English

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 γ\gamma-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

R2 v1 2026-06-22T10:14:23.194Z