Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Virtual crystals and fermionic formulas of type $D_{n+1}^{(2)}$,
  $A_{2n}^{(2)}$, and $C_n^{(1)}$
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex