Combinatorics of generalized Bethe equations
Exactly Solvable and Integrable Systems
2015-11-11 v1 Mathematical Physics
Combinatorics
math.MP
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 Z^M, and on the other hand, they count integer points in certain M-dimensional polytopes.
Cite
@article{arxiv.1205.2968,
title = {Combinatorics of generalized Bethe equations},
author = {Karol Kozlowski and Evgeny Sklyanin},
journal= {arXiv preprint arXiv:1205.2968},
year = {2015}
}