A curious symmetric decomposition of the (des, exc)-Eulerian polynomials
Combinatorics
2024-06-11 v1
Abstract
One of the most central result in combinatorics says that the descent statistic and the excedance statistic are equidistribued over the symmetric group. As a continuation of the work of Shareshian-Wachs (Adv. Math., 225(6) (2010), 2921--2966), we provide a curious -symmetric decomposition for the generating polynomial of the joint distribution of the descent and excedance statistics over the symmetric group.
Keywords
Cite
@article{arxiv.2406.06365,
title = {A curious symmetric decomposition of the (des, exc)-Eulerian polynomials},
author = {Shi-Mei Ma and Toufik Mansour and Yeong-Nan Yeh},
journal= {arXiv preprint arXiv:2406.06365},
year = {2024}
}
Comments
7 pages