Counting Stirling permutations by number of pushes
                    
                        
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                    چکیده
منابع مشابه
Legendre - Stirling Permutations ∗ Eric
We first give a combinatorial interpretation of Everitt, Littlejohn, and Wellman’s Legendre-Stirling numbers of the first kind. We then give a combinatorial interpretation of the coefficients of the polynomial (1 − x) ∑∞ n=0 { n+k n } x analogous to that of the Eulerian numbers, where { n k } are Everitt, Littlejohn, and Wellman’s Legendre-Stirling numbers of the second kind. Finally we use a r...
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A permutation σ of a multiset is called Stirling permutation if σ(s) ≥ σ(i) as soon as σ(i) = σ(j) and i < s < j. In our paper we study Stirling polynomials that arise in the generating function for descent statistics on Stirling permutations of any multiset. We develop generalizations of the classical Stirling numbers and present their combinatorial interpretations. Particularly, we apply the ...
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We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can be expressed as the reciprocal of a sum involving Euler numbers: ( 1− E1x + E3 x3 3! − E4 x4 4! + E6 x6 6! − E7 x7 7! + · · · )−1 , (∗) where ∑∞ n=0Enx n/n! ...
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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}.
متن کاملAnalysis of Statistics for Generalized Stirling Permutations
In this work we give a study of generalizations of Stirling permutations, a restricted class of permutations of multisets introduced by Gessel and Stanley [15]. First we give several bijections between such generalized Stirling permutations and various families of increasing trees extending the known correspondences of [20, 21]. Then we consider several permutation statistics of interest for ge...
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ژورنال
عنوان ژورنال: Pure Mathematics and Applications
سال: 2020
ISSN: 1788-800X
DOI: 10.1515/puma-2015-0038