{
  "id": "1109.0791",
  "version": "v2",
  "published": "2011-09-05T03:11:24.000Z",
  "updated": "2011-11-02T16:48:35.000Z",
  "title": "Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part",
  "authors": [
    "Hidefumi Ohsugi",
    "Kazuki Shibata"
  ],
  "comment": "4 pages, We changed the order of the auhors and omitted a lot of parts of the paper. (If you are interested in omitted parts, then please read v1)",
  "journal": "Discrete and Computational Geometry 47 (2012), 624--628",
  "categories": [
    "math.CO"
  ],
  "abstract": "The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as smooth Fano polytopes. In this paper, we show that if the length of the cycle is 127, then the Ehrhart polynomial has a root whose real part is greater than the dimension. As a result, we have a smooth Fano polytope that is a counterexample to the two conjectures on the roots of Ehrhart polynomials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-02T16:48:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "13P10"
    ],
    "keywords": [
      "smooth fano polytope",
      "ehrhart polynomial",
      "large real part",
      "del pezzo polytopes",
      "symmetric edge polytopes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.0791O"
    }
  }
}