منابع مشابه
Stirling permutations on multisets
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 ...
متن کاملLegendre - 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...
متن کاملOn Path diagrams and Stirling permutations
Any ordinary permutation τ ∈ Sn of size n, written as a word τ = τ1 . . . τn, can be locally classified according to the relative order of τj to its neighbours. This gives rise to four local order types called peaks (or maxima), valleys (or minima), double rises and double falls. By the correspondence between permutations and binary increasing trees the classification of permutations according ...
متن کاملStirling Permutations, Cycle Structure of Permutations and Perfect Matchings
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 کاملEnumeration formulæ for pattern restricted Stirling permutations
We classify k-Stirling permutations avoiding a set of ordered patterns of length three according to Wilf-equivalence. Moreover, we derive enumeration formulæ for all of the classes using a variety of techniques such as the kernel method, a bijection related to a classical result of Simion and Schmidt, and also structural decompositions of k-Stirling permutations via the so-called block decompos...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2014
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.08.002