{
  "id": "1610.05620",
  "version": "v1",
  "published": "2016-10-18T13:57:39.000Z",
  "updated": "2016-10-18T13:57:39.000Z",
  "title": "Collinear triples and quadruples for Cartesian products in $\\mathbb{F}_p^2$",
  "authors": [
    "Giorgis Petridis"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We combine a recent point-line incidence bound of Stevens and de Zeeuw with an older lemma of Bourgain, Katz and Tao to bound the number of collinear triples and quadruples in a Cartesian product in $\\mathbb{F}_p^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-18T13:57:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartesian product",
      "collinear triples",
      "quadruples",
      "point-line incidence bound",
      "older lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}