{
  "id": "0906.0748",
  "version": "v1",
  "published": "2009-06-03T17:57:42.000Z",
  "updated": "2009-06-03T17:57:42.000Z",
  "title": "Positivity for cluster algebras from surfaces",
  "authors": [
    "Gregg Musiker",
    "Ralf Schiffler",
    "Lauren Williams"
  ],
  "comment": "67 pages, 45 figures, comments welcome",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We give combinatorial formulas for the Laurent expansion of any cluster variable in any cluster algebra coming from a triangulated surface (with or without punctures), with respect to an arbitrary seed. Moreover, we work in the generality of principal coefficients. An immediate corollary of our formulas is a proof of the positivity conjecture of Fomin and Zelevinsky for cluster algebras from surfaces, in geometric type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-03T17:57:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S99",
      "05C70",
      "05E15"
    ],
    "keywords": [
      "laurent expansion",
      "combinatorial formulas",
      "principal coefficients",
      "immediate corollary",
      "positivity conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 67,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0748M"
    }
  }
}