{
  "id": "2301.13001",
  "version": "v1",
  "published": "2023-01-30T15:44:01.000Z",
  "updated": "2023-01-30T15:44:01.000Z",
  "title": "On the minimum size of linear sets",
  "authors": [
    "Sam Adriaensen",
    "Paolo Santonastaso"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, a lower bound was established on the size of linear sets in projective spaces, that intersect a hyperplane in a canonical subgeometry. There are several constructions showing that this bound is tight. In this paper, we generalize this bound to linear sets meeting some subspace $\\pi$ in a canonical subgeometry. We also give constructions of linear sets attaining equality in this bound, both in the case that $\\pi$ is a hyperplane, and in the case that $\\pi$ is a lower dimensional subspace.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-30T15:44:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "05B25"
    ],
    "keywords": [
      "minimum size",
      "lower dimensional subspace",
      "canonical subgeometry",
      "linear sets attaining equality",
      "hyperplane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}