@article{bae289a60d5948b7bd9191e4ff0e9c41,
title = "Hilbert series of algebras associated to directed graphs and order homology",
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.",
author = "Vladimir Retakh and Shirlei Serconek and Robert Wilson",
note = "Funding Information: The paper is organized in the following way. In Section 1 we recall basic facts about graphs, posets and their (co)homologies. Section 2 contains the definition of the algebras A(Γ ), A(Γ )! and B(Γ ). Our main theorem on homological description of the coefficients in the Hilbert polynomials for the algebras B(Γ ) and its corollaries are formulated in Section 3. Section 4 is devoted to numerical Koszulity of the algebras A(Γ ) and B(Γ ). Section 5 contains a number of examples including examplesofalgebraswithHilbertseriesequaltoP(−τ)−1whereP(τ)isapalindromicpolynomial.Calabi–Yaualgebrasalso have Hilbert series defined by palindromic polynomials (see [9]). During preparation of this paper Vladimir Retakh and Robert Wilson were supported by an NSA grant.",
year = "2012",
month = jun,
doi = "https://doi.org/10.1016/j.jpaa.2011.10.023",
language = "American English",
volume = "216",
pages = "1397--1409",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "6",
}