2 problems

Let $D_k$ be the plethystic operators defined by … where $\operatorname{Exp}[X] = \sum_{n \geq 0} h_n[X]$ and let $\Theta_k=\Pi\,\underline{e}_k^*\,\Pi^{-1}$, with…

Let $m,n$ be coprime positive integers, let $k\geq 1$, let $m_\lambda$ denote the monomial symmetric function indexed by a partition $\lambda$, and let $Q_{a,b}$ and…