{
  "id": "1211.5755",
  "version": "v2",
  "published": "2012-11-25T10:48:50.000Z",
  "updated": "2013-06-15T02:19:59.000Z",
  "title": "Integer decomposition property of dilated polytopes",
  "authors": [
    "David A. Cox",
    "Christian Haase",
    "Takayuki Hibi",
    "Akihiro Higashitani"
  ],
  "comment": "16 pages, comments welcome",
  "categories": [
    "math.CO",
    "math.AC",
    "math.AG"
  ],
  "abstract": "Let $\\mathcal{P} \\subset \\mathbb{R}^N$ be an integral convex polytope of dimension $d$ and write $k \\mathcal{P}$, where $k = 1, 2, \\ldots$, for dilations of $\\mathcal{P}$. We say that $\\mathcal{P}$ possesses the integer decomposition property if, for any integer $k = 1, 2, \\ldots$ and for any $\\alpha \\in k \\mathcal{P} \\cap \\mathbb{Z}^N$, there exist $\\alpha_{1}, \\ldots, \\alpha_k$ belonging to $\\mathcal{P} \\cap \\mathbb{Z}^N$ such that $\\alpha = \\alpha_1 + \\cdots + \\alpha_k$. A fundamental question is to determine the integers $k > 0$ for which the dilated polytope $k\\mathcal{P}$ possesses the integer decomposition property. In the present paper, combinatorial invariants related to the integer decomposition property of dilated polytopes will be proposed and studied.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-15T02:19:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "14Q15",
      "14M25"
    ],
    "keywords": [
      "integer decomposition property",
      "dilated polytope",
      "integral convex polytope",
      "fundamental question",
      "combinatorial invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5755C"
    }
  }
}