Applied Combinatorics

The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used book in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.

This book is designed for use by students with a wide range of ability and maturity (sophomores through beginning graduate students). The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used.

Table of Contents

PART ONE: GRAPH THEORY

CHAPTER 1: ELEMENTS OF GRAPH THEORY

CHAPTER 2: COVERING CIRCUITS AND GRAPH COLORING

CHAPTER 3: TREES AND SEARCHING

CHAPTER 4: NETWORK ALGORITHMS

PART TWO: ENUMERATION

CHAPTER 5: GENERAL COUNTING METHODS FOR ARRANGEMENTS AND SELECTIONS

CHAPTER 6: GENERATING FUNCTIONS

CHAPTER 7: RECURRENCE RELATIONS

CHAPTER 8: INCLUSION-EXCLUSION

PART THREE: ADDITIONAL TOPICS

CHAPTER 9: POLYA’S ENUMERATION FORMULA

CHAPTER 10: GAMES WITH GRAPHS

About the Author

Alan Tucker is Deputy Department Chair and Undergraduate Program Director in the Department of Applied Mathematics and Statistics at SUNY Stony Brook.