This trusted best-seller covers the key combinatorial ideas–including the pigeon-hole principle, counting techniques, permutations and combinations, Pólya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatorial structures (matchings, designs, graphs), and flows in networks. The 5th Edition incorporates feedback from users to the exposition throughout and adds a wealth of new exercises.
Features:
1) Covers a wide range of topics:
-Dilworth's Theorem
-Partitions of integers
-Counting sequences and generating functions
-Extensive graph theory coverage
2) A clear and accessible presentation, written from the student's perspective, facilitates understanding of basic concepts and principles.
3) An excellent treatment of Pólya’s Counting Theorem that does not assume students have studied group theory.
4) Many worked examples illustrate methods used.
Table of Contents:
Chapter 1. What is Combinatorics?
Chapter 2. The Pigeonhole Principle
Chapter 3. Permutations and Combinations
Chapter 4. Generating Permutations and Combinations
Chapter 5. The Binomial Coefficients
Chapter 6. The Inclusion-Exclusion Principle and Applications
Chapter 7. Recurrence Relations and Generating Functions
Chapter 8. Special Counting Sequences
Chapter 9. Systems of Distinct Representatives
Chapter 10. Combinatorial Designs
Chapter 11. Introduction to Graph Theory
Chapter 12. More on Graph Theory
Chapter 13. Digraphs and Networks
Chapter 14. Pólya Counting
About the Author
Richard A. Brualdi is Bascom Professor of Mathematics, Emeritus at the University of Wisconsin-Madison. He served as Chair of the Department of Mathematics from 1993-1999.
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