{
  "id": "1612.02884",
  "version": "v1",
  "published": "2016-12-09T01:27:55.000Z",
  "updated": "2016-12-09T01:27:55.000Z",
  "title": "W-Operator and Differential Equation for 3-Hurwitz Number",
  "authors": [
    "Hao Sun"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider a new type of Hurwitz number, the number of ordered transitive factorizations of an arbitrary permutation into d-cycles. In this paper, we focus on the special case d = 3. The minimal number of transitive factorizations of any permutation into 3-cycles has been worked out by David, Goulden and Jackson. Also, such factorizations for transpositions, the case d = 2, have been considered by Crescimanno and Taylor. Goulden and Jackson have proved the differential equation for the generating series of simple Hurwitz numbers. Based on their results, we use W-operator to prove a differential equation for the generating function of the new type Hurwitz number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-09T01:27:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential equation",
      "w-operator",
      "type hurwitz number",
      "simple hurwitz numbers",
      "arbitrary permutation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}