2 problems

Fix $(s,t,p,q)\in{\mathbb R}^4$. Let ${\cal Q}_n^{(s,t,p,q)}$ be the quadri-tilings of ${\cal Q}_n$ with first height change $(\lfloor ns\rfloor,\lfloor nt\rfloor)$ and second heig…

Let ${\mathbb T}$ be a periodically tiled torus with lattice of periods $\Lambda$, and let ${\mathbb T}_n={\mathbb T}/n\Lambda$ be such that ${\mathbb T}_n^*$ is bipartite. Let…