Combinatorics of Generalized Bethe Equations |
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Authors: | Karol K. Kozlowski Evgeny K. Sklyanin |
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Affiliation: | 1. Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, Université de Bourgogne, Dijon, France 2. Department of Mathematics, University of York, York, YO10 5DD, UK
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Abstract: | A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over ${mathbb{Z}^M}$ Z M , and on the other hand, they count integer points in certain M-dimensional polytopes. |
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