Introduction to Combinatorics

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.

Table of Contents

1 Basic Counting Methods

2 Generating Functions

3 The Pigeonhole Principle

4 Ramsey Theory

5 Error-Correcting Codes

6 Combinatorial Designs

About the Author

 Martin J. Erickson 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.