Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial proofs of Gowers' FIN$_k$ and FIN$_k^\pm$ theorem   A combinatorial proof of a pigeonhole principle of Gowers is found along with
its symmetric and approximate version, FIN$_k^\pm$ theorem. The proofs do not
use of the concept of ultrafilter.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg