On connection between division sequences and presentations of a free group

TL;DR

This paper introduces a method to estimate lower bounds on the number of equivalence classes of division sequences by analyzing group presentations related to free groups.

Contribution

It presents a novel approach linking division sequences with group theory to estimate equivalence class counts.

Findings

Method provides lower bounds on equivalence classes.

Group structures help analyze division sequences.

New connections between division sequences and free group presentations.

Abstract

This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of equivalence and studying properties of resulting groups as presentations of free group.