Convex-Ear Decompositions and the Flag h-Vector

Jay Schweig

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.


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