Appropriate for an undergraduate junior/senior level mathematics course on combinatorics.
This book emphasizes combinatorial ideas including the pigeon-hole principle, counting techniques, permutations and combinations, Pólya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs).
NEWIncludes new material on partially ordered sets and Dilworth's Theorem. Pg. __
NEWPresents new material on partitions of integers and generating functions. NEWChapters on graph theory have been completely revised with a new chapter on digraphs and networks.
Presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory.
The text is written in a very lively style. Most complete coverage of the undergraduate texts available in this market.
1. What is Combinatorics?
2. The Pigeonhole Principle.
3. Permutations and Combinations.
4. Generating Permutations and Combinations.
5. The Binomial Coefficients.
6. The Inclusion-Exclusion Principle and Applications.
7. Recurrence Relations and Generating Functions.
8. Special Counting Sequences.
9. Matchings in Bipartite Graphs.
10. Combinatorial Designs.
11. Introduction to Graph Theory.
12. Digraphs and Networks.
13. More on Graph Theory.
14. Pólya Counting.
Answers and Hints to Exercises.