{
  "id": "1102.2883",
  "version": "v1",
  "published": "2011-02-14T20:45:46.000Z",
  "updated": "2011-02-14T20:45:46.000Z",
  "title": "Contingency tables with uniformly bounded entries",
  "authors": [
    "Austin Shapiro"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We consider nonnegative integer matrices with specified row and column sums and upper bounds on the entries. We show that the logarithm of the number of such matrices is approximated by a concave function of the row and column sums. We give efficiently computable estimators for this function, including one suggested by a maximum-entropy random model; we show that these estimators are asymptotically exact as the dimension of the matrices goes to infinity. We finish by showing that, for kappa >= 2 and for sufficiently small row and column sums, the number of matrices with these row and column sums and with entries <= kappa is greater by an exponential factor than predicted by a heuristic of independence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-14T20:45:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniformly bounded entries",
      "contingency tables",
      "column sums",
      "maximum-entropy random model",
      "sufficiently small row"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.2883S"
    }
  }
}