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Developed from the authors’ introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya’s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths.
Introduction
Combinations and Permutations
Generating Functions
Principle of Inclusion and Exclusion
Stirling Numbers
Pó1ya's Theory of Counting
Outlook
Midterm Examination
Ramsey Theory
Matchings (Stable Marriages)
Matchings (Maximum Matchings)
Network Flow
Hamiltonian and Eulerian Paths
Planarity and the Four-Color Theorem
Final Examination