{
  "id": "0807.0891",
  "version": "v1",
  "published": "2008-07-06T07:44:08.000Z",
  "updated": "2008-07-06T07:44:08.000Z",
  "title": "The Coin Exchange Problem and the Structure of Cube Tilings",
  "authors": [
    "Andrzej P. Kisielewicz",
    "Krzysztof Przesławski"
  ],
  "comment": "3 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Let k_1,...,k_d be positive integers, and D be a subset of [k_1]x...x[k_d], whose complement can be decomposed into disjoint sets of the form {x_1}x...x{x_{s-1}}x[k_s]x{x_{s+1}}x...x{x_d}. We conjecture that the number of elements of D can be represented as a linear combination of the numbers k_1,..., k_d with non-negative integer coefficients. A connexion of this conjecture with the structure of periodical cube tilings is revealed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-06T07:44:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18",
      "52C22",
      "05B45",
      "11H99"
    ],
    "keywords": [
      "coin exchange problem",
      "non-negative integer coefficients",
      "linear combination",
      "disjoint sets",
      "periodical cube tilings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0891K"
    }
  }
}