{
  "id": "0902.3075",
  "version": "v1",
  "published": "2009-02-18T09:02:33.000Z",
  "updated": "2009-02-18T09:02:33.000Z",
  "title": "On Partitions of Finite vector Spaces",
  "authors": [
    "Antonino Giorgio Spera"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "In this note, we give a new necessary condition for the existence of non-trivial partitions of a finite vector space. Precisely, we prove that, if V is a finite vector space over a field of order q, then the number of the subspaces of minimum dimension t of a non-trivial partition of V is greater than or equal to q+t. Moreover, we give some extensions of a well known Beutelspacher-Heden's result on existence of T-partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-18T09:02:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A03",
      "05B30",
      "20D60"
    ],
    "keywords": [
      "finite vector space",
      "non-trivial partition",
      "minimum dimension",
      "necessary condition",
      "beutelspacher-hedens result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.3075S"
    }
  }
}