Dyck Words, Pattern Avoidance, and Automatic Sequences
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 $2n$.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- 10.48550/arXiv.2301.06145
- arXiv:
- arXiv:2301.06145
- Bibcode:
- 2023arXiv230106145M
- Keywords:
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- Computer Science - Discrete Mathematics;
- Computer Science - Formal Languages and Automata Theory;
- Mathematics - Combinatorics
- E-Print:
- Full version of a paper appearing in the conference proceedings of WORDS 2023