From the Bethe Ansatz to the Gessel-Viennot Theorem
Brak, R. ; Essam, J. W. ; Owczarek, A. L.
arXiv, 0006153 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-06-20
Classification:  Mathematics - Combinatorics,  Mathematical Physics,  05A15,  82B41 
@article{0006153,
     author = {Brak, R. and Essam, J. W. and Owczarek, A. L.},
     title = {From the Bethe Ansatz to the Gessel-Viennot Theorem},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0006153}
}

Brak, R.; Essam, J. W.; Owczarek, A. L. From the Bethe Ansatz to the Gessel-Viennot Theorem. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0006153/