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{\bf Jay Schweig}
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{\bf Convex-Ear Decompositions and the Flag h-Vector}
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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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