Optimal linear extensions by interchanging chains

Abstract

For a finite ordered set P P how can a linear extension L = C 1 ⊕ C 2 L = {C_1} \oplus {C_2} be constructed which minimizes the number m m of chains C i {C_i} of P P ? While this question remains largely unanswered we show that a natural "greedy" algorithm is actually optimal for a far wider class of ordered sets than was hitherto suspected.