{
  "id": "2012.12623",
  "version": "v1",
  "published": "2020-12-23T12:22:29.000Z",
  "updated": "2020-12-23T12:22:29.000Z",
  "title": "Correlations in totally symmetric self-complementary plane partitions",
  "authors": [
    "Arvind Ayyer",
    "Sunil Chhita"
  ],
  "comment": "38 pages, 14 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of a hexagon with free boundary to express them as perfect matchings of a family of non-bipartite planar graphs. Our main result is that the edges of the TSSCPPs form a Pfaffian point process, for which we give explicit formulas for the inverse Kasteleyn matrix. Preliminary analysis of these correlations are then used to give a precise conjecture for the limit shape of TSSCPPs in the scaling limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-23T12:22:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "60K35",
      "05C70",
      "05A17"
    ],
    "keywords": [
      "totally symmetric self-complementary plane partitions",
      "correlations",
      "non-bipartite planar graphs",
      "pfaffian point process",
      "inverse kasteleyn matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}