{
  "id": "2407.11826",
  "version": "v1",
  "published": "2024-07-16T15:14:18.000Z",
  "updated": "2024-07-16T15:14:18.000Z",
  "title": "Denominator conjecture for some surface cluster algebras",
  "authors": [
    "Changjian Fu",
    "Shengfei Geng"
  ],
  "comment": "28 pages, comments welcome",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "The denominator conjecture, proposed by Fomin and Zelevinsky, says that for a cluster algebra, the cluster monomials are uniquely determined by their denominator vectors with respect to an initial cluster. In this paper, for a cluster algebra from a marked surface with at least three boundary marked points, we establish this conjecture with respect to a given strong admissible tagged triangulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-16T15:14:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "surface cluster algebras",
      "denominator conjecture",
      "cluster monomials",
      "denominator vectors",
      "initial cluster"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}