{
  "id": "0706.1738",
  "version": "v2",
  "published": "2007-06-12T16:06:58.000Z",
  "updated": "2007-06-22T20:09:33.000Z",
  "title": "Permutations with Extremal number of Fixed Points",
  "authors": [
    "Guo-Niu Han",
    "Guoce Xin"
  ],
  "comment": "minor change about corollary 3",
  "categories": [
    "math.CO"
  ],
  "abstract": "We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting permutations we study their generating polynomials by number of excedances. Several techniques are used: Desarmenien's desarrangement combinatorics, Gessel's hook-factorization and the analytical properties of two new permutation statistics \"DEZ\" and \"lec\". Explicit formulas for the maximal case are derived by using symmetric function tools.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-22T20:09:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05E05"
    ],
    "keywords": [
      "extremal number",
      "fixed points",
      "extend stanleys work",
      "alternating permutations",
      "desarmeniens desarrangement combinatorics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1738H"
    }
  }
}