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 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.
Currie et al. (Wed,) studied this question.
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