{
  "id": "1107.4862",
  "version": "v2",
  "published": "2011-07-25T08:05:48.000Z",
  "updated": "2012-10-11T08:27:46.000Z",
  "title": "Ehrhart polynomials of integral simplices with prime volumes",
  "authors": [
    "Akihiro Higashitani"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For an integral convex polytope $\\Pc \\subset \\RR^N$ of dimension $d$, we call $\\delta(\\Pc)=(\\delta_0, \\delta_1,..., \\delta_d)$ the $\\delta$-vector of $\\Pc$ and $\\vol(\\Pc)=\\sum_{i=0}^d\\delta_i$ its normalized volume. In this paper, we will establish the new equalities and inequalities on $\\delta$-vectors for integral simplices whose normalized volumes are prime. Moreover, by using those, we will classify all the possible $\\delta$-vectors of integral simplices with normalized volume 5 and 7.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-11T08:27:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "52B12"
    ],
    "keywords": [
      "integral simplices",
      "prime volumes",
      "ehrhart polynomials",
      "normalized volume",
      "integral convex polytope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.4862H"
    }
  }
}