{
  "id": "1702.02607",
  "version": "v1",
  "published": "2017-02-08T20:50:42.000Z",
  "updated": "2017-02-08T20:50:42.000Z",
  "title": "On symmetric intersecting families",
  "authors": [
    "David Ellis",
    "Gil Kalai",
    "Bhargav Narayanan"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A family of sets is said to be {\\em symmetric} if its automorphism group is transitive, and {\\em intersecting} if any two sets in the family have nonempty intersection. Our purpose here is to study the following question: for $n, k\\in \\mathbb{N}$ with $k \\leq n/2$, how large can a symmetric intersecting family of $k$-element subsets of $\\{1,2,\\ldots,n\\}$ be? As a first step towards a complete answer, we prove that such a family has size at most \\[\\exp\\left(-\\frac{c(n-2k)\\log n}{k( \\log n - \\log k)} \\right) \\binom{n}{k},\\] where $c > 0$ is a universal constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-08T20:50:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "symmetric intersecting family",
      "nonempty intersection",
      "automorphism group",
      "element subsets",
      "first step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}