Matroid theory describes the polytopes of conic divisorial ideals for toric rings of signed posets, enabling computation of their divisor class groups and characterization of the Q-Gorenstein property in terms of the poset.
Divisorial linear algebra of normal semigroup rings.Algebras and Representation Theory, 6(2):139–168, 2003
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Toric rings of signed posets and conic divisorial ideals via matroid theory
Matroid theory describes the polytopes of conic divisorial ideals for toric rings of signed posets, enabling computation of their divisor class groups and characterization of the Q-Gorenstein property in terms of the poset.