Graphs of relations and Hilbert series

Peter Cameron, Natalia Iyudu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We 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 frac(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.

Original languageEnglish
Pages (from-to)1066-1078
Number of pages13
JournalJournal of Symbolic Computation
Issue number11-12
Publication statusPublished - 1 Nov 2007


  • Colored graph
  • Gröbner basis
  • Hilbert series
  • Quadratic algebras


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