  One of the central issues in extremal set theory is Sperner's theorem and its
generalizations. Among such generalizations is the best-known BLYM inequality
and the Ahlswede--Zhang (AZ) identity which surprisingly generalizes the BLYM
inequality into an identity. Sperner's theorem and the BLYM inequality has been
also generalized to a wide class of posets. Another direction in this research
was the study of more part Sperner systems. In this paper we derive AZ type
identities for regular posets. We also characterize all maximum 2-part Sperner
systems for a wide class of product posets.
