Articoli correlati a Introduction to Combinatorics
Sinossi
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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Contenuti
Introduction
Permutations and Combinations
The Inclusion-Exclusion Principle
Partitions
Stirling's Approximation
Partitions and Generating Functions
Generating Functions and Recurrence Relations
Permutations and Groups
Group Actions
Graphs
Counting Patterns
Polya's Theorem
Solutions to the Exercises
Suggestions for Further Reading
List of Symbols
Index
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