{
  "id": "2007.11767",
  "version": "v1",
  "published": "2020-07-23T03:14:30.000Z",
  "updated": "2020-07-23T03:14:30.000Z",
  "title": "Non-trivial $t$-intersecting families for vector spaces",
  "authors": [
    "Mengyu Cao",
    "Benjian Lv",
    "Kaishun Wang",
    "Sanming Zhou"
  ],
  "comment": "26 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $V$ be an $n$-dimensional vector space over a finite field $\\mathbb{F}_q$. In this paper we describe the structure of maximal non-trivial $t$-intersecting families of $k$-dimensional subspaces of $V$ with large size. We also determine the non-trivial $t$-intersecting families with maximum size. In the special case when $t=1$ our result gives rise to the well-known Hilton-Milner Theorem for vector spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-23T03:14:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05A30"
    ],
    "keywords": [
      "intersecting families",
      "dimensional vector space",
      "well-known hilton-milner theorem",
      "finite field",
      "maximal non-trivial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}