Emergent Mind
The analogue of overlap-freeness for the Fibonacci morphism
(2311.12962)
Published Nov 21, 2023
in
math.CO
and
cs.FL
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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