{
  "id": "1210.6299",
  "version": "v4",
  "published": "2012-10-23T17:23:55.000Z",
  "updated": "2014-01-13T19:33:39.000Z",
  "title": "Diagrammatic description of c-vectors and d-vectors of cluster algebras of finite type",
  "authors": [
    "Tomoki Nakanishi",
    "Salvatore Stella"
  ],
  "comment": "Final version published in the Electronic Journal of Combinatorics, 108 pages, 92 figures",
  "journal": "The Electronic Journal of Combinatorics, Volume 21, Issue 1 (2014), P1.3",
  "categories": [
    "math.RA",
    "math.CO",
    "math.RT"
  ],
  "abstract": "We provide an explicit Dynkin diagrammatic description of the c-vectors and the d-vectors (the denominator vectors) of any cluster algebra of finite type with principal coefficients and any initial exchange matrix. We use the surface realization of cluster algebras for types A_n and D_n, then we apply the folding method to D_{n+1} and A_{2n-1} to obtain types B_n and C_n. Exceptional types are done by direct inspection with the help of a computer algebra software. We also propose a conjecture on the root property of c-vectors for a general cluster algebra.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-01-13T19:33:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60"
    ],
    "keywords": [
      "finite type",
      "explicit dynkin diagrammatic description",
      "computer algebra software",
      "general cluster algebra",
      "initial exchange matrix"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 108,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6299N"
    }
  }
}