Foundations of Combinatorics with Applications

by

Edward A. Bender & S. Gill Williamson

Dover (2006) ISBN 0-486-44603-4

468 pages

Intended audience: Upper division/beginning graduate. Some ability to construct proofs is assumed.

Background: Some familiarity with calculus and proofs is assumed.

Comments and errata are appreciated. ebender@ucsd.edu

You may download a copy for personal use from this web page at no charge.



This material is intended for double sided reproduction. All files start on a right hand page.

ps pdf Preface and Table of Contents

ps pdf Part I: Counting and Listing -- Introduction . . . page 1

ps pdf Chapter 1: Basic Counting . . . page 3

ps pdf Chapter 2: Functions . . . page 37

ps pdf Chapter 3: Decision Trees . . . page 61

ps pdf Chapter 4: Sieving Methods [Symmetries and Inclusion-Exclusion] . . . page 89

ps pdf Part II: Graph Theory -- Introduction . . . page 113

ps pdf Chapter 5: Basic Concepts in Graph Theory . . . page 115

ps pdf Chapter 6: A Sampler of Graph Topics . . . page 143

ps pdf Part III: Recursion --Introduction . . . page 189

ps pdf Chapter 7: Induction and Recursion . . . page 191

ps pdf Chapter 8: Sorting Theory . . . page 219

ps pdf Chapter 9: Rooted Plane Trees . . . page 239

ps pdf Part IV: Generating Functions -- Introduction . . . page 259

ps pdf Chapter 10: Ordinary Generating Functions . . . page 261

ps pdf Chapter 11: Generating Function Topics . . . page 297

ps pdf Appendices . . . page 351

Appendix A: Induction

Appendix B: Rates of Growth and Analysis of Algorithms

Appendix C: Basic Probability

Appendix D: Partial Fractions

ps pdf Solutions to Odd Exercises . . . page 383

ps pdf Index . . . page 449