{
  "id": "1302.3081",
  "version": "v2",
  "published": "2013-02-13T13:33:12.000Z",
  "updated": "2013-06-02T19:10:02.000Z",
  "title": "Distinct distances on two lines",
  "authors": [
    "Micha Sharir",
    "Adam Sheffer",
    "József Solymosi"
  ],
  "categories": [
    "math.CO",
    "cs.CG"
  ],
  "abstract": "Let P_1 and P_2 be two sets of points in the plane, so that P_1 is contained in a line L_1, P_2 is contained in a line L_2, and L_1 and L_2 are neither parallel nor orthogonal. Then the number of distinct distances determined by the pairs of P_1xP_2 is \\Omega(\\min{|P_1|^{2/3}|P_2|^{2/3},|P_1|^2, |P_2|^2}). In particular, if |P_1|=|P_2|=m, then the number of these distinct distances is \\Omega(m^{4/3}), improving upon the previous bound \\Omega(m^{5/4}) of Elekes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-02T19:10:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orthogonal",
      "distinct distances"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3081S"
    }
  }
}