{
  "id": "1207.0672",
  "version": "v1",
  "published": "2012-07-03T13:37:01.000Z",
  "updated": "2012-07-03T13:37:01.000Z",
  "title": "Octants are Cover-Decomposable into Many Coverings",
  "authors": [
    "Balázs Keszegh",
    "Dömötör Pálvölgyi"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1101.3773",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an m(k) such that any m(k)-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into k coverings. As a corollary, we obtain that any m(k)-fold covering of any subset of the plane with a finite number of homothetic copies of a given triangle can be decomposed into k coverings. Previously only some weaker bounds were known for related problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-03T13:37:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite number",
      "cover-decomposable",
      "multiple coverings",
      "homothetic copies",
      "weaker bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0672K"
    }
  }
}