{
  "id": "1206.0966",
  "version": "v2",
  "published": "2012-06-05T15:43:49.000Z",
  "updated": "2012-06-10T12:04:45.000Z",
  "title": "Permutations all of whose patterns of a given length are distinct",
  "authors": [
    "Peter Hegarty"
  ],
  "comment": "9 pages, no figures. This is Version 2: A small error at the very end of the proof in Section 2 has been corrected",
  "categories": [
    "math.CO"
  ],
  "abstract": "For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation \\sigma \\in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \\lfloor \\sqrt{2k-3} \\rfloor + e_k, where e_k \\in {-1,0} for every k. Suggestions for further investigations along these lines are discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-10T12:04:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05B40"
    ],
    "keywords": [
      "permutation",
      "suggestions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.0966H"
    }
  }
}