{
  "id": "0911.4462",
  "version": "v1",
  "published": "2009-11-23T18:16:27.000Z",
  "updated": "2009-11-23T18:16:27.000Z",
  "title": "Quantum F-polynomials in Classical Types",
  "authors": [
    "Thao Tran"
  ],
  "comment": "40 pages",
  "categories": [
    "math.RA",
    "math.CO"
  ],
  "abstract": "In their \"Cluster Algebras IV\" paper, Fomin and Zelevinsky defined F-polynomials and g-vectors, and they showed that the cluster variables in any cluster algebra can be expressed in a formula involving the appropriate F-polynomial and g-vector. In \"F-polynomials in Quantum Cluster Algebras,\" the predecessor to this paper, we defined and proved the existence of quantum F-polynomials, which are analogs of F-polynomials in quantum cluster algebras in the sense that cluster variables in any quantum cluster algebra can be expressed in a similar formula in terms of quantum F-polynomials and g-vectors. In this paper, we give formulas for both F-polynomials and quantum F-polynomials for cluster algebras of classical type when the initial exchange matrix is acyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-23T18:16:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S99",
      "05E15",
      "20G42"
    ],
    "keywords": [
      "quantum f-polynomials",
      "classical type",
      "quantum cluster algebra",
      "cluster variables",
      "initial exchange matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4462T"
    }
  }
}