{
  "id": "1611.04700",
  "version": "v1",
  "published": "2016-11-15T04:10:34.000Z",
  "updated": "2016-11-15T04:10:34.000Z",
  "title": "W-Operator and Hurwitz Number",
  "authors": [
    "Hao Sun"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "W-operators are differential operators on the polynomial ring. Mironov, Morosov and Natanzon construct the generalized Hurwitz numbers. They use the W-operator to prove a formula for the generating function of the generalized Hurwitz numbers. A special example of W-operators is the cut-and-join operator. Goulden and Jackson use the cut-and-join operator to calculate the simple Hurwitz number. In this paper, we study the relation between W-operator W([d]) and the central elements in CS_n. We also give another proof for the formula proved by Mironov et al..",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-15T04:10:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "w-operator",
      "generalized hurwitz numbers",
      "cut-and-join operator",
      "simple hurwitz number",
      "natanzon construct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}