Repetition Threshold for Binary Automatic Sequences
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.06513
- arXiv:
- arXiv:2406.06513
- Bibcode:
- 2024arXiv240606513A
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- Computer Science - Formal Languages and Automata Theory