The analogue of overlap-freeness for the Fibonacci morphism
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 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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