Eulerian polynomials for multipermutations and signed multipermutations

2019/07/30 by Ma, Shi-Mei, Ma, Jun, Yeh, Yeong-Nan
#05A05 #05E45 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.13082

Abstract

In this paper, we study Eulerian polynomials for permutations and signed permutations of the multiset \1,1,2,2,…,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.

Related

• The 1/k-Eulerian polynomials and k-Stirling permutations
• Eulerian polynomials, perfect matchings and Stirling permutations of the second kind
• Multivariate Stable Eulerian Polynomials on Segmented Permutations
• Commuting Eulerian operators
• Eulerian pairs and Eulerian recurrence systems