3 problems

Let ${\mathcal{UZ}}_{n,m,r}$ be the upper rook placement locus and let $R({\mathcal{UZ}}_{n,m,r})$ be its orbit harmonics ring, with the natural…

Let $\lambda\in\mathcal{D}_n$ be a fixed partition, and let $\varepsilon>0$. For a uniformly random rook placement $\pi\sim\operatorname{Unif}(\operatorname{RP}(N\odot\lambda))$, w…

Let $D$ and $E$ be the operators, and let $\langle W|$ and $|V\rangle$ be the vectors, occurring in the matrix formula for the refined enumeration; let $y$ and $q$ be indeterminate…