Low complexity binary words avoiding $(5/2)^+$-powers - Currie, James; Rampersad, Narad (Discrete mathematics and theoretical computer science, 2025)
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. 12 pages; main structure theorem restated to cover all cases for complementation/reversal of factors