Convex-ear decompositions and the flag h-vector

Abstract

We prove a theorem allowing us to find convex-ear decompositions for rank- selected subposets of posets that are unions of Boolean sublattices in a coherent fashion. We then apply this theorem to geometric lattices and face posets of shellable complexes, obtaining new inequalities for their h-vectors. Finally, we use the latter decomposition to give a new interpretation to inequalities satisfied by the flag h-vectors of face posets of Cohen-Macaulay complexes.