{
  "id": "1205.5215",
  "version": "v3",
  "published": "2012-05-23T16:00:03.000Z",
  "updated": "2014-03-17T08:59:13.000Z",
  "title": "A simple formula for the series of constellations and quasi-constellations with boundaries",
  "authors": [
    "Gwendal Collet",
    "Eric Fusy"
  ],
  "comment": "23 pages, full paper version of v1, with results extended to constellations and quasi constellations",
  "categories": [
    "math.CO"
  ],
  "abstract": "We obtain a very simple formula for the generating function of bipartite (resp. quasi-bipartite) planar maps with boundaries (holes) of prescribed lengths, which generalizes certain expressions obtained by Eynard in a book to appear. The formula is derived from a bijection due to Bouttier, Di Francesco and Guitter combined with a process (reminiscent of a construction of Pitman) of aggregating connected components of a forest into a single tree. The formula naturally extends to $p$-constellations and quasi-$p$-constellations with boundaries (the case $p=2$ corresponding to bipartite maps).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-17T08:59:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple formula",
      "boundaries",
      "quasi-constellations",
      "single tree",
      "di francesco"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5215C"
    }
  }
}