{
  "id": "2002.06930",
  "version": "v1",
  "published": "2020-02-17T12:57:34.000Z",
  "updated": "2020-02-17T12:57:34.000Z",
  "title": "The gamma-positivity of Eulerian polynomials and succession statistics",
  "authors": [
    "Shi-Mei Ma",
    "Jun Ma",
    "Jean Yeh",
    "Yeong-Nan Yeh"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper is concerned with multivariate refinements of the gamma-positivity of Eulerian polynomials by using the succession and fixed point statistics. Properties of the enumerative polynomials for permutations, signed permutations and derangements, including generating functions and gamma-positivity are studied, which generalize and unify earlier results of Athanasiadis, Brenti, Chow, Petersen, Roselle, Stembridge, Shin and Zeng. In particular, we derive a formula expressing the joint distribution of excedance number and negative number statistics over the type B derangements in terms of the derangement polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-17T12:57:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "eulerian polynomials",
      "succession statistics",
      "gamma-positivity",
      "multivariate refinements",
      "negative number statistics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}