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Infinite words containing squares at every position

Published online by Cambridge University Press:  11 February 2010

James Currie
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada;,
Narad Rampersad
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada;,
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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.

Research Article
© EDP Sciences, 2010

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