A CONVEX-EAR DECOMPOSITION FOR RANK-SELECTED SUBPOSETS OF SUPERSOLVABLE LATTICES.

Let L be a supersolvable lattice with nonzero Möbius function. We show that the order complex of any rank-selected subposet of L admits a convex-ear decomposition. This proves many new inequalities for the h-vectors of such complexes, and shows that their g-vectors are Mvectors. [ABSTRACT FROM AUTHOR]