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arXiv · 2111.07857

Extending Dekking's construction of an infinite binary word avoiding abelian $4$-powers

James Currie·Lucas Mol·Narad Rampersad·Jeffrey Shallit
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Abstract

We construct an infinite binary word with critical exponent 3 that avoids abelian 4-powers. Our method gives an algorithm to determine if certain types of morphic sequences avoid additive powers. We also show that there are $Ω(1.172^n)$ binary words of length $n$ that avoid abelian 4-powers, which improves on previous estimates.

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James Currie, Lucas Mol, Narad Rampersad, Jeffrey Shallit. 2021-11-15. Extending Dekking's construction of an infinite binary word avoiding abelian $4$-powers. https://arxiv.org/abs/2111.07857

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