2 problems

Let $k$ be a positive integer and let $\lambda,\mu\vdash k$ be partitions. Write $\vec z=\vec z'\circ\lambda$ and $\vec w=\vec w'\circ\mu$, where $\vec z'$ has length…

Let $k$ be a positive integer, let $\boldsymbol\lambda\vdash k$ be a partition with length $\ell(\lambda)$, and let $\vec z'$ and $\vec w'$ have $\ell(\lambda)$ variables. Write…