Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of generalized Bethe equations   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.

10
The categories of this paper are: q-bio
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The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat