Infinite words containing squares at every position
Department of Mathematics and Statistics,
University of Winnipeg, 515 Portage Avenue, Winnipeg,
Manitoba R3B 2E9, Canada; firstname.lastname@example.org, email@example.com
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.
Mathematics Subject Classification: 68R15.
Key words: Infinite words / power-free words / squares.
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