Repetition Threshold for Binary Automatic Sequences
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911463383236608 |
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| author | Allouche, J. -P. Rampersad, N. Shallit, J. |
| author_facet | Allouche, J. -P. Rampersad, N. Shallit, J. |
| contents | The critical exponent of an infinite word $\bf x$ is the supremum, over all finite nonempty factors $f$, of the exponent of $f$. In this note we show that for all integers $k\geq 2,$ there is a binary infinite $k$-automatic sequence with critical exponent $\leq 7/3$. The same conclusion holds for Fibonacci-automatic and Tribonacci-automatic sequences. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_06513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Repetition Threshold for Binary Automatic Sequences Allouche, J. -P. Rampersad, N. Shallit, J. Combinatorics Discrete Mathematics Formal Languages and Automata Theory The critical exponent of an infinite word $\bf x$ is the supremum, over all finite nonempty factors $f$, of the exponent of $f$. In this note we show that for all integers $k\geq 2,$ there is a binary infinite $k$-automatic sequence with critical exponent $\leq 7/3$. The same conclusion holds for Fibonacci-automatic and Tribonacci-automatic sequences. |
| title | Repetition Threshold for Binary Automatic Sequences |
| topic | Combinatorics Discrete Mathematics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2406.06513 |