Hilbert series of algebras associated to direct graphs and order homology
arXiv:1010.6295
Abstract
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of homological properties of the graphs. We use our results to construct algebras with a prescribed Hilbert series.
final version, to appear in "Journal of Pure and Apllied Algebra"