Density of growth rates of subgroups of a free group -- an alternative proof

TL;DR

This paper provides an alternative proof that the growth rates of finitely generated subgroups of a free group are densely distributed within a specific interval, enhancing understanding of subgroup growth behaviors.

Contribution

The paper offers a new proof of the density of subgroup growth rates, contributing a different approach to a recent theorem by Louvaris, Wise, and Yehuda.

Findings

Growth rates of finitely generated subgroups are dense in [1, 2r-1]

Provides an alternative proof to existing theorems

Enhances understanding of subgroup growth dynamics

Abstract

We give an alternative proof to the theorem recently proved by Louvaris, Wise and Yehuda, that the growth rates of finitely generated subgroups of $F_r$ are dense in $[1,2r-1]$.