{
  "id": "1103.1934",
  "version": "v1",
  "published": "2011-03-10T03:18:07.000Z",
  "updated": "2011-03-10T03:18:07.000Z",
  "title": "2-cancellative hypergraphs and codes",
  "authors": [
    "Zoltán Füredi"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A family of sets F (and the corresponding family of 0-1 vectors) is called t-cancellative if for all distict t+2 members A_1,... A_t and B,C from F the union of A_1,..., A_t and B differs from the union of A_1, ..., A_t and C. Let c(n,t) be the size of the largest t-cancellative family on n elements, and let c_k(n,t) denote the largest k-uniform family. We significantly improve the previous upper bounds, e.g., we show c(n,2)< 2^0.322n (for n> n_0). Using an algebraic construction we show that the order of magnitude of c_{2k}(n,2) is n^k for each k (when n goes to infinity).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-10T03:18:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "11T06",
      "05D40"
    ],
    "keywords": [
      "hypergraphs",
      "algebraic construction",
      "upper bounds",
      "largest k-uniform family"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1934F"
    }
  }
}