{
  "id": "1203.1307",
  "version": "v4",
  "published": "2012-03-06T20:24:43.000Z",
  "updated": "2013-03-04T16:08:30.000Z",
  "title": "Linear independence of cluster monomials for skew-symmetric cluster algebras",
  "authors": [
    "Giovanni Cerulli Irelli",
    "Bernhard Keller",
    "Daniel Labardini-Fragoso",
    "Pierre-Guy Plamondon"
  ],
  "comment": "14 pages. v2: Bibliography expanded. v3: Added results 3.7, 3.8, 4.7, 4.8 and 5.6. v4: Added reference and minor changes",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choice of coefficients. We confirm these conjectures for all skew-symmetric cluster algebras.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-03-04T16:08:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "18E30"
    ],
    "keywords": [
      "skew-symmetric cluster algebras",
      "cluster monomials",
      "linear independence",
      "cluster complex",
      "exchange graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.1307C"
    }
  }
}