On Saturated $k$-Sperner Systems

[摘要] Given a set $X$, a collection $\mathcal{F}\subseteq\mathcal{P}(X)$ is said to be $k$-Sperner if it does not contain a chain of length $k+1$ under set inclusion and it is saturated if it is maximal with respect to this property. Gerbner et al. conjectured

[学科分类] 离散数学和组合数学

[关键词] Minimum saturation;Set Systems;Sperner Systems