Prefixes of the Fibonacci word that end with a cube
The Fibonacci word $\mathbf{f} = 010010100100101\cdots $ 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 fo...
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.408/ |
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| author | Rampersad, Narad |
| author_facet | Rampersad, Narad |
| author_sort | Rampersad, Narad |
| collection | DOAJ |
| description | The Fibonacci word $\mathbf{f} = 010010100100101\cdots $ 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. |
| format | Article |
| id | doaj-art-85b9e64149e7448197b5d37a7e1b66a7 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-85b9e64149e7448197b5d37a7e1b66a72025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G132333010.5802/crmath.40810.5802/crmath.408Prefixes of the Fibonacci word that end with a cubeRampersad, Narad0Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Ave., Winnipeg, MB, R3B 2E9, CanadaThe Fibonacci word $\mathbf{f} = 010010100100101\cdots $ 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.408/ |
| spellingShingle | Rampersad, Narad Prefixes of the Fibonacci word that end with a cube Comptes Rendus. Mathématique |
| title | Prefixes of the Fibonacci word that end with a cube |
| title_full | Prefixes of the Fibonacci word that end with a cube |
| title_fullStr | Prefixes of the Fibonacci word that end with a cube |
| title_full_unstemmed | Prefixes of the Fibonacci word that end with a cube |
| title_short | Prefixes of the Fibonacci word that end with a cube |
| title_sort | prefixes of the fibonacci word that end with a cube |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.408/ |
| work_keys_str_mv | AT rampersadnarad prefixesofthefibonacciwordthatendwithacube |