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Simultaneous avoidance of large squares and fractional powers in infinite binary words

Jeffrey Shallit
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Abstract

In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with y >= 4 nor cubes xxx. We show that `cube' can be replaced by any fractional power > 5/2. We also consider the analogous problem where `4' is replaced by any integer. This results in an interesting and subtle hierarchy.

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Jeffrey Shallit. 2003-04-29. Simultaneous avoidance of large squares and fractional powers in infinite binary words. https://arxiv.org/abs/math/0304476

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