{
  "id": "1007.2870",
  "version": "v2",
  "published": "2010-07-16T21:10:56.000Z",
  "updated": "2011-04-07T15:02:54.000Z",
  "title": "The Number System of the Permutations Generated by Cyclic Shift",
  "authors": [
    "Stéphane Legendre"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code describing the symmetry properties of the set of permutations generated by cyclic shift. This code is conjectured to be a combinatorial Gray code listing the set of permutations: this corresponds to an Hamiltonian path of minimal weight in an appropriate regular digraph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-07T15:02:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "cyclic shift",
      "permutations",
      "number system",
      "appropriate regular digraph",
      "minimal weight"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2870L"
    }
  }
}