Martin J. Erickson

Introduction to Combinatorics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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 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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 244
• Erscheinungstermin: 14. Juli 2014
• Englisch
• ISBN-13: 9781118640210
• Artikelnr.: 41208966

Autorenporträt

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.

Inhaltsangabe

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(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