{
  "id": "1910.01747",
  "version": "v1",
  "published": "2019-10-03T22:15:22.000Z",
  "updated": "2019-10-03T22:15:22.000Z",
  "title": "The $γ$-coefficients of Branden's $(p,q)$-Eulerian polynomials and André permutations",
  "authors": [
    "Qiong Qiong Pan",
    "Jiang Zeng"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "P. Br\\\"and\\'en (European J. Combin. 29 (2008), no. 2, 514--531) studied a $(p,q)$-analogue of the classical Eulerian polynomials $A_n(p,q,t)$ and conjectured that its $\\gamma$-coefficient $a_{n,k}(p,q)$ is divisible by $(p+q)^k$. The aim of this paper is to show that the quotient $d_{n,k}(p,q):=a_{n,k}(p,q)/(p+q)^k$ is the enumerative polynomial of Andr\\'e permutations of the second kind of size $n$ with $k$ descents. In addition, our result leads to a combinatorial model for G.-N. Han's recent $q$-Euler numbers (arXiv:1906.00103v1).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-03T22:15:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coefficient",
      "classical eulerian polynomials",
      "andre permutations",
      "second kind",
      "combinatorial model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}