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On $Q$-deformations of Postnikov-Shapiro algebras
Published 22 Aug 2017 in math.CO and math.AC | (1708.06815v1)
Abstract: For any given loopless graph $G$, we introduce $Q$ - deformations of its Postnikov-Shapiro algebras counting spanning trees, counting spanning forests and $Q$ - deformations of internal algebra of $G$. We determine the total dimension of the algebras; our proof also gives a new proof of the formula for the total dimensions of the usual Postnikov-Shapiro algebras. Furthermore, we construct "square-free" definition of usual internal algebra of $G$.
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