Matroid theory describes conic divisorial ideals via polytopes in toric rings from root systems; for signed-poset rings R_P the divisor class group is computed and the Q-Gorenstein property is characterized in terms of P, extending Hibi-ring results.
Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions.Selecta Mathematica, 25(5):78
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Toric rings associated with root systems and conic divisorial ideals via matroid theory
Matroid theory describes conic divisorial ideals via polytopes in toric rings from root systems; for signed-poset rings R_P the divisor class group is computed and the Q-Gorenstein property is characterized in terms of P, extending Hibi-ring results.