Ju n 20 00 From the Bethe Ansatz to the Gessel - Viennot Theorem
نویسندگان
چکیده
We state and prove several theorems that demonstrate how the coordinate Bethe Ansatz for the eigenvectors of suitable transfer matrices of a generalised inhomogeneous five-vertex model on the square lattice, given certain conditions hold, is equivalent to the Gessel-Viennot determinant for the number of configurations of N non-intersecting directed lattice paths, or vicious walkers, with various boundary conditions. Our theorems are sufficiently general to allow generalisation to any regular planar lattice.fer Matrix method.
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