The 1/k-Eulerian polynomials of type B

2020/01/22 by Ma, Shi-Mei, Ma, Jun, Yeh, Jean +1
#05A05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.07833

Abstract

In this paper, we give a type B analogue of the 1/k-Eulerian polynomials. Properties of this kind of polynomials, including combinatorial interpretations, recurrence relations and gamma-positivity are studied. In particular, we show that the 1/k-Eulerian polynomials of type B are gamma-positive when k>0. Moreover, we obtain the corresponding results for derangements of type B. We show that a type B 1/k-derangement polynomials d_n^B(x;k) are bi-gamma-positive when k≥ 1/2. In particular, we get a symmetric decomposition of d_n^B(x;1/2) in terms of the classical derangement polynomials.

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