{
  "id": "math/0112067",
  "version": "v1",
  "published": "2001-12-07T02:30:09.000Z",
  "updated": "2001-12-07T02:30:09.000Z",
  "title": "A unifying generalization of Sperner's theorem",
  "authors": [
    "Matthias Beck",
    "Xueqin Wang",
    "Thomas Zaslavsky"
  ],
  "comment": "12 pages",
  "journal": "More Sets, Graphs and Numbers: A Salute to Vera Sos and Andras Hajnal (E. Gyari, G. O. H. Katona, and L. Lovasz, eds.) Bolyai Society Mathematical Studies 15, pp. 9-24. Springer, Berlin, and Janos Bolyai Mathematical Society, Budapest, 2006",
  "categories": [
    "math.CO"
  ],
  "abstract": "Sperner's bound on the size of an antichain in the lattice P(S) of subsets of a finite set S has been generalized in three different directions: by Erdos to subsets of P(S) in which chains contain at most r elements; by Meshalkin to certain classes of compositions of S; by Griggs, Stahl, and Trotter through replacing the antichains by certain sets of pairs of disjoint elements of P(S). We unify Erdos's, Meshalkin's, and Griggs-Stahl-Trotter's inequalities with a common generalization. We similarly unify their accompanying LYM inequalities. Our bounds do not in general appear to be the best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-12-07T02:30:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "06A07"
    ],
    "keywords": [
      "sperners theorem",
      "unifying generalization",
      "finite set",
      "general appear",
      "sperners bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12067B"
    }
  }
}