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.
Non-commutative crepant resolutions of Hibi rings with small class group.Journal of Pure and Applied Algebra, 223(8):3461–3484, 2019
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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.