A unifying generalization of Sperner's theorem
组合数学
2007-05-25 v1
摘要
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.
引用
@article{arxiv.math/0112067,
title = {A unifying generalization of Sperner's theorem},
author = {Matthias Beck and Xueqin Wang and Thomas Zaslavsky},
journal= {arXiv preprint arXiv:math/0112067},
year = {2007}
}
备注
12 pages