arXiv math/00061532000-06-21math.COmath-phmath.MP

From the Bethe Ansatz to the Gessel-Viennot Theorem

R. Brak, J. W. Essam, A. L. Owczarek

发表信息：: Annals of Combinatorics 3 (1999) 251-263

英文摘要：

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.

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