The alternating run polynomials of permutations
Combinatorics
2019-05-01 v3
Abstract
In this paper, we first consider a generalization of the David-Barton identity which relate the alternating run polynomials to Eulerian polynomials. By using context-free grammars, we then present a combinatorial interpretation of a family of q-alternating run polynomials. Furthermore, we introduce the definition of semi-gamma-positive polynomial and we show the semi-gamma-positivity of the alternating run polynomials of dual Stirling permutations. A connection between the up-down run polynomials of permutations and the alternating run polynomials of dual Stirling permutations is established.
Cite
@article{arxiv.1904.11437,
title = {The alternating run polynomials of permutations},
author = {Shi-Mei Ma and Jun Ma and Yeong-Nan Yeh},
journal= {arXiv preprint arXiv:1904.11437},
year = {2019}
}
Comments
14 pages