Eulerian polynomials for multipermutations and signed multipermutations

Abstract

In this paper, we study Eulerian polynomials for permutations and signed permutations of the multiset $\{1,1,2,2,\dots ,n,n\}$. Properties of these polynomials, including recurrence relations and unimodality are discussed. In particular, we give a unified proof of the fact that these polynomials are unimodal with modes in the middle.

14 pages

References in corpus (1)

• Gamma-positivity in combinatorics and geometry

Cited by in corpus (1)

• Stability of combinatorial polynomials and its applications