Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: The set of ratios of derangements to permutations in digraphs is dense
  in $[0, 1/2]$
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio