Tuesday, May 15, 2012

1205.2968 (Karol Kozlowski et al.)

Combinatorics of generalized Bethe equations    [PDF]

Karol Kozlowski, Evgeny Sklyanin
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.
View original: http://arxiv.org/abs/1205.2968

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