4 problems

Let $k\geq 1$, and let $\mathbf{x}_k$ be the Thue-Morse-like sequence described in the source. The critical exponent is the supremum of the exponents of its finite factors, while t…

Let $k\geq 1$, and let $\mathbf{x}_k$ be the Thue-Morse-like sequence obtained from the family described in the source. For a binary sequence, its factor complexity $p(n)$ is the n…

Let $p,q,n\in\mathbb{N}^{+}$, set $Q=p+q$, and let $A_{p,q}(d)$ denote the maximum length of an arithmetic progression of difference $d$ occurring in the generalised Thue–Morse seq…

Let $r\geqslant 2$ and let $n$ be the length of a word over a two-letter alphabet. An $r$-regular word is a word satisfying the corresponding regularity condition, and…