Introduction to Combinatorics

Introduces basic ideas of combinatorics by concentrating on counting problems. The topics covered include combinations, permutations, the inclusion-exclusion principle, partitions, Stirling's formula, generating functions, recurrence relations, group actions and graphs. Exercises are provided.

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By concentrating on counting problems, Introduction to Combinatorics conveys basic ideas of its subject.
Topics include combinations, permutations, the inclusion-exclusion principles, partitions, Stirling's Formula, generating functions, recurrence relations, groups, group actions, and graphs. The final two chapters discuss the application of group theory to counting patterns, via Burnside's Theorem and Polya's Theorem.
Slomson's approach is to begin with concrete problems, and to use them as a lead-in to general theory.
Numerous exercises-most of which are provided with detailed answers-are included for the advanced student. Among the applications considered are approaches to probability problems, especially in card games.