On Q-deformations of Postnikov-Shapiro algebras
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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