{
  "id": "2401.09704",
  "version": "v1",
  "published": "2024-01-18T03:25:37.000Z",
  "updated": "2024-01-18T03:25:37.000Z",
  "title": "Mutation invariants of cluster algebras of rank 2",
  "authors": [
    "Zhichao Chen",
    "Zixu Li"
  ],
  "comment": "33 pages",
  "categories": [
    "math.RT",
    "math.CO",
    "math.RA"
  ],
  "abstract": "We consider the mutation invariants of cluster algebras of rank 2. We characterize the mutation invariants of finite type. Two examples are provided for the affine type and we prove the non-existence of Laurent mutation invariants of non-affine type. As an application, a class of Diophantine equations encoded with cluster algebras are studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-18T03:25:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "11D09",
      "11D25"
    ],
    "keywords": [
      "cluster algebras",
      "laurent mutation invariants",
      "non-affine type",
      "diophantine equations",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}