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 n on-intersecting walks interacting with one or two walls parallel to the dir ection of the walks is calculated exactly utilizing a theorem recently prov ed concerning the Bethe ansatz for the eigenvectors of the transfer matrix of the five-vertex model. This theorem shows that the completeness of the B ethe ansatz eigenvectors for the N-walk transfer matrix can be deduced from the completeness of the one-walk eigenvectors.