2 problems

Alternating and c-noncrossing face conjecture. If $(\widetilde\beta,\widetilde\gamma)\in\widetilde R$ span a two-dimensional face of the normal fan of $P$, then $(\beta,\gamma)$ mu…

Let $\mathcal{A}(\widetilde{\sf M})$ be a finite-type cluster algebra, and let $\widetilde{\sf M}$ be its mutation matrix. Consider the Newton polytopes of the cluster variables an…