Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On the non-existence of some Steiner $t$-$(v,k)$ trades of certain
  volumes
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an