Families that Remain $k$-Sperner Even After Omitting an Element of their Ground Set

[摘要] A family $\mathcal{F}\subseteq 2^{[n]}$ of sets is said to be $l$-trace $k$-Sperner if for any $l$-subset $L \subset [n]$ the family $\mathcal{F}|_L=\{F|_L:F \in \mathcal{F}\}=\{F \cap L: F \in \mathcal{F}\}$ is $k$-Sperner, i.e. does not contain any chai

[学科分类] 离散数学和组合数学

[关键词] extremal set systems;chains;traces