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On Highly Repetitive and Power Free Words
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Narad Rampersad

Department of Mathematics and Statistics

University of Winnipeg

Canada

Elise Vaslet

Department of Mathematics

University of Turku

Finland

**Abstract:**

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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