2 problems

Let $d53d$ be a field, let $\alpha$ be as in the definition of $\mathcal{C}_{\rho}^{n,d}(\alpha)$, and let $\mathcal{M}^{n,d}$ be the set of $d$-element multisets with elements in…

Let $d53d$ be a field, let $S_{n,d}(d53d)$ denote the space of homogeneous degree-$d$ polynomials in $n$ variables, and let $\operatorname{d}_{\operatorname{ess}}$ be the essential…