6533b86efe1ef96bd12cca35
RESEARCH PRODUCT
Combinatorics of generalized Bethe equations
Evgeny SklyaninKarol K. Kozlowskisubject
Mathematics::CombinatoricsNonlinear Sciences - Exactly Solvable and Integrable Systems010308 nuclear & particles physics010102 general mathematicsScalar (mathematics)Complex systemFOS: Physical sciencesStatistical and Nonlinear PhysicsPolytopeMathematical Physics (math-ph)Permutation group01 natural sciencesBethe ansatzCombinatorics0103 physical sciencesEnumerationFOS: MathematicsMathematics - CombinatoricsCombinatorics (math.CO)0101 mathematicsExactly Solvable and Integrable Systems (nlin.SI)Complex numberComplex planeMathematical PhysicsMathematicsdescription
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 \({\mathbb{Z}^M}\), and on the other hand, they count integer points in certain M-dimensional polytopes.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-05-14 |