Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Combinatorial properties of virtual braids
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph