{
  "id": "1503.05739",
  "version": "v1",
  "published": "2015-03-19T12:32:53.000Z",
  "updated": "2015-03-19T12:32:53.000Z",
  "title": "Ehrhart polynomial roots of reflexive polytopes",
  "authors": [
    "Gábor Hegedüs",
    "Akihiro Higashitani",
    "Alexander Kasprzyk"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Recent work has focused on the roots z of the Ehrhart polynomial of a lattice polytope P. The case when Re(z) = -1/2 is of particular interest: these polytopes satisfy Golyshev's \"canonical line hypothesis\". We characterise such polytopes when dim(P) <= 7. We also consider the \"half-strip condition\", where all roots z satisfy -dim(P)/2 <= Re(z) <= dim(P)/2-1, and show that this holds for any reflexive polytope with dim(P) <= 5. We give an example of a 10-dimensional reflexive polytope which violates the half-strip condition, thus improving on an example by Ohsugi--Shibata in dimension 34.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-19T12:32:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "05A15",
      "14M25"
    ],
    "keywords": [
      "ehrhart polynomial roots",
      "reflexive polytope",
      "half-strip condition",
      "polytopes satisfy golyshevs",
      "canonical line hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}