A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory

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World Scientific, 2011 - Mathematics - 546 pages
2 Reviews
This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity.As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.
 

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A very interesting one, good for start-up.

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Awwwsome book man , Everything is written clearly, This book clear all my confusions its a better book than C.L. liu

Contents

Chapter 1 Seven Is More Than Six The PigeonHole Principle
1
Chapter 2 One Step at a Time The Method of Mathematical Induction
21
Chapter 3 There Are A Lot Of Them Elementary Counting Problems
39
Chapter 4 No Matter How You Slice It The Binomial Theorem and Related Identities
67
Chapter 5 Divide and Conquer Partitions
93
Chapter 6 Not So Vicious Cycles Cycles in Permutations
113
Chapter 7 You Shall Not Overcount The Sieve
135
Chapter 8 A Function Is Worth Many Numbers Generating Functions
149
Chapter 13 Does It Clique? Ramsey Theory
293
Chapter 14 So Hard To Avoid Subsequence Conditions on Permutations
313
Chapter 15 Who Knows What It Looks Like But It Exists The Probabilistic Method
349
Chapter 16 At Least Some Order Partial Orders and Lattices
381
Chapter 17 As Evenly As Possible Block Designs and Error Correcting Codes
413
Chapter 18 Are They Really Different? Counting Unlabeled Structures
447
Chapter 19 The Sooner The Better Combinatorial Algorithms
481
Chapter 20 Does Many Mean More Than One? Computational Complexity
509

Chapter 9 Dots and Lines The Origins of Graph Theory
189
Chapter 10 Staying Connected Trees
215
Chapter 11 Finding A Good Match Coloring and Matching
247
Chapter 12 Do Not Cross Planar Graphs
275

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