  Here we examine various aspects of the pairing mechanism for two models, the
two-dimensional and two-leg ladder Hubbard models. Both of these models exhibit
pairing correlations with d_{x^2-y^2} symmetry. However, the undoped insulating
states of these two systems are different with the two-dimensional lattice
characterized by a ground state with long-range antiferromagnetic order and the
two-leg ladder having a spin gap in its ground state. Our aim is to gain a
better understanding of the underlying pairing mechanism which causes
d_{x^2-y^2} pairing in these two models.
