Eulerian Polynomials, Stirling Permutations of the Second Kind and Perfect Matchings
نویسندگان
چکیده
منابع مشابه
Eulerian Polynomials, Stirling Permutations of the Second Kind and Perfect Matchings
In this paper, we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the second kind by their cycle ascent plateaus, fixed points and cycles. Moreover, we get an expansion of the ordinary derangement polynomials in terms of the Stirling derangement polynomials. Finally, we present constructive proofs of a kind of combinatorial expansions of the ...
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In this paper we provide constructive proofs that the following three statistics are equidistributed: the number of ascent plateaus of Stirling permutations of order n, a weighted variant of the number of excedances in permutations of length n and the number of blocks with even maximal elements in perfect matchings of the set {1, 2, 3, . . . , 2n}.
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We study Eulerian polynomials as the generating polynomials of the descent statistic over Stirling permutations – a class of restricted multiset permutations. We develop their multivariate refinements by indexing variables by the values at the descent tops, rather than the position where they appear. We prove that the obtained multivariate polynomials are stable, in the sense that they do not v...
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The papers [18], [9], [21], [14], [23], [6], [24], [2], [3], [8], [10], [1], [22], [7], [11], [20], [16], [19], [4], [5], [13], [12], [17], and [15] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: k, l, m, n, i, j denote natural numbers, K, N denote non empty subsets of N, K1, N1, M1 denote subsets of N, and X, Y denote sets. Let us consid...
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Say an integer n is exceptional if the maximum Stirling number of the second kind S(n, k) occurs for two (of necessity consecutive) values of k. We prove that the number of exceptional integers less than or equal to x is O(x), for any ! > 0. We derive a similar result for partitions of n into exactly k integers.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/7288