Introduction to Combinatorics by Martin J. Erickson (English) Hardcover Book

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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...

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

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 undergraduate-level 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 problem-solving 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 step-by-step through three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Pólya's graph enumeration formula, and Leech's 24-dimensional lattice.  Along with updated tables and references that reflect recent advances in various areas, such as error-correcting codes and combinatorial designs, the Second Edition also features: Many new exercises to help readers understand and apply combinatorial techniques and ideasA deeper, investigative study of combinatorics through exercises requiring the use of computer programsOver fifty new examples, ranging in level from routine to advanced, that illustrate important combinatorial conceptsBasic 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 two-semester sequence in combinatorics, graph theory, and discrete mathematics at the upper-undergraduate level. The book is also an excellent reference for anyone interested in the various applications of elementary combinatorics.

Back Cover

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 undergraduate-level 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 problem-solving 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 step-by-step through three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, P

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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 undergraduate-level 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 problem-solving 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 step-by-step through three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, P

Author Biography

MARTIN J. ERICKSON, PhD, is Professor in the Department of Mathematics at Truman State University. The author of numerous books, including Mathematics for the Liberal Arts (Wiley), he is a member of the American Mathematical Society, Mathematical Association of America, and American Association of University Professors.

Table of 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 Pólya'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® 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

Review

"Indeed, Erickson's Introduction to Combinatoricsis appealing on precisely the count that it is very user-friendly."  (MAA Reviews, 5 January 2014)

Long Description

Praise for the First Edition "This excellent text should prove a useful accoutrement for any developing mathematics program . . . its short, its sweet, its beautifully written." The Mathematical Intelligencer "Erickson has prepared an exemplary work . . . strongly recommended for inclusion in undergraduate-level 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 Alcuins sequence, Rook paths, and Leechs lattice. The book also presents fundamental results, discusses interconnection and problem-solving 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 step-by-step through three major achievements of combinatorics: Van der Waerdens theorem on arithmetic progressions, Plyas graph enumeration formula, and Leechs 24-dimensional lattice. Along with updated tables and references that reflect recent advances in various areas, such as error-correcting 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 two-semester sequence in combinatorics, graph theory, and discrete mathematics at the upper-undergraduate level. The book is also an excellent reference for anyone interested in the various applications of elementary combinatorics.

Review Text

?Indeed, Erickson?s Introduction to Combinatoricsis appealing on precisely the count that it is very user-friendly.?  (MAA Reviews, 5 January 2014)

Review Quote

"Indeed, Erickson's Introduction to Combinatoricsis appealing on precisely the count that it is very user-friendly." ( MAA Reviews , 5 January 2014)

Details ISBN1118637534 Publisher John Wiley & Sons Inc Series Wiley Series in Discrete Mathematics and Optimization Year 2013 Edition 2nd ISBN-10 1118637534 ISBN-13 9781118637531 Format Hardcover Imprint John Wiley & Sons Inc Place of Publication New York Country of Publication United States Short Title INTRO TO COMBINATORICS 2/E Language English Media Book Series Number 78 DEWEY 511.6 Pages 244 Illustrations Yes UK Release Date 2013-05-31 AU Release Date 2013-04-08 NZ Release Date 2013-04-08 Author Martin J. Erickson Edition Description 2nd edition Publication Date 2013-05-31 Replaces 9780471154082 Audience Undergraduate US Release Date 2013-05-31 We've got this

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