Lattice Paths and the Constant Term

We firstly review the constant term method (CTM), illustrating its combinatorial connections and show how it can be used to solve a cer-tain class of lattice path problems. We show the connection between the CTM, the transfer matrix method (eigenvectors and eigenvalues), partial difference equations, the Bethe Ansatz and orthogonal polyno-mials. Secondly, we solve a lattice path problem first posed in 1971. The model stated in 1971 was only solved for a special case – we solve the full model.