Wei duality, Fomin-Greene duality and demimatroids

Abstract

The Fomin-Greene Duality Theorem for finite posets and Wei's Duality Theorem for demimatroids each relate sets of extremal invariants via seemingly similar dualities. This paper describes precisely how these two dualities relate. It is shown that the chain and antichain numbers each satisfy a Wei-type duality with antichain- and chain-deletion numbers, respectively, and that, for each poset with at least two elements, its chain and antichain demimatroids are not related by any composition of standard demimatroid duality operations. Their upper Wei-number numbers do however determine each other via Fomin-Greene duality. The two dualities thereby coincide for Wei numbers but not for the underlying rank functions.