Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum arrangements of nonattacking kings on the $2n\times 2n$
  chessboard   To count the number of maximum independent arrangements of $n^2$ kings on a
$2n\times 2n$ chessboard, we build a $2^n \times (n+1)$ matrix whose entries
are independent arrangements of $n$ kings on $2\times 2n$ rectangles. Utilizing
upper and lower bound functions dependent of the entries of the matrix, we
recursively construct independent solutions, and provide a straight-forward
formula and algorithm.

31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg