{
  "id": "1908.06390",
  "version": "v1",
  "published": "2019-08-18T07:51:13.000Z",
  "updated": "2019-08-18T07:51:13.000Z",
  "title": "On sets of $n$ points in general position that determine lines that can be pierced by $n$ points",
  "authors": [
    "Chaya Keller",
    "Rom Pinchasi"
  ],
  "comment": "9 pages, 5 figures",
  "categories": [
    "math.CO",
    "cs.CG"
  ],
  "abstract": "Let $P$ be a set of $n$ points in general position in the plane. Let $R$ be a set of $n$ points disjoint from $P$ such that for every $x,y \\in P$ the line through $x$ and $y$ contains a point in $R$ outside of the segment delimited by $x$ and $y$. We show that $P \\cup R$ must be contained in a cubic curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-18T07:51:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "68R10"
    ],
    "keywords": [
      "general position",
      "determine lines",
      "points disjoint",
      "cubic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}