{
  "id": "1506.00467",
  "version": "v1",
  "published": "2015-06-01T12:16:06.000Z",
  "updated": "2015-06-01T12:16:06.000Z",
  "title": "Negative coefficients of Ehrhart polynomials",
  "authors": [
    "Takayuki Hibi",
    "Akihiro Higashitani",
    "Akiyoshi Tsuchiya"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is shown that, for each $d \\geq 3$ and $1 \\leq k \\leq d-2$, there exists an integral convex polytope $\\mathcal{P}$ of dimension $d$ such that the coefficient of $n$ of the Ehrhart polynomial $i(\\mathcal{P},n)$ of $\\mathcal{P}$ is negative and its remaining coefficients are all positive. Moreover, it is also shown that for a given integer $3 \\leq d \\leq 6$ and integers $i_1,\\ldots,i_q$ with $1 \\leq i_1 < \\cdots < i_q \\leq d-2$, there exists an integral convex polytope of dimension $d$ whose Ehrhart polynomial satisfies that all the coefficients of $n^{i_1}, \\ldots, n^{i_q}$ are negative and all the remaining coefficients are positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-01T12:16:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "52B11"
    ],
    "keywords": [
      "negative coefficients",
      "integral convex polytope",
      "remaining coefficients",
      "ehrhart polynomial satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150600467H"
    }
  }
}