Generating Functions for Permutations which Contain a Given Descent Set
نویسندگان
چکیده
منابع مشابه
Generating Functions for Permutations which Contain a Given Descent Set
A large number of generating functions for permutation statistics can be obtained by applying homomorphisms to simple symmetric function identities. In particular, a large number of generating functions involving the number of descents of a permutation σ, des(σ), arise in this way. For any given finite set S of positive integers, we develop a method to produce similar generating functions for t...
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The purpose of this paper is to count permutations in S , with a given cycle structure and a given descent set. Our main result (Theorem 2.1) asserts that the number of these permutations can be expressed as a scalar product of two symmetric functions, one associated with the cycle structure and the other with the descent set. Both of these symmetric functions can be interpreted as characterist...
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Let Sn denote the symmetric group of all permutations π = a1 . . . an of {1, . . . , n}. An index i is a peak of π if ai−1 < ai > ai+1 and we let P (π) be the set of peaks of π. Given any set S of positive integers we define P (S;n) to be the set π ∈ Sn with P (π) = S. Our main result is that for all fixed subsets of positive integers S and all sufficiently large n we have #P (S;n) = p(n)2n−#S−...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/299