Geodesic
Combinatoire
Prefixes of the Fibonacci word that end with a cube
Rampersad, Narad1
1 Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Ave., Winnipeg, MB, R3B 2E9, Canada
Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 323-330

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The Fibonacci word f=010010100100101⋯ is one of the most well-studied words in the area of combinatorics on words. It is not periodic, but nevertheless contains many highly periodic factors (contiguous subwords). For example, it contains many cubes (i.e., non-empty words of the form xxx). We study the prefixes of the Fibonacci word that end with a cube. Using the computer prover Walnut, we obtain an exact description of the positions of the Fibonacci word at which a cube ends. This gives a certain measure of how close the Fibonacci word is to being periodic.

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DOI : 10.5802/crmath.408
Classification : 68R15

Rampersad, Narad 1

1 Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Ave., Winnipeg, MB, R3B 2E9, Canada
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Prefixes of the {Fibonacci} word that end with a cube},
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Rampersad, Narad. Prefixes of the Fibonacci word that end with a cube. Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 323-330. doi: 10.5802/crmath.408

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