Saturating Sperner families
arXiv:1105.4453
Abstract
A family $\cF \subseteq 2^{[n]}$ saturates the monotone decreasing property $\cP$ if $\cF$ satisfies $\cP$ and one cannot add any set to $\cF$ such that property $\cP$ is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the -Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of -sets and -sets.
10 pages