7 problems

Let $w$ be the Fibonacci word, and let the recurrence quotient of an infinite word be the quotient discussed in the surrounding context. Among all non-periodic infinite words, Rauz…

Abelian-period conjecture. The abelian period set of a Sturmian word of slope $\alpha$ is

Let $\boldsymbol{u}$ be a Sturmian word whose slope has bounded coefficients in its continued fraction. For each positive integer $n$, let ${\mathrm{PL}_{\boldsymbol{u}}}(n)$ be th…

Let $s$ be a Sturmian word over $\{0,1\}$, and let $T: \{0,1\} \to \{0,1\}$ be a morphism such that $T(s)$ is aperiodic. Denote by $f_{T(s)}(n)$ the permutation complexity of…

Saari's conjecture. If $n\ne 6$ and $w$ is minimal, then $w$ is a Christoffel word.

Let $t$ be the Thue–Morse word, and let $\mathpzc{A}_n(t)$ denote the number of privileged factors of $t$ of length $n$. A zero gap is a consecutive interval of lengths on which…

Let $\ell(n)$ be the minimum number of Lyndon factors among Lyndon words of length $n$: … A minimizer conjecture. If $w$ is a Lyndon word with $|w|\neq 6$ and…