Correlation in Partially Ordered Sets.
22 October 1992
Correlation in partially ordered sets is a very active research area. In this paper we review basic results for correlation within posets that focus on distributive lattices, systems of subsets ordered by proper inclusion, and the family of linear extensions of an arbitrary finite poset. Included are the Ahlswede-Daykin theorem, the FKG theorem, the nonstrict and strict xyz inequalities, and the universal correlation theorems of Winkler and Brightwell. We also mention several corollaries and applications, and note some open problems. Proofs of many of the theorems are included.