? How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.Trade Review"The definitions are followed by examples to help explain their meaning, along with counterexamples ... . Therefore, very little basic knowledge is required for this introduction to logical methods ... which is written in an accessible style ... . contained in the book are several hundred small figures; arrow, Venn, and Hasse diagrams; and simplifies visual representations ... . The author has also elected to use color to draw the reader's attention ... ." “From personal teaching experience, knowledge of these mathematical areas is necessary for disparate fields of CS and informatics. These foundations are needed for many fields, from database theory to various domains of information systems applications. The book’s presentation of topics and incentives for problem-solving, along with its exercises, is very useful for university-level instructors and students. The compact chapters contain clear explanations, diagrams, and brief descriptions of interesting facts.” (Bálint Molnár, Computing Reviews, July 27, 2021)Table of ContentsPreface.- 0 The Art of Thinking Abstractly and Mathematically.- 1 Basic Set Theory.- 2 Propositional Logic.- 3 Semantics from Propositional Logic.- 4 Concepts in Propositional Logic.- 5 Proofs, Conjectures, and Counterexamples.- 6 Relations.- 7 Functions.- 8 A Little More Set Theory.- 9 Closures and Inductively Defined Sets.- 10 Recursively Defined Functions.- 11 Mathematical Induction.- 12 Structural Induction.- 13 First-Order Languages.- 14 Representation of Quantified Statements.- 15 Interpretation in Models.- 16 Reasoning About Models.- 17 Abstraction with Equivalences and Partitions.- 18 Combinatorics.- 19 A Little More Combinatorics.- 20 A Bit of Abstract Algebra.- 21 Graph Theory.- 22 Walks in Graphs.- 23 Formal Languages and Grammars.- 24 Natural Deduction.- The Road Ahead.- Index. Symbols.

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Book SynopsisThis textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.Trade Review“The wide variety of slightly unusual topics makes the book an excellent resource for the instructor who wants to craft a combinatorics course that contains a diverse collection of attractive results … . The attentive student will certainly come away from a course based on this book with a solid understanding of the combinatorial way of thinking. … the book is an excellent resource for anyone teaching a class in combinatorics.” (Timothy Y. Chow, Mathematical Reviews, March, 2023)“A whole book whose backbone is enumeration by codifying the objects to be enumerated as words. … They do this in a skillfully structured fashion which makes the connections natural and unforced. … One of the remarkable features of this book is the care the authors have taken to make it reader-friendly and accessible to a wide range of students following a graduate mathematics course or an honours undergraduate course in mathematics and computer science.” (Josef Lauri, zbMATH 1478.05001, 2022)Table of Contents1. Basic Combinatorial Structures.- 2. Partitions and Generating Functions.- 3. Planar Trees and the Lagrange Inversion Formula.- 4. Cayley Trees.- 5. The Cayley–Hamilton Theorem.- 6. Exponential Structures and Polynomial Operators.- 7. The Inclusion-Exclusion Principle.- 8. Graphs, Chromatic Polynomials and Acyclic Orientations.- 9. Matching and Distinct Representatives.

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Book SynopsisIn the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs.Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.Table of ContentsPart I Line Graphs.- 1 Fundamentals of Line Graphs.- 2 Line Graph Isomorphisms.- 3 Characterization of Line Graphs.- 4 Spectral Properties of Line Graphs.- 5 Planarity of Line Graphs.- 6 Connectivity of Line Graphs.- 7 Tranversability in Line Graphs.- 8 Colorability in Line Graphs.- 9 Distance and Transitivity in Line Graphs.- Part II Line Digraphs.- 10 Fundamentals of Line Digraphs.- 11 Characterizations of Line Digraphs.- 12 Iterated Line Digraphs.- Part III Generalizations.- 13 Total Graphs and Total Digraphs.- 14 Path Graphs and Path Digraphs.- 15 Super Line Graphs and Super Line Digraphs.- 16 Line Graphs of Signed Graphs.- 17 The Krausz Dimension of Graph.- Reference. Index of Names.- Index of Definitions.

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This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. Features: This book provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics such as the nature of theorem proving; examines the field of software engineering, including software reliability and dependability and describes formal methods; investigates probability and statistics and presents an overview of operations research and financial mathematics.

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Book SynopsisGraph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, such as approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms.Table of Contents1. Introduction.- 2. Algorithmic Techniques.- 3. Tree Traversal.- 4. Tree Isomorphism.- 5. Graph Traversal.- 6. Clique, Independent Set, and Vertex Cover.- 7. Graph Isomorphism.

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This textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for parallel processing of algebraic graph algorithms. Example code is presented in pseudocode, together with case studies in Python and MPI. The text assumes readers have a background in graph theory and/or graph algorithms.

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Book SynopsisThis book constitutes the refereed proceedings of the First Workshop on Monte Carlo Search, MCS 2020, organized in conjunction with IJCAI 2020. The event was supposed to take place in Yokohama, Japan, in July 2020, but due to the Covid-19 pandemic was held virtually on January 7, 2021. The 9 full papers of the specialized project were carefully reviewed and selected from 15 submissions. The following topics are covered in the contributions: discrete mathematics in computer science, games, optimization, search algorithms, Monte Carlo methods, neural networks, reinforcement learning, machine learning.Table of ContentsThe αµ Search Algorithm for the Game of Bridge.- Stabilized Nested Rollout Policy Adaptation.- zoNNscan: A Boundary-Entropy Index for Zone Inspection of Neural Models.- Ordinal Monte Carlo Tree Search.- Monte Carlo Game Solver.- Generalized Nested Rollout Policy Adaptation.- Monte Carlo Inverse Folding.- Monte Carlo Graph Coloring.- Enhancing Playout Policy Adaptation for General Game Playing.

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Book SynopsisThis textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.Table of ContentsPreface.- List of Algorithms.- List of Bibliographical Notes.- Part 1. Topics in network optimisation.- 1. An introduction to graphs.- 2. Graph connectedness.- 3. Algorithmic complexity.- 4. Optimal paths.- 5. Trees.- 6. Location problems.- 7. Maximum flow networks.- 8. Minimum-cost network flows.- Part 2. Topics in classical graph theory.- 9. Matchings.- 10. Eulerian graphs.- 11. Hamiltonian graphs.- 12. Graph connectivity.- 13. Planarity.- 14. Graph colouring.- 15. Oriented graphs. Part 3. Topics in modern graph theory.- 16. Domination in graphs.- 17. Ramsey Theory.- 18. Extremal graph theory.- 19. Graph enumeration.- 20. The probabilistic method.- Index.

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Book SynopsisThis proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world – many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia.The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work.This volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.Table of ContentsRatio Balancing Numbers(Bartz et al).- An Unexpected Digit Permutation from Multiplying in any Number Base(Qu et al).- A & Z Sequences for Double Riordan Arrays (Branch et al).- Constructing Clifford Algebras for Windmill and Dutch Windmill Graphs; A New Proof of The Friendship Theorem(Myers).- Finding Exact Values of a Character Sum (Peart et al).- On Minimum Index Stanton 4-cycle Designs (Bunge et al).- k-Plane Matroids and Whiteley’s Flattening Conjectures (Servatius et al).- Bounding the edge cover of a hypergraph (Shahrokhi).- A Generalization on Neighborhood Representatives (Holliday).- Harmonious Labelings of Disconnected Graphs involving Cycles and Multiple Components Consisting of Starlike Trees(Abueida et al).- On Rainbow Mean Colorings of Trees (Hallas et al).- Examples of Edge Critical Graphs in Peg Solitaire (Beeler et al).- Regular Tournaments with Minimum Split Domination Number and Cycle Extendability (Factor et al).- Independence and Domination of Chess Pieces on Triangular Boards and on the Surface of a Tetrahedron(Munger et al).- Efficient and Non-efficient Domination of Z-stacked Archimedean Lattices (Paskowitz et al).- On subdivision graphs which are 2-steps Hamiltonian graphs and hereditary non 2-steps Hamiltonian graphs (Lee et al).- On the Erd}os-S_os Conjecture for graphs with circumference at most k + 1 (Heissan et al).- Regular graph and some vertex-deleted subgraph (Egawa et al).- Connectivity and Extendability in Digraphs (Beasle).-On the extraconnectivity of arrangement graphs (Cheng et al).- k-Paths of k-Trees(Bickle).-Rearrangement of the Simple Random Walk(Skyers et al).- On the Energy of Transposition Graphs(DeDeo).- A Smaller Upper Bound for the (4; 82) Lattice Site Percolation Threshold(Wierman).

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Book SynopsisThis book constitutes the refereed proceedings of the 15th International Conference on Graph Transformation, ICGT 2022, which took place Nantes, France in July 2022.The 10 full papers and 1 tool paper presented in this book were carefully reviewed and selected from 19 submissions. The conference focuses on describing new unpublished contributions in the theory and applications of graph transformation as well as tool presentation papers that demonstrate main new features and functionalities of graph-based tools.Table of ContentsTheoretical Advances.- Application Domains.- Tool Presentation.

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Book SynopsisThis book constitutes the proceedings of the 16th International Conference on Algorithmic Aspects in Information and Management, AAIM 2022, which was held online during August 13-14, 2022. The conference was originally planned to take place in Guangzhou, China, but changed to a virtual event due to the COVID-19 pandemic.The 41 regular papers included in this book were carefully reviewed and selected from 59 submissions. Table of ContentsAn improvement of the bound on the odd chromatic number of 1-planar graphs.- AoI Minimizing of Wireless Rechargeable Sensor Network based on Trajectory Optimization of Laser-Charged UAV.- Monotone k-Submodular Knapsack Maximization: An Analysis of the Greedy+Singleton Algorithm.- The constrained parallel-machine scheduling problem with divisible processing times and penalties.- Energy-constrained Geometric Covering Problem.- Fast searching on $k$-combinable graphs.- Three Algorithms for Converting Control Flow Statements from Python to XD-M.- Class Ramsey numbers involving induced graphs.- An Approximation Algorithm for the Clustered Path Travelling Salesman Problem.- Hyperspectral Image Reconstruction for SD-CASSI systems based on Residual Attention Network.- Improved Approximation Algorithm for the Asymmetric Prize-Collecting TSP.- Injective edge coloring of power graphs and necklaces.- Guarantees for Maximization of $k$-Submodular Functions with a Knapsack and a Matroid Constraint.- Incremental SDN Deployment to Achieve Load Balance in ISP Networks.- Approximation scheme for single-machine rescheduling with job delay and rejection.- Defense of Scapegoating Attack in Network Tomography.- A Binary Search Double Greedy Algorithm for Non-monotone DR-submodular Maximization.- Streaming Adaptive Submodular Maximization.- Constrained Stochastic Submodular Maximization with State-Dependent Costs.- Online early work maximization problem on two hierarchical machines with buffer or rearrangements.- Polynomial time algorithm for k-vertex-edge dominating problem in interval graphs.- Adaptive Competition-based Diversified-profit Maximization with Online Seed Allocation.- Collaborative Service Caching in Mobile Edge Nodes.- A Decentralized Auction Framework with Privacy Protection in Mobile Crowdsourcing.- On-line single machine scheduling with release dates and submodular rejection penalties.- Obnoxious Facility Location Games with Candidate Locations.- Profit Maximization for Multiple Products in Community-based Social Networks.- MCM: A Robust Map Matching Method by Tracking Multiple Road Candidates.- Security on Ethereum: Ponzi Scheme Detection in Smart Contract.- Cyclically orderable generalized Petersen graphs.- The r-dynamic chromatic number of planar graphs without special short cycles.- Distance Labeling of the Halved Folded $n$-Cube.- Signed network embedding based on muti-attention mechanism.- Balanced Graph Partitioning based on Mixed 0-1 Linear Programming and Iteration Vertex Relocation Algorithm.- Partial inverse min-max spanning tree problem under the weighted bottleneck Hamming distance.- Mixed Metric Dimension of Some Plane Graphs.- The Optimal Dynamic Rationing Policy in the Stock-Rationing Queue.- Pilot Pattern Design with Branch and Bound in PSA-OFDM System.- Bicriteria Algorithms for Maximizing the Difference Between Submodular Function and Linear Function under Noise.- On the Transversal Number of k-Uniform Connected Hypergraphs.- Total coloring of planar graphs without some adjacent cycles.

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