Istvan Heckenberger, Volkmar Welker
Published 2011-09-09Version 1
A deformation of the Orlik-Solomon algebra of a matroid M is defined as a quotient of the free associative algebra over a commutative ring R with 1. It is shown that the given generators form a Groebner basis and that after suitable homogenization the deformation and the Orlik-Solomon have the same Hilbert series as R-algebras. For supersolvable matroids, equivalently fiber type arrangements, there is a quadratic Groebner basis and hence the algebra is Koszul
Homological properties of Orlik-Solomon algebras
$(q,t)$-deformations of multivariate hook product formulae
Hilbert series in the category of trees with contractions
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