3 problems

For $1\leq k\leq n$, let $\mathbb{V}_{n,k}$ be the smallest subspace of $\Omega_n[y_1,\dots,y_n]$ containing the superspace Vandermonde $\delta_{n,k}$, closed under…

For $1\leq k\leq n$, let $\delta_{n,k}\in\Omega_n$ be the superspace Vandermonde, and let $V_{n,k}$ be the smallest linear subspace of $\Omega_n$ containing $\delta_{n,k}$ and clos…

Let $F$ be a symmetric function with a positive monomial-basis expansion, let $G$ be a symmetric function with a positive Schur-basis expansion, and let $\Delta_F$ and $\Xi$ denote…