  Let R be the quotient of a polynomial ring over a field k by an ideal
generated by monomials. We derive a formula for the multigraded Poincare'
series of R, i.e., the generating function for the ranks of the modules in a
minimal multigraded free resolution of k over R. The formula can be expressed
in terms of the homology of lower intervals in a certain lattice associated to
the minimal set of generators for the ideal.
