2014-07-292012-03-082011-08-31REIS, Bruno Trindade. Hilbert series of algebras associated to directed graphs using cohomology of partially ordered sets. 2011. 53 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2011.http://repositorio.bc.ufg.br/tede/handle/tde/1948We begin with a definition of the algebras Qn, who originated the study of algebra associated to directed graphs. Then, we define key concepts such as Hilbert series, graded and filtered algebras. Among the quadratic algebras, we introduce the Koszul algebras. The Hilbert series is a useful tool to study the Koszulity of a quadratic algebra. The homological interpretation of the coefficients of the Hilbert series of algebras associated with direct graphs allowed us to give conditions Koszulity these algebras in terms of the homological properties of the graph. We use this interpretation to construct algebras with Hilbert series prescribed.application/pdfAcesso AbertoSéries de HilbertGrafos orientadosGrupos de homologiaHilbert seriesDirected graphsOrder homologyMatemática-Álgebra; Série de Hilbert; Grafos orientados; Grupos de homologiaCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRADissertação