{
  "id": "math/0301033",
  "version": "v3",
  "published": "2003-01-05T15:58:10.000Z",
  "updated": "2003-03-02T08:25:56.000Z",
  "title": "A generalization of the Simion-Schmidt bijection for restricted permutations",
  "authors": [
    "Astrid Reifegerste"
  ],
  "comment": "8 pages; added results",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the two permutation statistics which count the distinct pairs obtained from the last two terms of occurrences of patterns t_1...t_{m-2}m(m-1) and t_1...t_{m-2}(m-1)m in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution over the symmetric group. As special case we derive a one-to-one correspondence between permutations which avoid each of the patterns t_1...t_{m-2}m(m-1) in S_m and such ones which avoid each of the patterns t_1...t_{m-2}(m-1)m. For m=3, this correspondence coincides with the bijection given by Simion and Schmidt in their famous paper on restricted permutations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-03-02T08:25:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "restricted permutations",
      "simion-schmidt bijection",
      "generalization",
      "correspondence coincides",
      "distinct pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1033R"
    }
  }
}