2 problems

Let $\hat{\mathcal G}$ be obtained by adjoining to a graph $\mathcal G$ its reflection across the real axis while retaining one copy of vertices on the real axis. Let $M$ be an inf…

For any $z>0$, superimpose two independent free boundary dimer models in the upper half-plane, and consider the resulting collection of boundary-touching curves. Free-boundary dime…