LAUSR

Abstract The first example of a non unimodal Gorenstein h-vector was given by Stanley, it is ( 1 , 13 , 12 , 13 , 1 ) . In [14] the authors showed that Stanley's example is optimal, i.e., the vector ( 1 , 12 , 11 , 12 , 1 ) is not a Gorenstein h-vector. Our main result is a generalization of this result. We also give a simple proof of Stanley's conjecture on the asymptotic behavior of the Hilbert function in socle degree four. We present a conjecture about the asymptotic behavior of the Hilbert function for those algebras that are presented by quadrics.