{
  "id": "2103.11117",
  "version": "v1",
  "published": "2021-03-20T07:02:50.000Z",
  "updated": "2021-03-20T07:02:50.000Z",
  "title": "Non-trivial $t$-intersecting families for the distance-regular graphs of bilinear forms",
  "authors": [
    "Mengyu Cao",
    "Benjian Lv",
    "Kaishun Wang"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $V$ be an $(n+\\ell)$-dimensional vector space over a finite field, and $W$ a fixed $\\ell$-dimensional subspace of $V$. Write ${V\\brack n,0}$ to be the set of all $n$-dimensional subspaces $U$ of $V$ satisfying $\\dim(U\\cap W)=0$. A family $\\mathcal{F}\\subseteq{V\\brack n,0}$ is $t$-intersecting if $\\dim(A\\cap B)\\geq t$ for all $A,B\\in\\mathcal{F}$. A $t$-intersecting family $\\mathcal{F}\\subseteq{V\\brack n,0}$ is called non-trivial if $\\dim(\\cap_{F\\in\\mathcal{F}}F)<t$. In this paper, we describe the structure of non-trivial $t$-intersecting families of ${V\\brack n,0}$ with large size. In particular, we show the structure of the non-trivial $t$-intersecting families with maximum size, which extends the Hilton-Milner Theorem for ${V\\brack n,0}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-20T07:02:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05A30"
    ],
    "keywords": [
      "intersecting family",
      "distance-regular graphs",
      "bilinear forms",
      "non-trivial",
      "dimensional subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}