A curious symmetric decomposition of the (des, exc)-Eulerian polynomials

2024/06/10 by Ma, Shi-Mei, Mansour, Toufik, Yeh, Yeong-Nan
#05A05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.06365

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 t-symmetric decomposition for the generating polynomial of the joint distribution of the descent and excedance statistics over the symmetric group.

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