{
  "id": "1505.03067",
  "version": "v1",
  "published": "2015-05-12T15:45:40.000Z",
  "updated": "2015-05-12T15:45:40.000Z",
  "title": "Bilinear equations and $q$-discrete Painlevé equations satisfied by variables and coefficients in cluster algebras",
  "authors": [
    "Naoto Okubo"
  ],
  "comment": "16 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct cluster algebras the variables and coefficients of which satisfy the discrete mKdV equation, the discrete Toda equation and other integrable bilinear equations, several of which lead to q-discrete Painlev\\'e equations. These cluster algebras are obtained from quivers with an infinite number of vertices or with the mutation-period property. We will also show that a suitable transformation of quivers corresponds to a reduction of the difference equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-12T15:45:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A20"
    ],
    "keywords": [
      "coefficients",
      "discrete mkdv equation",
      "discrete toda equation",
      "construct cluster algebras"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/48/35/355201",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2015,
      "month": "Aug",
      "volume": 48,
      "number": 35,
      "pages": 355201
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JPhA...48I5201O"
    }
  }
}