Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition theorems for involutive solutions to the Yang-Baxter
  equation   Motivated by the proof of Rump of a conjecture of Gateva-Ivanova on the
decomposability of square-free solutions to the Yang-Baxter equation, we
present several other decomposability theorems based on the cycle structure of
a certain permutation associated with the solution.

5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin