Combinatorics of generalized Bethe equations

Evgeny Sklyanin FRS, Karol Kozlowski

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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.
Original languageEnglish
Pages (from-to)1047-1077
Number of pages31
JournalLetters in Mathematical Physics
Issue number10
Publication statusPublished - 1 Oct 2013

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