| Issue |
RAIRO-Theor. Inf. Appl.
Volume 59, 2025
|
|
|---|---|---|
| Article Number | 7 | |
| Number of page(s) | 16 | |
| DOI | https://doi.org/10.1051/ita/2025009 | |
| Published online | 29 August 2025 | |
The analogue of overlap-freeness for the Fibonacci morphism
Department of Mathematics & Statistics, The University of Winnipeg,
Manitoba,
Canada
* Corresponding author: j.currie@uwinnipeg.ca
Received:
26
June
2024
Accepted:
6
August
2025
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.
Mathematics Subject Classification: 68R15
Key words: Fibonacci word / Fife’s theorem / lexicographically least word / 4− powers
© The authors. Published by EDP Sciences, 2025
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