Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Third Edition)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. |
Contents
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 |
537 | |
541 | |
Other editions - View all
A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory Mikl Ba Limited preview - 2011 |
A Walk Through Combinatorics: An Introduction to Enumeration and Graph ... Mikl贸s B贸na Limited preview - 2016 |
A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory Mikl髎 B髇a No preview available - 2011 |
Common terms and phrases
adjacent algorithm apply bijection blocks blue called Chapter choices choose claim coefficient color complete compute connected consider consists contain count cycle defined definition denote digit directed divisible edges elements entries equal exactly Example Exercise exists faces fact Figure Find finite five fixed follows formula four function given graph hand holds identical implies induction larger least Lemma length Let G Let us assume machine matching matrix means multiset n-permutations Note obtained pairs partition path permutation play players polynomial poset positive integers possible probability problem proof Proposition Prove reader result right-hand side rooted satisfies selected sequence shows simple Solution square statement step subsets teams term Theorem trees triangle true values vertex vertices