A permutation $\sigma$ of the multiset $\{1,1,2,2,\ldots,n,n\}$ is called a Stirling permutation of order $n$ if $\sigma_s>\sigma_i$ as long as $\sigma_i=\sigma_j$ and $i. In this paper, we present a unified refinement of the ascent polynomials and the ascent-plateau polynomials of Stirling permutations. In particular, by using Foata and Strehl's group action, we prove that the pairs of statistics (left ascent-plateau, ascent) and (left ascent-plateau, plateau) are equidistributed over Stirling permutations of given order, and we show the $\gamma$-positivity of the enumerative polynomial of left ascent-plateaus, double ascents and descent-plateaus. A connection between the $\gamma$-coefficients of this enumerative polynomial and Eulerian numbers is also established.
@article{10_37236_8008,
author = {Shi-Mei Ma and Jun Ma and Yeong-Nan Yeh},
title = {The ascent-plateau statistics on {Stirling} permutations},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {2},
doi = {10.37236/8008},
zbl = {1409.05013},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8008/}
}
TY - JOUR
AU - Shi-Mei Ma
AU - Jun Ma
AU - Yeong-Nan Yeh
TI - The ascent-plateau statistics on Stirling permutations
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/8008/
DO - 10.37236/8008
ID - 10_37236_8008
ER -
%0 Journal Article
%A Shi-Mei Ma
%A Jun Ma
%A Yeong-Nan Yeh
%T The ascent-plateau statistics on Stirling permutations
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/8008/
%R 10.37236/8008
%F 10_37236_8008
Shi-Mei Ma; Jun Ma; Yeong-Nan Yeh. The ascent-plateau statistics on Stirling permutations. The electronic journal of combinatorics, Tome 26 (2019) no. 2. doi: 10.37236/8008
