The 1/k-Eulerian polynomials and k-Stirling permutations
The 1/k-Eulerian polynomials and k-Stirling permutations
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1/k-欧拉多项式和 k-斯特林排列
DOI：
10.1016/j.disc.2015.03.015
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发表时间：
2014-09
影响因子：
0.8
通讯作者：
Toufik Mansour
中科院分区：
文献类型：
--
作者：
马世美;Toufik Mansour
在Savage和Viswanathan（2012）最近的工作中，在研究n维k-反转序列的集合时，引入了所谓的1/k-欧拉多项式，它被认为是这种反转序列中上升次数的生成多项式。在本文中，我们发现1/k多项式也生成k-Stirling排列的最长上升平台数的多项式。此外，我们还引入了斯特林排列的对偶集。
In a recent work of Savage and Viswanathan (2012), during studies of the set of n-dimensional k-inversion sequences, the so-called 1/k-Eulerian polynomials have been introduced, which are given as generating polynomials of the number of ascents in such inversion sequences. In this paper, we discover that the 1/k-polynomials are also generating polynomials of the number of the longest ascent plateaus of k-Stirling permutations. Moreover, we also introduce the dual set of Stirling permutations.