1 research outputs found
On the Number of Disjoint Pairs of S-permutation Matrices
In [Journal of Statistical Planning and Inference (141) (2011) 3697-3704],
Roberto Fontana offers an algorithm for obtaining Sudoku matrices. Introduced
by Geir Dahl concept disjoint pairs of S-permutation matrices [Linear Algebra
and its Applications (430) (2009) 2457-2463] is used in this algorithm.
Analyzing the works of G. Dahl and R. Fontana, the question of finding a
general formula for counting disjoint pairs of S-permutation
matrices as a function of the integer naturally arises. This is an
interesting combinatorial problem that deserves its consideration. The present
work solves this problem. To do that, the graph theory techniques have been
used. It has been shown that to count the number of disjoint pairs of S-permutation matrices, it is sufficient to obtain some numerical
characteristics of the set of all bipartite graphs of the type , where is the set of vertices, and is the set
of edges of the graph , , .Comment: 14 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1202.040