On an algorithm for receiving Sudoku matrices

TL;DR

This paper presents an algorithmic approach to generate Sudoku matrices by defining specific matrix concepts and using set theory to produce disjoint matrix tuples, simplifying the construction process.

Contribution

It introduces the concepts of $ abla$-matrices and disjoint matrices, and proposes an algorithm for constructing Sudoku matrices based on these definitions.

Findings

The algorithm efficiently constructs Sudoku matrices from disjoint $ abla$-matrices.

Using set theory simplifies the process of generating valid Sudoku matrices.

The approach provides a systematic method for obtaining Sudoku solutions.

Abstract

This work examines the problem to describe an efficient algorithm for obtaining $n^2 \times n^2$ Sudoku matrices. For this purpose, we define the concepts of $n\times n$ $\Pi_n$-matrix and disjoint $\Pi_n$-matrices. The article, using the set-theoretical approach, describes an algorithm for obtaining $n^2$-tuples of $n\times n$ mutually disjoint $\Pi_n$ matrices. We show that in input $n^2$ mutually disjoint $\Pi_n$ matrices, it is not difficult to receive a Sudoku matrix.