Graded gorenstein artin algebras whose hilbert functions have a large number of valleys

Abstract

In [4] Stanley showed that the Hilbert function of graded Goren-stein Artin algebras need not be unimodal. In this article we prove the exis¬tence of graded Gorenstein Artin algebras whose Hilbert functions have local maxima at any given set of points with the symmetry and the socle degree as the only restrictions.