Infinite words containing squares at every position
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Currie, James, and Narad Rampersad. "Infinite words containing squares at every position." RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications 44(1) (2010): 113-124. DOI: 10.1051/ita/2010007.
Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve this question in the case of a binary alphabet by showing that the answer is α = 7/3.