The Repetition Threshold for Rote Sequences

TL;DR

This paper determines the repetition threshold for Rote words, infinite binary sequences with specific complexity, establishing it as 5/2 through computational methods involving automata and theorem proving.

Contribution

It introduces a new computational approach using Walnut and automata generation to analyze the repetition threshold for Rote words.

Findings

Repetition threshold for Rote words is 5/2.

Developed a purely computational proof technique.

Applied automata generation from morphisms.

Abstract

We consider Rote words, which are infinite binary words with factor complexity $2n$. We prove that the repetition threshold for this class is $5/2$. Our technique is purely computational, using the Walnut theorem prover and a new technique for generating automata from morphisms due to the first author and his co-authors.