4 problems

Let $\mathfrak{h}=\mathbb{Q}\langle x,y\rangle$ be the noncommutative polynomial algebra over $\mathbb{Q}$, let $\mathfrak{h}^0=\mathbb{Q}+x\mathfrak{h}y$, and let $\tau$ be the an…

For positive integers $n,k_1,k_2,\ldots,k_n$ with $k_1\geqslant 2$, let $\zeta(k_1,\ldots,k_n)$ be the multiple zeta value of weight $k_1+\cdots+k_n$ and depth $n$. Consider the su…

Derivation-relation conjecture. For every $m,n\geq 3$,

Let $\mathfrak H^1$ be the relevant noncommutative polynomial algebra of words, let $z=x+y$, and let $\partial_l$ be the derivation indexed by $l\in\mathbb Z_{\geq1}$. For…