The 1/k-Eulerian polynomials and k-Stirling permutations

Shi Mei Ma; Toufik Mansour

doi:10.1016/j.disc.2015.03.015

The 1/k-Eulerian polynomials and k-Stirling permutations

Shi Mei Ma, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1468-1472
Number of pages	5
Journal	Discrete Mathematics
Volume	338
Issue number	8
DOIs	https://doi.org/10.1016/j.disc.2015.03.015
State	Published - 6 Aug 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

Keywords

1 / k-Eulerian polynomials
Alternating runs
Longest ascent plateaus
k-Stirling permutations

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2015.03.015

Cite this

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AB - 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.

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KW - Alternating runs

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JO - Discrete Mathematics

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ER -

The 1/k-Eulerian polynomials and k-Stirling permutations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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