Betti numbers of points in projective space

In this paper we study the graded minimal free resolution of a finite set of points in P^n. We find conditions for the minimal number of generators of their ideal and for the Cohen-Macaulay type of their coordinate ring to have the expected minimum value. In some special cases we find that all the Betti numbers of the points are determined. We the explicitely compute tham, by means of a compact formula, which allows us to avoid the recursive computation based upon the additivity of the Hibert function.