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TitleGraphs of relations and Hilbert series
Author(s) Natalia Iyudu, Chris Peterson
TypeArticle in Journal
AbstractWe are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n−1)/2 relations for n ⩽ 7 . Then we investigate combinatorial structure of colored graph associated with relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated with each color are pairwise 2-isomorphic.
KeywordsQuadratic algebras, Hilbert series, Gröbner basis, Colored graph
URL http://www.sciencedirect.com/science/article/pii/S0747717107001058
JournalJournal of Symbolic Computation
Pages1066 - 1078
NoteNon-commutative Gröbner bases and applications
Translation No
Refereed No