{
  "id": "2410.20185",
  "version": "v1",
  "published": "2024-10-26T14:01:04.000Z",
  "updated": "2024-10-26T14:01:04.000Z",
  "title": "$s$-almost $t$-intersecting families for sets",
  "authors": [
    "Dehai Liu",
    "Kaishun Wang",
    "Tian Yao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{F}$ be a family of $k$-subsets of an $n$-set. Write $\\mathcal{D}_{\\mathcal{F}}(H;t)=\\left\\{ F\\in\\mathcal{F}: \\left|F\\cap H\\right|<t\\right\\}$ for a set $H$. The family $\\mathcal{F}$ is called $s$-almost $t$-intersecting if $\\left|\\mathcal{D}_{\\mathcal{F}}(F;t)\\right|\\leq s$ for each $F\\in \\mathcal{F}$. In this paper, we prove that $s$-almost $t$-intersecting families with maximum size are $t$-intersecting. We also consider $s$-almost $t$-intersecting families which are not $t$-intersecting, and characterize such families with maximum size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-26T14:01:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "intersecting families",
      "maximum size"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}