{
  "id": "1609.06646",
  "version": "v1",
  "published": "2016-09-21T17:28:10.000Z",
  "updated": "2016-09-21T17:28:10.000Z",
  "title": "The local $h$-polynomial of the edgewise subdivision of the simplex",
  "authors": [
    "Christos A. Athanasiadis"
  ],
  "comment": "11 pages, 3 figures; to appear in the Bulletin of the Hellenic Mathematical Society",
  "categories": [
    "math.CO"
  ],
  "abstract": "The $r$-fold edgewise subdivision is a well studied flag triangulation of the simplex with interesting algebraic, combinatorial and geometric properties. An important enumerative invariant, namely the local $h$-polynomial, of this triangulation is computed and shown to be $\\gamma$-nonnegative by providing explicit combinatorial interpretations to the corresponding coefficients. A construction of a flag triangulation of the seven-dimensional simplex whose local $h$-polynomial is not real-rooted is also described.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-21T17:28:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "05A05"
    ],
    "keywords": [
      "polynomial",
      "flag triangulation",
      "explicit combinatorial interpretations",
      "seven-dimensional simplex",
      "fold edgewise subdivision"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}