{
  "id": "0708.2643",
  "version": "v1",
  "published": "2007-08-20T18:32:06.000Z",
  "updated": "2007-08-20T18:32:06.000Z",
  "title": "On fixed points of permutations",
  "authors": [
    "Persi Diaconis",
    "Jason Fulman",
    "Robert Guralnick"
  ],
  "comment": "30 pages",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The number of fixed points of a random permutation of 1,2,...,n has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention to primitive actions, a complete classification of the limiting distributions is given. For most examples, they are trivial -- almost every permutation has no fixed points. For the usual action of the symmetric group on k-sets of 1,2,...,n, the limit is a polynomial in independent Poisson variables. This exhausts all cases. We obtain asymptotic estimates in some examples, and give a survey of related results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-20T18:32:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B30",
      "20B35",
      "05A16",
      "60C07"
    ],
    "keywords": [
      "fixed points",
      "symmetric group",
      "independent poisson variables",
      "random permutation",
      "asymptotic estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2643D"
    }
  }
}