Duality for semiantichains and unichain coverings in products of special posets (Q1013994)

A semiantichain in the product \(P\times Q\) of posets \(P\) and \(Q\) is a family in which elements may be incomparable or may be comparable if they differ in both coordinates, and a unichain is a chain that is constant in one coordinate. The main result of the paper is Theorem 2.3 stating that if \(P\) and \(Q\) are posets of width 2, then the maximum size of a semiantichain in \(P\times Q\) equals the minimum size of a unichain covering of \(P\times Q\). There are also some observations about the cases where both factors have height 2 or both factors have dimension 2.