October 2, 2025Open Access

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

Key Points

Rote words that avoid (5/2)^+-powers can contain infinite sequences of factors, enhancing understanding of their structure.
The existence of such rote words and the avoidance of (5/2)^+-powers is confirmed, aligning with previously established findings.
A new structure theorem provides clarity on the properties and classifications of these specialized words.
The research confirms conjectures made by Ollinger and Shallit, marking advancements in combinatorial word theory.

Abstract

Rote words are infinite words that contain 2n factors of length n for every n 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.

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Cite This Study

Rampersad et al. (Mon,) studied this question.

synapsesocial.com/papers/68de84bf5b556a9128e1bb24 https://doi.org/https://doi.org/10.48550/arxiv.2506.19050