{
  "id": "1504.01642",
  "version": "v1",
  "published": "2015-04-07T15:24:57.000Z",
  "updated": "2015-04-07T15:24:57.000Z",
  "title": "Quantitative $(p,q)$ theorems in combinatorial geometry",
  "authors": [
    "Pablo Soberón"
  ],
  "comment": "18 pages",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "We show quantitative versions of classic results in discrete geometry, where we require in the conclusion to find sets which contain either many points from a given discrete set or to have large volume. We give versions of this kind for the classic first selection lemma of B\\'ar\\'any, the existence of weak epsilon-nets for convex sets and the $(p,q)$ theorem of Alon and Kleitman.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-07T15:24:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial geometry",
      "classic first selection lemma",
      "discrete set",
      "classic results",
      "discrete geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401642R"
    }
  }
}