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g-elements of matroid complexes

Edward Swartz
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Abstract

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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Edward Swartz. 2002-10-24. g-elements of matroid complexes. https://arxiv.org/abs/math/0210376

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