{
  "id": "1407.1968",
  "version": "v2",
  "published": "2014-07-08T06:31:45.000Z",
  "updated": "2014-09-02T08:25:57.000Z",
  "title": "Strong q-log-convexity of the Eulerian polynomials of Coxeter groups",
  "authors": [
    "Lily Li Liu",
    "Bao-Xuan Zhu"
  ],
  "comment": "13pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we prove the strong $q$-log-convexity of the Eulerian polynomials of Coxeter groups using their exponential generating functions. Our proof is based on the theory of exponential Riordan arraya and a criterion for determining the strong $q$-log-convexity of polynomials sequences, whose generating functions can be given by the continued fraction. As consequences, we get the strong $q$-log-convexity the Eulerian polynomials of type $A_n,B_n$, their $q$-analogous and the generalized Eulerian polynomials associated to the arithmetic progression $\\{a,a+d,a+2d,a+3d,\\ldots\\}$ in a unified manner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-08T06:31:45.000Z",
      "abstract": "In this paper we prove the strong $q$-log-convexity of the Eulerian polynomials of Coxeter groups using their exponential generating functions. Our proof is based on the theory of exponential Riordan arraya and a criterion for determining the strong $q$-log-convexity of polynomials sequences, whose generating functions can be given by the continued fraction. As consequences, we get that the Eulerian polynomials of type $A_n,B_n$, their $q$-analogous and the generalized Eulerian polynomials associated to the arithmetic progression $\\{a,a+d,a+2d,a+3d,\\ldots\\}$ are $q$-log-convexity respectively",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-02T08:25:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "05A15",
      "30F70"
    ],
    "keywords": [
      "coxeter groups",
      "strong q-log-convexity",
      "exponential riordan arraya",
      "exponential generating functions",
      "polynomials sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1968L"
    }
  }
}