{
  "id": "1304.7587",
  "version": "v2",
  "published": "2013-04-29T08:10:03.000Z",
  "updated": "2013-08-14T06:54:34.000Z",
  "title": "Roots of the Ehrhart polynomial of hypersimplices",
  "authors": [
    "Hidefumi Ohsugi",
    "Kazuki Shibata"
  ],
  "comment": "18 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Ehrhart polynomial of the $d$-th hypersimplex $\\Delta(d,n)$ of order $n$ is studied. By computational experiments and a known result for $d=2$, we conjecture that the real part of every roots of the Ehrhart polynomial of $\\Delta(d,n)$ is negative and larger than $- \\frac{n}{d}$ if $n \\geq 2d$. In this paper, we show that the conjecture is true when $d=3$ and that every root $a$ of the Ehrhart polynomial of $\\Delta(d,n)$ satisfies $-\\frac{n}{d} < {\\rm Re} (a) < 1$ if $4 \\leq d \\ll n$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-14T06:54:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20"
    ],
    "keywords": [
      "ehrhart polynomial",
      "hypersimplices",
      "th hypersimplex",
      "computational experiments",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7587O"
    }
  }
}