4 problems

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

For an infinite word $\mathbf{w}$, let the palindromic length $|u|_{\rm pal}$ of a finite factor or prefix $u$ be the least number $Q$ of palindromes whose concatenation is $u$. Un…

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…