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Full Description
The third edition of this popular text presents the tools of combinatorics for a first undergraduate course. After introducing fundamental counting rules, tools of graph theory and relations, the focus is on three basic problems of combinatorics: counting, existence, and optimization problems. They discuss advanced tools for dealing with the counting problem, including generating functions, recurrences, inclusion/exclusion, and Polya theory. Combinatorial design, coding theory, and special problems in graph theory are also covered. It also illustrates the basic ideas of combinatorial optimization through a study of graphs and networks. The authors present many contemporary applications.
Contents
Chapter 1Chapter 2: Basic Counting Rules; Chapter 3: Introduction to Graph Theory; Chapter 4 Relations; THE COUNTING PROBLEM Chapter 5: Generating Functions and Their Applications; Chapter 6: Recurrence Relations; Chapter 7: The Principle of Inclusion and Exclusion; Chapter 8: The Polya Theory of Counting; THE EXISTENCE PROBLEM Chapter 9: Combinatorial Designs; Chapter 10: Coding Theory; Chapter 11: Existence Problems in Graph Theory; COMBINATORIAL OPTIMIZATION Chapter 12: Matching and Covering; Chapter 13: Optimization Problems for Graphs and Networks; Appendix: Answers to Selected Exercises; Author Index; Subject Index; References appear at the end of each chapter.
