Fontana, the question of finding a general formula for counting disjoint pairs of n 2 × n 2 S-permutation matrices as a function of the integer n 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 n 2 × n 2 S-permutation matrices, it is sufficient to obtain some numerical characteristics of the set of all bipartite graphs of the type g = R g ∪ C g , E g , where V = R g ∪ C g is the set of vertices, and E g is the set of edges of the graph g, R g ∩ C g = ∅, |R g | = |C g | = n.

Some numerical characteristics of bipartite graphs in relation to the problem of finding all disjoint pairs of S-permutation matrices in the general n 2 × n 2 case are discussed in this paper. All bipartite graphs of the type g = Rg ∪ Cg, Eg , where |Rg| = |Cg| = 2 or |Rg| = |Cg| = 3 are provided. The cardinality of the sets of mutually disjoint S-permutation matrices in both the 4 × 4 and 9 × 9 cases are calculated.

Abstract-in the work we discuss the benefit of using bitwise operations in programming. Some interesting examples in this respect have been shown. What is described in detail is an algorithm for sorting an integer array with the substantial use of the bitwise operations. Besides its correctness we strictly prove that the described algorithm works in time O(n). In the work during the realization of each of the examined algorithms we use the apparatus of the object-oriented programming with the syntax and the semantics of the programming language C++

Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an example is the demonstrated algorithm for solving the widespread nowadays "Sudoku" puzzle. This is made, because of the connection with the term set and putting it into practice in the programming. Using the so built program there are solved some combinatorial problems, connected to the Sudoku matrices.

Abstract:The concept of S-permutation matrix is considered. A general formula for counting all disjoint pairs of n 2 × n 2 S-permutation matrices as a function of the positive integer n is formulated and proven in this paper. To do that, the graph theory techniques have been used. It has been shown that to count the number of disjoint pairs of n 2 × n 2 S-permutation matrices, it is sufficient to obtain some numerical characteristics of all n × n bipartite graphs.