Exact solution of N directed non-intersecting walks interacting with one or two boundaries

The partition function for the problem of an arbitrary number of directed nonintersecting walks interacting with one or two walls parallel to the direction of the walks is calculated exactly utilizing a theorem recently proved concerning the Bethe ansatz for the eigenvectors of the transfer matrix of the five-vertex model. This theorem shows that the completeness of the Bethe ansatz eigenvectors for the N -walk transfer matrix can be deduced from the completeness of the one-walk eigenvectors.