Introduction to combinatorics
By: Martin J. Erickson, Department of Mathematics and Computer Science, Truman State University, Kirksville, MO
Edition: Second Edition
Series: Wiley series in discrete mathematics and optimization -- 78
Publisher: John Wiley & Sons
Published: 2013
Place of publication: Hoboken, New Jersey
Language: eng
Number of pages: 230
ISBN-13: 9781118637531
Copyright date: 2013
Subjects: Combinatorial analysis; MATHEMATICS / Discrete Mathematics
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." --ChoiceFeaturing 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, Polya'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"--
Notes: Bibliographical references (pages 223-224) and index.
Table of contents: title: Machine generated contents note: Preface xi1 Basic Counting Methods 11.1 The multiplication principle 11.2 Permutations 41.3 Combinations 61.4 Binomial coefficient identities 101.5 Distributions 191.6 The principle of inclusion and exclusion 231.7 Fibonacci numbers 311.8 Linear recurrence relations 331.9 Special recurrence relations 411.10 Counting and number theory 45Notes 502 Generating Functions 532.1 Rational generating functions 532.2 Special generating functions 632.3 Partition numbers 762.4 Labeled and unlabeled sets 802.5 Counting with symmetry 862.6 Cycle indexes 932.7 Polya's theorem 962.8 The number of graphs 982.9 Symmetries in domain and range 1022.10 Asymmetric graphs 103Notes 1053 The Pigeonhole Principle 1073.1 Simple examples 1073.2 Lattice points, the Gitterpunktproblem, and SET(r) 1103.3 Graphs 1153.4 Colorings of the plane 1183.5 Sequences and partial orders 1193.6 Subsets 124Notes 1264 Ramsey Theory 1314.1 Ramsey's theorem 1314.2 Generalizations of Ramsey's theorem 1354.3 Ramsey numbers, bounds, and asymptotics 1394.4 The probabilistic method 1434.5 Sums 1454.6 Van der Waerden's theorem 146Notes 1505 Codes 1535.1 Binary codes 1535.2 Perfect codes 1565.3 Hamming codes 1585.4 The Fano Configuration 162Notes 1686 Designs 1716.1 t-designs 171CONTENTS ix6.2 Block designs 1756.3 Projective planes 1806.4 Latin squares 1826.5 MOLS and OODs 1856.6 Hadamard matrices 1886.7 The Golay code and S(5, 8, 24) 1946.8 Lattices and sphere packings 1976.9 Leech's lattice 199Notes 201A Web Resources 205B Notation 207Exercise Solutions 211References 225Index 227.