Inhaltsangabe
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.
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Reseña del editor
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.
Reseña del editor
This book 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, groups, group actions and graphs. The final chapters discuss the application of group theory to counting patterns, via Burnside's theorem and Polya's theorem. The book uses concrete problems to lead to the general theory. Exercises for the student are provided, as well as the answers to them. Among the applications considered are those to probability problems, especially in card games.
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