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Dyck Words, Pattern Avoidance, and Automatic Sequences
- Publication Year :
- 2023
- Publisher :
- arXiv, 2023.
-
Abstract
- We study various aspects of Dyck words appearing in binary sequences, where $0$ is treated as a left parenthesis and $1$ as a right parenthesis. We show that binary words that are $7/3$-power-free have bounded nesting level, but this no longer holds for larger repetition exponents. We give an explicit characterization of the factors of the Thue-Morse word that are Dyck, and show how to count them. We also prove tight upper and lower bounds on $f(n)$, the number of Dyck factors of Thue-Morse of length $2n$.<br />Comment: Full version of a paper to be submitted to WORDS 2023
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....6b8754aa847cea86583be14b314b97c5
- Full Text :
- https://doi.org/10.48550/arxiv.2301.06145