# Equivariant thinning over a free group

## TL;DR

This paper constructs entropy-increasing monotone factors within Bernoulli shifts over free groups of rank two or more, advancing understanding of entropy dynamics in non-abelian group actions.

## Contribution

It introduces a novel method for creating entropy-increasing monotone factors in Bernoulli shifts over free groups, a previously unexplored area.

## Key findings

- Established existence of entropy-increasing factors
- Extended entropy theory to free group actions
- Provided new tools for studying non-abelian group dynamics

## Abstract

We construct entropy increasing monotone factors in the context of a Bernoulli shift over the free group of rank at least two.