{
  "id": "1608.03314",
  "version": "v1",
  "published": "2016-08-10T23:57:58.000Z",
  "updated": "2016-08-10T23:57:58.000Z",
  "title": "On symmetric 3-wise intersecting families",
  "authors": [
    "David Ellis",
    "Bhargav Narayanan"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A family of sets is said to be {\\em symmetric} if its automorphism group is transitive, and {\\em $3$-wise intersecting} if any three sets in the family have nonempty intersection. Frankl conjectured in 1981 that if $\\mathcal{A}$ is a symmetric $3$-wise intersecting family of subsets of $\\{1,2,\\ldots,n\\}$, then $|\\mathcal{A}| = o(2^n)$. Here, we give a short proof of Frankl's conjecture, using a `sharp threshold' result of Friedgut and Kalai.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T23:57:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "intersecting family",
      "automorphism group",
      "nonempty intersection",
      "short proof",
      "frankls conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}