Applied combinatorics
著者
書誌事項
Applied combinatorics
Chapman & Hall/CRC, c2009
2nd ed
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注記
"A Chapman & Hall book"
Includes bibliographical references and indexes
内容説明・目次
内容説明
Now with solutions to selected problems, Applied Combinatorics, Second Edition presents the tools of combinatorics from an applied point of view. This bestselling textbook offers numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply into the topics.
After introducing fundamental counting rules and the tools of graph theory and relations, the authors focus 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. The text then covers combinatorial design, coding theory, and special problems in graph theory. It also illustrates the basic ideas of combinatorial optimization through a study of graphs and networks.
目次
What Is Combinatorics? THE BASIC TOOLS OF COMBINATORICS: Basic Counting Rules. Introduction to Graph Theory. Relations. THE COUNTING PROBLEM: Generating Functions and Their Applications. Recurrence Relations. The Principle of Inclusion and Exclusion. The Polya Theory of Counting. THE EXISTENCE PROBLEM: Combinatorial Designs. Coding Theory. Existence Problems in Graph Theory. COMBINATORIAL OPTIMIZATION: Matching and Covering. Optimization Problems for Graphs and Networks. Appendix. Indices.
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