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 $2n$.

翻译：我们研究二进制序列中出现的Dyck词的各种性质，其中0视为左括号，1视为右括号。我们证明，无7/3重复幂的二进制词具有有界的嵌套层次，但对于更大的重复指数这一性质不再成立。我们给出了Thue-Morse词中属于Dyck词的因子的明确刻画，并展示了如何对其计数。此外，我们还证明了关于f(n)（Thue-Morse词中长度为2n的Dyck因子数量）的紧的上下界。