{
  "id": "1108.4398",
  "version": "v3",
  "published": "2011-08-22T19:13:56.000Z",
  "updated": "2011-08-25T22:54:24.000Z",
  "title": "VC density and dp rank",
  "authors": [
    "Hunter Johnson"
  ],
  "comment": "Error in Theorem 4.2",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "We derive that dpR(n) \\leq dens(n) \\leq dpR(n)+1, where dens(n) is the supremum of the VC density of all formulas in n parameters, and dpR(n) is the maximum depth of an ICT pattern in n variables. Consequently, strong dependence is equivalent to finite VC density.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-08-25T22:54:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12L12",
      "03C45",
      "03C98"
    ],
    "keywords": [
      "dp rank",
      "finite vc density",
      "maximum depth",
      "strong dependence",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4398J"
    }
  }
}