{
  "id": "1704.08057",
  "version": "v1",
  "published": "2017-04-26T11:15:52.000Z",
  "updated": "2017-04-26T11:15:52.000Z",
  "title": "Local $h$-vectors of Quasi-Geometric and Barycentric Subdivisions",
  "authors": [
    "Martina Juhnke-Kubitzke",
    "Satoshi Murai",
    "Richard Sieg"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we answer two questions on local $h$-vectors, which were asked by Athanasiadis. First, we characterize all possible local $h$-vectors of quasi-geometric subdivisions of a simplex. Second, we prove that the local $\\gamma$-vector of the barycentric subdivision of any CW-regular subdivision of a simplex is nonnegative. Along the way, we derive a new recurrence formula for the derangement polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-26T11:15:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "05A05"
    ],
    "keywords": [
      "barycentric subdivision",
      "quasi-geometric subdivisions",
      "cw-regular subdivision",
      "recurrence formula",
      "derangement polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}