Sperner定理在压缩滤子上的推广研究

Extension Research of Sperner’s Theorem on Compressed Filters

令Bn为[n]={1,2,...,n}的所有子集按包含关系构成的偏序集。Sperner定理说明Bn中最大的Sperner集族的密度为。本文研究Sperner定理在凸集上的推广,并证明Sperner定理在压缩滤子上成立。

Let [n]={1,2,...,n} and Bn={A,A⊆[n]}. Sperner theorem states that the density of the largest Sperner family in Bn is . Our paper focuses on the extension of Sperner theorem on convex family and proves that Sperner theorem is valid on compressed filters.