{
  "id": "2208.14773",
  "version": "v1",
  "published": "2022-08-31T11:16:17.000Z",
  "updated": "2022-08-31T11:16:17.000Z",
  "title": "Blocking subspaces with points and hyperplanes",
  "authors": [
    "Sam Adriaensen",
    "Maarten De Boeck",
    "Lins Denaux"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we characterise the smallest sets $B$ consisting of points and hyperplanes in $\\text{PG}(n,q)$, such that each $k$-space is incident with at least one element of $B$. If $k > \\frac {n-1} 2$, then the smallest construction consists only of points. Dually, if $k < \\frac{n-1}2$, the smallest example consists only of hyperplanes. However, if $k = \\frac{n-1}2$, then there exist sets containing both points and hyperplanes, which are smaller than any blocking set containing only points or only hyperplanes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T11:16:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B25",
      "51E21"
    ],
    "keywords": [
      "hyperplanes",
      "blocking subspaces",
      "smallest example consists",
      "smallest construction consists",
      "smallest sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}