g-elements of matroid complexes

Details g-elements of matroid complexes g-elements of matroid complexes

2002-10-24

arxiv.org/abs/math/0210376v1

Mathematics

Combinatorics

6 pages. Will appear in J. Comb. Theory Ser. B

Scientific paper

Let K be the face ring of the independence complex of a matroid. We show that
if T is a generic linear system of parameters, then K/T satisfies a weak form
of the Hard Lefschetz Theorem. As a result, the first half of the h-vector of
the complex satisfies inequalities similar to the g-theorem for simplicial
polytopes.

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