Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Problem of Pawns   Using a bijective proof, we show the number of ways to arrange a maximum
number of nonattacking pawns on a $2m\times 2m$ chessboard is ${2m\choose
m}^2$, and more generally, the number of ways to arrange a maximum number of
nonattacking pawns on a $2n \times 2m$ chessboard is ${m+n\choose n}^2$.

5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph