On the monotonicity of Hilbert functions

In this paper we show that a large class of one-dimensional Cohen-Macaulay local rings (A, m) has the property that if M is a maximal Cohen-Macaulay A-module then the Hilbert function of M (with respect to m) is non-decreasing. Examples include (1) complete intersections A = Q/(f, g) where (Q, n) is regular local of dimension three and f is an element of n(2) \ n(3); (2) one dimensional Cohen-Macaulay quotients of a two dimensional Cohen-Macaulay local ring with pseudo-rational singularity.