{
  "id": "0710.5611",
  "version": "v1",
  "published": "2007-10-30T11:22:53.000Z",
  "updated": "2007-10-30T11:22:53.000Z",
  "title": "Universal cycles for permutations",
  "authors": [
    "J. Robert Johnson"
  ],
  "comment": "14 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers are used. This is best possible and proves a conjecture of Chung, Diaconis and Graham.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-30T11:22:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A99"
    ],
    "keywords": [
      "universal cycle",
      "permutations",
      "distinct integers occurs",
      "cyclic interval",
      "relative orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.5611J"
    }
  }
}