The multiplicity of an m-primary ideal I of a Cohen-Macaulay local ring (A,m) of dimension d can be written as e(I) = λ(I/I)−(d−1)λ(A/I)+K−1 for some integer K ≥ 1. In the case K = 1, 2, the Hilbert function of I and the depth of the associated graded ring of A with respect to I are very well understood. In this paper we are dealing with the case K = 3 and we determine the possible Hilbert functions of stretched ideals whose Cohen-Macaulay type is not too big. Our main result extends to a… CONTINUE READING