Introduction to combinatorics
 Author/Creator
 Erickson, Martin J., 1963
 Language
 English.
 Edition
 Second Edition.
 Publication
 Hoboken, New Jersey : John Wiley & Sons, [2013]
 Copyright notice
 ©2013
 Physical description
 xii, 230 pages : illustrations ; 25 cm.
 Series
 Wiley series in discrete mathematics and optimization.
Access
Available online

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QA164 .E74 2013

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QA164 .E74 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages 223224) and index.
 Contents

 Preface xi 1 Basic Counting Methods 1 1.1 The multiplication principle 1 1.2 Permutations 4 1.3 Combinations 6 1.4 Binomial coefficient identities 10 1.5 Distributions 19 1.6 The principle of inclusion and exclusion 23 1.7 Fibonacci numbers 31 1.8 Linear recurrence relations 33 1.9 Special recurrence relations 41 1.10 Counting and number theory 45 Notes 50 2 Generating Functions 53 2.1 Rational generating functions 53 2.2 Special generating functions 63 2.3 Partition numbers 76 2.4 Labeled and unlabeled sets 80 2.5 Counting with symmetry 86 2.6 Cycle indexes 93 2.7 Polya's theorem 96 2.8 The number of graphs 98 2.9 Symmetries in domain and range 102 2.10 Asymmetric graphs 103 Notes 105 3 The Pigeonhole Principle 107 3.1 Simple examples 107 3.2 Lattice points, the Gitterpunktproblem , and SET(R) 110 3.3 Graphs 115 3.4 Colorings of the plane 118 3.5 Sequences and partial orders 119 3.6 Subsets 124 Notes 126 4 Ramsey Theory 131 4.1 Ramsey's theorem 131 4.2 Generalizations of Ramsey's theorem 135 4.3 Ramsey numbers, bounds, and asymptotics 139 4.4 The probabilistic method 143 4.5 Sums 145 4.6 Van der Waerden's theorem 146 Notes 150 5 Codes 153 5.1 Binary codes 153 5.2 Perfect codes 156 5.3 Hamming codes 158 5.4 The Fano Configuration 162 Notes 168 6 Designs 171 6.1 t designs 171 CONTENTS ix 6.2 Block designs 175 6.3 Projective planes 180 6.4 Latin squares 182 6.5 MOLS and OODs 185 6.6 Hadamard matrices 188 6.7 The Golay code and S (5 , 8 , 24) 194 6.8 Lattices and sphere packings 197 6.9 Leech's lattice 199 Notes 201 A Web Resources 205 B Notation 207 Exercise Solutions 211 References 225 Index 227.
 (source: Nielsen Book Data)
 Publisher's Summary
 Praise for the First Edition "This excellent text should prove a useful accoutrement for any developing mathematics program ...it's short, it's sweet, it's beautifully written."  The Mathematical Intelligencer "Erickson has prepared an exemplary work ...strongly recommended for inclusion in undergraduatelevel library collections."  Choice Featuring a modern approach, Introduction to Combinatorics, Second Edition illustrates the applicability of combinatorial methods and discusses topics that are not typically addressed in literature, such as Alcuin's sequence, Rook paths, and Leech's lattice.The book also presents fundamental results, discusses interconnection and problemsolving techniques, and collects and disseminates open problems that raise questions and observations. Many important combinatorial methods are revisited and repeated several times throughout the book in exercises, examples, theorems, and proofs alike, allowing readers to build confidence and reinforce their understanding of complex material. In addition, the author successfully guides readers stepbystep through three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24dimensional lattice. Along with updated tables and references that reflect recent advances in various areas, such as errorcorrecting codes and combinatorial designs, the Second Edition also features: Many new exercises to help readers understand and apply combinatorial techniques and ideas A deeper, investigative study of combinatorics through exercises requiring the use of computer programs Over fifty new examples, ranging in level from routine to advanced, that illustrate important combinatorial concepts Basic principles and theories in combinatorics as well as new and innovative results in the field Introduction to Combinatorics, Second Edition is an ideal textbook for a one or twosemester sequence in combinatorics, graph theory, and discrete mathematics at the upperundergraduate level. The book is also an excellent reference for anyone interested in the various applications of elementary combinatorics.
(source: Nielsen Book Data)  Supplemental links
 Cover image
Subjects
 Subject
 Combinatorial analysis.
Bibliographic information
 Publication date
 2013
 Copyright date
 2013
 Responsibility
 Martin J. Erickson, Department of Mathematics and Computer Science, Truman State University, Kirksville, MO.
 Series
 Wiley series in discrete mathematics and optimization ; 78
 Available in another form
 Online version: Erickson, Martin J., 1963 Introduction to combinatorics Second [edition]. Hoboken, New Jersey : John Wiley & Sons, 2013 9781118640210 (DLC) 2013015019
 ISBN
 9781118637531 (hardback)
 1118637534 (hardback)