Matrix representation of a solution of a combinatorial problem of the group theory

TL;DR

This paper introduces a matrix-based approach to solving a combinatorial problem in group theory, specifically focusing on an equivalence relation within the symmetric group and providing an algorithm to count equivalence classes.

Contribution

It presents a novel matrix representation and an algorithm for calculating the number of equivalence classes in the symmetric group for any positive integer.

Findings

Algorithm effectively computes equivalence class counts

Matrix representation simplifies the combinatorial problem

Applicable to arbitrary positive integers

Abstract

An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.