{
  "id": "2406.05840",
  "version": "v1",
  "published": "2024-06-09T16:01:45.000Z",
  "updated": "2024-06-09T16:01:45.000Z",
  "title": "Almost $t$-intersecting families for vector spaces",
  "authors": [
    "Dehai Liu",
    "Kaishun Wang",
    "Tian Yao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $V$ be a finite dimensional vector space over a finite field. A family $\\mathcal{F}$ consisting of $k$-subspcaes of $V$ is called almost $t$-intersecting if for each $F\\in \\mathcal{F}$ there is at most one $F^{\\prime}\\in \\mathcal{F}$ with $\\dim(F\\cap F^{\\prime})\\leq t-1$. In this paper, we determine the maximum value and the extremal structure of almost $t$-intersecting families. We also solve the same problems for almost $t$-intersecting families but not $t$-intersecting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-09T16:01:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05A30"
    ],
    "keywords": [
      "intersecting families",
      "finite dimensional vector space",
      "finite field",
      "extremal structure",
      "maximum value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}