  We establish three rank inequalities for the reduced flavor of Heegaard Floer
homology of Seifert fibered integral homology spheres. Combining these
inequalities with the known classifications of non-zero degree maps between
Seifert fibered spaces, we prove that a map f from Y' to Y between Seifert
homology spheres yields the inequality that |deg f| rank HFred(Y) is at most
rank HFred(Y'). These inequalities are also applied in conjunction with an
algorithm of Nemethi to give a method to solve the botany problem for the
Heegaard Floer homology of these manifolds.
