{
  "id": "2412.08659",
  "version": "v1",
  "published": "2024-12-01T12:14:42.000Z",
  "updated": "2024-12-01T12:14:42.000Z",
  "title": "$s$-almost $t$-intersecting families for vector spaces",
  "authors": [
    "Shuhui Yu",
    "Lijun Ji"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{F}$ be a family of $k$-dimensional subspaces of an $n$-dimensional vector space. Write $\\mathcal{D}_{\\mathcal{F}}(H;t)=\\{F\\in \\mathcal{F}\\colon \\dim(F\\cap H)\\leq t \\}$ for a subspace $H$. The family $\\mathcal{F}$ is called $s$-almost $t$-intersecting if $|\\mathcal{D}_{\\mathcal{F}}(F;t)|\\leq s$ for each $F\\in \\mathcal{F}$. In this note, we prove that $s$-almost $t$-intersecting families with maximum size are $t$-intersecting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-01T12:14:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intersecting families",
      "dimensional vector space",
      "dimensional subspaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}