Combinatorics of generalized Bethe equations

TY - JOUR

T1 - Combinatorics of generalized Bethe equations

AU - Sklyanin FRS, Evgeny

AU - Kozlowski, Karol

PY - 2013/10/1

Y1 - 2013/10/1

N2 - 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.

AB - 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.

U2 - 10.1007/s11005-013-0630-9

DO - 10.1007/s11005-013-0630-9

M3 - Article

VL - 103

SP - 1047

EP - 1077

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 1573-0530

IS - 10

ER -