A unifying generalization of Sperner's theorem
| dc.creator | Beck, Matthias | |
| dc.creator | Wang, Xueqin | |
| dc.creator | Zaslavsky, Thomas | |
| dc.date | 2001-12-07 | |
| dc.date.accessioned | 2026-07-07T08:03:08Z | |
| dc.date.available | 2026-07-07T08:03:08Z | |
| dc.description | 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. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112067 | |
| dc.identifier | http://arxiv.org/abs/math/0112067 | |
| dc.identifier | 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 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129470 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D05; 06A07 | |
| dc.title | A unifying generalization of Sperner's theorem | |
| dc.type | text |