  From a Macaulay's paper it follows that a lex-segment ideal has the greatest
number of generators (the 0-th Betti number $\b_0$) among all the homogeneous
ideals with the same Hilbert function. In this paper we prove that this fact
extends to every Betti number, in the sense that all the Betti numbers of a
minimal free resolution of a lex segment ideal are bigger than or equal to the
ones of any homogeneous ideal with the same Hilbert function.
