{
  "id": "1608.03189",
  "version": "v1",
  "published": "2016-08-10T14:38:35.000Z",
  "updated": "2016-08-10T14:38:35.000Z",
  "title": "A generalisation of Sylvester's problem to higher dimensions",
  "authors": [
    "Simeon Ball",
    "Joaquim Monserrat"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "In this article we consider $S$ to be a set of points in $d$-space with the property that any $d$ points of $S$ span a hyperplane and not all the points of $S$ are contained in a hyperplane. The aim of this article is to introduce the function $e_d(n)$, which denotes the minimal number of hyperplanes meeting $S$ in precisely $d$ points, minimising over all such sets of points $S$ with $|S|=n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T14:38:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51M04",
      "52C35"
    ],
    "keywords": [
      "higher dimensions",
      "sylvesters problem",
      "generalisation",
      "hyperplane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}