A unifying generalization of Sperner's theorem

dc.creatorBeck, Matthias
dc.creatorWang, Xueqin
dc.creatorZaslavsky, Thomas
dc.date2001-12-07
dc.date.accessioned2026-07-07T08:03:08Z
dc.date.available2026-07-07T08:03:08Z
dc.descriptionSperner'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.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0112067
dc.identifierhttp://arxiv.org/abs/math/0112067
dc.identifierMore 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
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129470
dc.subjectCombinatorics
dc.subject05D05; 06A07
dc.titleA unifying generalization of Sperner's theorem
dc.typetext

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