4 problems

Let $\mathfrak{U}_{\mathsf{DY}}^1$ be the universal Drinfeld–Yetter algebra, with unit-labelled element $r_1^{\mathsf{id}}$. Center-generation conjecture. The center of…

Let $\mathfrak{L}_{n,m}$ be the family of looms and write $H_{n,m}=\lvert\mathfrak{L}_{n,m}\rvert$. Let $T_{m,k}$ be defined by … with $T_{0,0}=1$ and $T_{0,k}=0$ for every…

For $n\geq 1$, define the reversal permutation … Let $r_n^{\pi_n}$ be the corresponding element of $\mathfrak{U}_{\mathsf{DY}}^1$, and let $p_{n,m}$ denote the coefficient of…

Let $c_{n,m}$ denote the coefficient introduced in Proposition, and let $r_n^\mathsf{id}$ and $r_m^\mathsf{id}$ be the corresponding elements of the universal Drinfeld–Yetter algeb…