{
  "id": "1010.5206",
  "version": "v1",
  "published": "2010-10-25T17:48:36.000Z",
  "updated": "2010-10-25T17:48:36.000Z",
  "title": "Set systems without a 3-simplex",
  "authors": [
    "Michael E. Picollelli"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A 3-simplex is a collection of four sets A_1,...,A_4 with empty intersection such that any three of them have nonempty intersection. We show that the maximum size of a set system on n elements without a 3-simplex is $2^{n-1} + \\binom{n-1}{0} + \\binom{n-1}{1} + \\binom{n-1}{2}$ for all $n \\ge 1$, with equality only achieved by the family of sets either containing a given element or of size at most 2. This extends a result of Keevash and Mubayi, who showed the conclusion for n sufficiently large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-25T17:48:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "set system",
      "nonempty intersection",
      "collection",
      "conclusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5206P"
    }
  }
}