Convex-ear decompositions and the flag \(h\)-vector (Q625362)

Summary: We prove a theorem allowing us to find convex-ear decompositions for rankselected 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.