{
  "id": "0901.2008",
  "version": "v1",
  "published": "2009-01-14T13:53:27.000Z",
  "updated": "2009-01-14T13:53:27.000Z",
  "title": "Two Enumerative Results on Cycles of Permutations",
  "authors": [
    "Richard P. Stanley"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Answering a question of Bona, it is shown that for n>1 the probability that 1 and 2 are in the same cycle of a product of two n-cycles on the set {1,2,...,n} is 1/2 if n is odd and 1/2 - 2/(n-1){n+2) if n is even. Another result concerns the generating function P_h(q) for the number of cycles of the product (1,2,...,n)w, where w ranges over all permutations of 1,2,...,n of cycle type h. A formula is obtained for P_h(q) from which it is proved that the zeros of P_h(q) have real part 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-14T13:53:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05E05"
    ],
    "keywords": [
      "enumerative results",
      "permutations",
      "result concerns",
      "real part",
      "cycle type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}