# Preservation of normality by non-oblivious group selection

## TL;DR

This paper proves that non-oblivious group selection methods preserve the normality of sequences, using two different mathematical approaches involving incompressibility and dynamical systems.

## Contribution

It introduces two novel proofs demonstrating that non-oblivious group selection preserves sequence normality, expanding understanding of sequence transformations.

## Key findings

- Non-oblivious group selection preserves normality.
- Two distinct proofs provided: incompressibility and dynamical systems.
- Enhances theoretical understanding of sequence normality preservation.

## Abstract

We give two different proofs of the fact that non-oblivious selection via regular group sets preserves normality. Non-oblivious here means that whether or not a symbol is selected can depend on the symbol itself. One proof relies on the incompressibility of normal sequences, the other on the use of augmented dynamical systems.