This note confirms a conjecture of Ollinger and Shallit, revealing properties of rote words that avoid (5/2)^+-powers.
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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Rampersad et al. (2025) studied this question.
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