{
  "id": "1412.8334",
  "version": "v1",
  "published": "2014-12-29T13:28:42.000Z",
  "updated": "2014-12-29T13:28:42.000Z",
  "title": "Topological recursion for irregular spectral curves",
  "authors": [
    "Norman Do",
    "Paul Norbury"
  ],
  "comment": "28 pages",
  "categories": [
    "math.GT",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We study topological recursion on the irregular spectral curve $xy^2-xy+1=0$, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve $xy^2=1$, which takes the place of the Airy curve $x=y^2$ to describe asymptotic behaviour of enumerative problems associated to irregular spectral curves. In particular, we calculate all one-point invariants of the spectral curve $xy^2=1$ via a new three-term recursion for the number of dessins d'enfant with one face.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-29T13:28:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "05A15",
      "32G15"
    ],
    "keywords": [
      "irregular spectral curve",
      "dessins denfant",
      "study topological recursion",
      "one-point invariants",
      "asymptotic behaviour"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.8334D"
    }
  }
}