We firstly review the constant term method (CTM), illustrating its combinatorial connections and show how it can be used to solve a certain 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 polynomials. 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.
Counting Complexity: An international workshop on statistical mechanics and combinatorics. Journal of Physics: Conference Series, Volume 42 (Dunk Island, Qld 10-15 July, 2005) p. 47-58