{
  "id": "1312.1141",
  "version": "v2",
  "published": "2013-12-04T12:39:19.000Z",
  "updated": "2014-03-27T08:12:43.000Z",
  "title": "On the number of coverings of the sphere ramified over given points",
  "authors": [
    "Boris Bychkov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present the generating function for the numbers of isomorphism classes of coverings of the two-dimensional sphere by the genus $g$ compact oriented surface not ramified outside of a given set of $m+1$ points in the target, fixed ramification type over one point, and arbitrary ramification types over the remaining $m$ points. We present the genus expansion of this generating function and prove, that the generating function of coverings of genus $0$ satisfies some system of differential equations. We show that this generating function is a specialization of the function from paper \\cite{GJ} and, therefore, satisfies the KP-hierarchy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-27T08:12:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generating function",
      "arbitrary ramification types",
      "fixed ramification type",
      "two-dimensional sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1141B"
    }
  }
}