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arXiv · 2506.19050

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

James Currie·Narad Rampersad
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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.

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James Currie, Narad Rampersad. 2025-10-17. Low complexity binary words avoiding $(5/2)^+$-powers. https://doi.org/10.46298/dmtcs.15939

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