English

Symmetric unimodal expansions of excedances in colored permutations

Combinatorics 2022-03-22 v3

Abstract

We consider several generalizations of the classical γ\gamma-positivity of Eulerian polynomials (and their derangement analogues) using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove an expansion formula for inversions and excedances as well as a similar expansion for derangements. We also prove the γ\gamma-positivity for Eulerian polynomials for derangements of type BB. More general expansion formulae are also given for Eulerian polynomials for rr-colored derangements. Our results answer and generalize several recent open problems in the literature.

Keywords

Cite

@article{arxiv.1411.6184,
  title  = {Symmetric unimodal expansions of excedances in colored permutations},
  author = {Heesung Shin and Jiang Zeng},
  journal= {arXiv preprint arXiv:1411.6184},
  year   = {2022}
}

Comments

27 pages, 10 figures