A Note on the Metric of Thompson's group V

TL;DR

This paper improves the known bounds on the word metric for Thompson's group V, aligning it with existing bounds for groups F and T, thereby advancing understanding of these algebraic structures.

Contribution

It introduces a new, tighter bound on the word metric for Thompson's group V, refining previous results from 2004.

Findings

New bound on the word metric for Thompson's group V

Bound matches known bounds for groups F and T

Enhances understanding of group metric properties

Abstract

In this short note, a bound on the word metric for Thompson's group V given by Birget in 2004 is improved to a new bound, which agrees with the known bounds for Thompson's groups F and T.