{
  "id": "1911.06690",
  "version": "v1",
  "published": "2019-11-15T15:20:28.000Z",
  "updated": "2019-11-15T15:20:28.000Z",
  "title": "Asymptotics and statistics on Fishburn matrices and their generalizations",
  "authors": [
    "Hsien-Kuei Hwang",
    "Emma Yu Jin"
  ],
  "comment": "54 pages, 20 figures",
  "categories": [
    "math.CO",
    "math.NT",
    "math.PR"
  ],
  "abstract": "A direct saddle-point analysis (without relying on any modular forms, identities or functional equations) is developed to establish the asymptotics of Fishburn matrices and a large number of other variants with a similar sum of-finite-product form for their (formal) general functions. In addition to solving some conjectures, the application of our saddle-point approach to the distributional aspects of statistics on Fishburn matrices is also examined with many new limit theorems characterized, representing the first of their kind for such structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-15T15:20:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "11P82",
      "05A05",
      "05A15",
      "11M50",
      "60C05",
      "60F05"
    ],
    "keywords": [
      "fishburn matrices",
      "asymptotics",
      "statistics",
      "generalizations",
      "similar sum of-finite-product form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}