Low complexity binary words avoiding $(5/2)^+$-powers

TL;DR

This paper characterizes the structure of Rote words that avoid $(5/2)^+$-powers, confirming a conjecture and advancing understanding of power-avoiding infinite words.

Contribution

It provides a structure theorem for Rote words avoiding $(5/2)^+$-powers, confirming a previous conjecture and detailing their properties.

Findings

Rote words avoiding $(5/2)^+$-powers have a specific structure.

The paper confirms a conjecture by Ollinger and Shallit.

It establishes the optimality of avoiding $(5/2)^+$-powers in Rote words.

Abstract

Rote words are infinite words that contain $2n$ factors of length $n$ for every $n \geq 1$. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid $(5/2)^+$-powers and that this is best possible. In this note we give a structure theorem for the Rote words that avoid $(5/2)^+$-powers, confirming a conjecture of Ollinger and Shallit.