{
  "id": "2410.14554",
  "version": "v1",
  "published": "2024-10-18T15:56:05.000Z",
  "updated": "2024-10-18T15:56:05.000Z",
  "title": "A determinantal formula for cluster variables in cluster algebras from surfaces",
  "authors": [
    "Javier De Loera"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weighted biadjacency matrix of the associated snake graphs, thus circumventing the enumeration of their perfect matchings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-18T15:56:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "05C70",
      "05C22"
    ],
    "keywords": [
      "cluster variables",
      "cluster algebras",
      "perfect matchings",
      "simple determinantal formula",
      "weighted biadjacency matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}