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arXiv · 2311.12962

The analogue of overlap-freeness for the Fibonacci morphism

James D. Currie·Narad Rampersad
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Abstract

A $4^-$-power is a non-empty word of the form $XXXX^-$, where $X^-$ is obtained from $X$ by erasing the last letter. A binary word is called {\em faux-bonacci} if it contains no $4^-$-powers, and no factor 11. We show that faux-bonacci words bear the same relationship to the Fibonacci morphism that overlap-free words bear to the Thue-Morse morphism. We prove the analogue of Fife's Theorem for faux-bonacci words, and characterize the lexicographically least and greatest infinite faux-bonacci words.

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James D. Currie, Narad Rampersad. 2023-11-21. The analogue of overlap-freeness for the Fibonacci morphism. https://arxiv.org/abs/2311.12962

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