5 problems

Let $w$ be an Arnoux–Rauzy infinite word. Its $2$-binomial complexity and subword complexity are functions assigning to each positive integer the number of equivalence classes of f…

Chen–Wen–Wu conjecture. For every $k\geqslant 3$, the function $\mathsf{b}_{\mathbf{t}_m}^{(k)}$ is ultimately periodic with period $m^k$.

Additive complexity conjecture. The additive complexity of a $k$-automatic sequence is a $k$-regular sequence.

Let $p(q)$ denote the word complexity of a subshift, namely the number of distinct words of length $q$, and suppose the subshift admits a weakly mixing probability measure. The qua…

Let $\mathbf u$ be a binary generalized pseudostandard word, and let $\mathcal C_{\mathbf u}(n)$ denote its complexity, namely the number of factors of length $n$ in $\mathbf u$. T…