On two unimodal descent polynomials
Combinatorics
2019-02-06 v2
Abstract
The descent polynomials of separable permutations and derangements are both demonstrated to be unimodal. Moreover, we prove that the -coefficients of the first are positive with an interpretation parallel to the classical Eulerian polynomial, while the second is spiral, a property stronger than unimodality. Furthermore, we conjecture that they are both real-rooted.
Keywords
Cite
@article{arxiv.1507.05184,
title = {On two unimodal descent polynomials},
author = {Shishuo Fu and Zhicong Lin and Jiang Zeng},
journal= {arXiv preprint arXiv:1507.05184},
year = {2019}
}
Comments
16 pages, 4 figures