  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 n(n-1)/2
relations for n less or equal then 7. Then we investigate combinatorial
structure of colored graph associated to 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 to each color are pairwise 2-isomorphic.
