2 problems

Let $\xi_n=\prod_{1\leq i<j\leq n}(x_i-x_j)$ be the Vandermonde determinant, and for an integer partition $\lambda\vdash n$, let $\xi_\lambda$ be the product of the Vandermonde det…

Let $1\leq m\leq n$. Let $\lambda\vdash n(n-1)$ satisfy $n-1\leq\ell(\lambda)\leq n$ and … Let $\mu\vdash n(n+1)$ satisfy … and, if $m<n$, $\mu_j=\lambda_{j-1}$ for…