{
  "id": "1811.02455",
  "version": "v1",
  "published": "2018-11-06T16:07:55.000Z",
  "updated": "2018-11-06T16:07:55.000Z",
  "title": "On the Number of Order Types in Integer Grids of Small Size",
  "authors": [
    "Luis E. Caraballo",
    "José-Miguel Díaz-Báñez",
    "Ruy Fabila-Monroy",
    "Carlos Hidalgo-Toscano",
    "Jesús Leaños",
    "Amanda Montejano"
  ],
  "categories": [
    "cs.CG",
    "math.CO"
  ],
  "abstract": "Let $\\{p_1,\\dots,p_n\\}$ and $\\{q_1,\\dots,q_n\\}$ be two sets of $n$ labeled points in general position in the plane. We say that these two point sets have the same order type if for every triple of indices $(i,j,k)$, $p_k$ is above the directed line from $p_i$ to $p_j$ if and only if $q_k$ is above the directed line from $q_i$ to $q_j$. In this paper we give the first non-trivial lower bounds on the number of different order types of $n$ points that can be realized in integer grids of polynomial",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-06T16:07:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "order type",
      "integer grids",
      "small size",
      "first non-trivial lower bounds",
      "directed line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}