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

AZ-identities and Strict 2-part Sperner Properties of Product Posets