Every d-flag sortable simplicial complex is claimed to be vertex decomposable, and its associated toric and Rees algebras are Koszul, normal Cohen-Macaulay domains.
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Sortable simplicial complexes and their associated toric rings
Every d-flag sortable simplicial complex is claimed to be vertex decomposable, and its associated toric and Rees algebras are Koszul, normal Cohen-Macaulay domains.