2 problems

Let $\eta\in\mathcal{A}^{\mathbb{Z}^2}$, let $X_{\eta}:=\overline{\mathcal{O}(\eta)}$ be its translation orbit closure, and for a finite set $\mathcal{S}\subseteq\mathbb{Z}^2$ defi…

Let $\eta\in\mathcal{A}^{\mathbb{Z}^2}$, let $X_{\eta}:=\overline{\mathcal{O}(\eta)}$ be its orbit closure under the translation action, and let $P_{\eta}(n,k)$ be the number of di…