{
  "id": "2012.13570",
  "version": "v1",
  "published": "2020-12-25T13:20:21.000Z",
  "updated": "2020-12-25T13:20:21.000Z",
  "title": "Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow",
  "authors": [
    "Hsien-Kuei Hwang",
    "Emma Yu Jin",
    "Michael J. Schlosser"
  ],
  "comment": "35 pages, comments are welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "We establish the asymptotic normality of the dimension of large-size random Fishburn matrices by a complex-analytic approach. The corresponding dual problem of size distribution under large dimension is also addressed and follows a quadratic type normal limit law. These results represent the first of their kind and solve two open questions raised in the combinatorial literature. They are presented in a general framework where the entries of the Fishburn matrices are not limited to binary or nonnegative integers. The analytic saddle-point approach we apply, based on a powerful transformation for $q$-series due to Andrews and Jel\\'inek, is also useful in solving a conjecture of Stoimenow in Vassiliev invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-25T13:20:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05A15",
      "60C05",
      "60F05"
    ],
    "keywords": [
      "dimension distribution",
      "asymptotic",
      "quadratic type normal limit law",
      "conjecture",
      "statistics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}