Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of mutually disjoint pairs of S-permutation matrices   This work examines the concept of S-permutation matrices, namely $n^2 \times
n^2$ permutation matrices containing a single 1 in each canonical $n \times n$
subsquare (block). The article suggests a formula for counting mutually
disjoint pairs of $n^2 \times n^2$ S-permutation matrices in the general case
by restricting this task to the problem of finding some numerical
characteristics of the elements of specially defined for this purpose
factor-set of the set of $n \times n$ binary matrices. The paper describe an
algorithm that solves the main problem. To do that, every $n\times n$ binary
matrix is represented uniquely as a n-tuple of integers.

19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys