Journal of Integer Sequences, Vol. 16 (2013), Article 13.2.7

On Highly Repetitive and Power Free Words

Narad Rampersad
Department of Mathematics and Statistics
University of Winnipeg

Elise Vaslet
Department of Mathematics
University of Turku


Answering a question of Richomme, Currie and Rampersad proved that 7/3 is the infimum of the real numbers α > 2 such that there exists an infinite binary word that avoids powers but is highly 2-repetitive, i.e., contains arbitrarily large squares beginning at every position. In this paper, we prove similar statements about β-repetitive words, for some other β's, over the binary and the ternary alphabets.

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(Concerned with sequence A010060.)

Received June 28 2012; revised version received November 12 2012. Published in Journal of Integer Sequences, March 2 2013.

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