{
  "id": "math/0407373",
  "version": "v1",
  "published": "2004-07-22T07:29:45.000Z",
  "updated": "2004-07-22T07:29:45.000Z",
  "title": "Largest family without A union B contained in C intersect D",
  "authors": [
    "Annalisa De Bonis",
    "Gyula O. H. Katona",
    "Konrad J. Swanepoel"
  ],
  "comment": "6 pages",
  "journal": "J. Combin. Theory Ser. A 111 (2005), no. 2, 331--336",
  "doi": "10.1016/j.jcta.2005.01.002",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let F be a family of subsets of an n-element set not containing four distinct members such that A union B is contained in C intersect D. It is proved that the maximum size of F under this condition is equal to the sum of the two largest binomial coefficients of order n. The maximum families are also characterized. A LYM-type inequality for such families is given, too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-22T07:29:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "largest family",
      "largest binomial coefficients",
      "maximum families",
      "n-element set",
      "distinct members"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7373D"
    }
  }
}