Abstract
Several important simplicial complexes including matroid complexes and broken circuit complexes are known to be shellable. We show that the lexicographic order of the bases of a matroid can be reversed to obtain a shelling. We prove that the h-vectors of such reversibly shellable complexes of rank d, which have an empty boundary must satisfy the inequality h o + h 1 … + h i ⩽ h d + h d−1 + … + h d− i for i⩽[ d/2]. In particular, this gives a necessary condition for the h-vector of matroids without coloops.
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