We study a min-max relation conjectured by Saks and West: For any two posets
P and Q the size of a maximum semiantichain and the size of a minimum
unichain covering in the product P×Q are equal. For positive we state
conditions on P and Q that imply the min-max relation. Based on these
conditions we identify some new families of posets where the conjecture holds
and get easy proofs for several instances where the conjecture had been
verified before. However, we also have examples showing that in general the
min-max relation is false, i.e., we disprove the Saks-West conjecture.Comment: 10 pages, 3 figure