{
  "id": "2010.12969",
  "version": "v1",
  "published": "2020-10-24T19:59:22.000Z",
  "updated": "2020-10-24T19:59:22.000Z",
  "title": "Asymptotic Enumeration of Binary Contingency Tables and Comparison with Independent Heuristic",
  "authors": [
    "Da Wu"
  ],
  "comment": "10 pages, 1 figure. Comments are welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "For parameters $n,\\delta,B,C$, we obtain sharp asymptotic formula for number of $(n+\\lfloor n^\\delta\\rfloor)^2$ dimensional binary contingency tables with non-uniform margins $\\lfloor BCn\\rfloor$ and $\\lfloor Cn\\rfloor$. Furthermore, we compare our results with the classical \\textit{independent heuristic} and prove that the independent heuristic overestimates by a factor of $e^{\\Theta(n^{2\\delta})}$. Our comparison is based on the analysis of the \\textit{correlation ratio} and we obtain the explicit bound for the constant in $\\Theta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-24T19:59:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic enumeration",
      "comparison",
      "dimensional binary contingency tables",
      "sharp asymptotic formula",
      "independent heuristic overestimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}