On two-part Sperner systems for regular posets (Extended Abstract)

In the Boolean lattice the BLYM inequality holds with equality if and only if the Sperner family consists of one complete level of subsets. In this paper we extend this strict BLYM-property to a subclass of normal posets. On the basis of this result we prove a strict two-part Sperner theorem of the direct product of any two posets from the same subclass.