An Introduction to Combinatorics
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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Permutations and combinations
The inclusionexclusion principle
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algebraic asymptotic axes joining binomial coefficients bridge hands Burnside's Theorem Cayley table chapter chessboard choices choose chosen combinatorial conjugacy classes contains corresponding cosets count the number counting problems cube cycle index cycle notation cycle type cycles of length defined diagram different graphs different patterns element of G element of order example Exercise expression follows formula G. H. Hardy given gp-i group action group G group of permutations Hardy-Ramanujan Hence identity element inequality integer isomorphism labellings Lemma mapping mathematics matrix midpoints of opposite Multinomial Theorem multiple natural numbers number of different number of elements number of partitions obtain orbits pack partition numbers pattern inventory pk(n polynomial function positive integer power series Prove qk(n Ramanujan recurrence relation riffle shuffle rotational symmetries solution of equation square Stirling's subgroup of G Subgroups of order suit distributions Suppose theory total number vertex vertices write