Ideals attaining a given Hilbert function

We improve the result of Charalambous and Evans [C-E] to show that the Bett i number sequence in their example of incomparable minimals among the resol utions for a fixed Hilbert function is indeed minimal. Their example was de pendent upon the graded betti numbers. We give an example of a finite lengt h Hilbert function and two cyclic finite length modules attaining the Hilbe rt function for which the betti number sequences are incomparable, i.e., in dependent of the grading.