Computational Enumeration of Independent Generating Sets of Finite Symmetric Groups

TL;DR

This paper introduces computer algebra tools to enumerate conjugacy classes of independent and generating sets in symmetric groups up to size 7, providing initial analysis of these structures.

Contribution

The work presents novel computational methods for enumerating and analyzing independent generating sets in symmetric groups, extending previous theoretical approaches.

Findings

Enumerated conjugacy classes of independent sets up to n=7

Analyzed the structure of generating sets in symmetric groups

Provided initial insights into the distribution of these sets

Abstract

We developed computer algebra tools for enumerating conjugacy classes of independent subsets and generating sets of symmetric groups up to $n=7$, and carried out an initial analysis of the obtained results.