Dominant-coefficient conjecture for the universal Drinfeld–Yetter algebra

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 algebra. Dominant-coefficient conjecture. The coefficient $c_{n,m}$ is the dominant term of $r_n^\mathsf{id} \circ r_m^\mathsf{id}$, meaning that it is the term with greatest absolute value. This conjecture concerns the leading term in products in the universal Drinfeld–Yetter algebra; the supplied text gives no evidence of a proof or disproof.