{
  "id": "1101.1488",
  "version": "v1",
  "published": "2011-01-07T18:06:26.000Z",
  "updated": "2011-01-07T18:06:26.000Z",
  "title": "Lines induced by bichromatic point sets",
  "authors": [
    "Louis Theran"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An important theorem of Beck says that any point set in the Euclidean plane is either ``nearly general position'' or ``nearly collinear'': there is a constant C>0 such that, given n points in the plane with at most r$ of them collinear, the number of lines induced by the points is at least Cr(n-r). Recent work of Gutkin-Rams on billiards orbits requires the following elaboration of Beck's Theorem to bichromatic point sets: there is a constant C>0 such that, given n red points and n blue points in the plane with at most r of them collinear, the number of lines spanning at least one point of each color is at least Cr(2n-r).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-07T18:06:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bichromatic point sets",
      "beck says",
      "becks theorem",
      "general position"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1488T"
    }
  }
}