5 problems

A Lyndon word over $\{0,1\}$ is a word that is the unique minimum among all of its rotations. For $k\geq2$, let $\alpha=(1,0,0,\dots,0)$ be the prefix of length $k$, and let…

Let $\Delta^+$ be the set of positive roots, let $d\in\mathbb{Z}$, and let $\ell(\alpha,d)$ denote the Lyndon loop word of degree $(\alpha,d)$. Let $\Phi^L$ be the homomorphism fro…

Let $A$ be a finite alphabet, and let $w$ be a finite generalized Lyndon word over $A$. The length of $w$ is denoted by $|w|$. Extendability conjecture. Every finite generalized Ly…

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…

Let $\zeta(s_1,\ldots,s_k)$ denote a multiple zeta value of weight $s_1+\cdots+s_k$. A word in the alphabet $\{2,3\}$ is called Lyndon when it is strictly smaller than each of its…