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arXiv · 2301.06145

Dyck Words, Pattern Avoidance, and Automatic Sequences

Lucas Mol·Narad Rampersad·Jeffrey Shallit
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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 $2n$.

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Lucas Mol, Narad Rampersad, Jeffrey Shallit. 2024-07-31. Dyck Words, Pattern Avoidance, and Automatic Sequences. https://doi.org/10.46298/cm.12695

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