{
  "id": "1511.05535",
  "version": "v1",
  "published": "2015-11-17T20:19:17.000Z",
  "updated": "2015-11-17T20:19:17.000Z",
  "title": "Solutions to the T-systems with Principal Coefficients",
  "authors": [
    "Panupong Vichitkunakorn"
  ],
  "categories": [
    "math.CO",
    "math.DS"
  ],
  "abstract": "The $A_\\infty$ T-system, also called the octahedron recurrence, is a dynamical recurrence relation. It can be realized as mutation in a coefficient-free cluster algebra (Kedem 2008, Di Francesco and Kedem 2009). We define T-systems with principal coefficients from cluster algebra aspect, and give combinatorial solutions with respect to any valid initial condition in terms of partition functions of perfect matchings, non-intersecting paths and networks. This also provides a solution to other systems with various choices of coefficients on T-systems including Speyer's octahedron recurrence (Speyer 2007), generalized lambda-determinants (Di Francesco 2013) and (higher) pentagram maps (Schwartz 1992, Ovsienko et al. 2010, Glick 2011, Gekhtman et al. 2014).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-17T20:19:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "05C22",
      "82B20"
    ],
    "keywords": [
      "principal coefficients",
      "di francesco",
      "speyers octahedron recurrence",
      "cluster algebra aspect",
      "valid initial condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151105535V"
    }
  }
}