4 problems

Let ${\mathcal A}$ be a linear LP algebra of rank $r$. Simple-polytope conjecture. There exists a convex simple polytope $P({\mathcal A})$ of dimension $r$ such that its vertices a…

Let $\Gamma$ be a graph and let $\widetilde{\mathcal N}(\Gamma)$ denote its extended nested complex. Extended nested complex polytope conjecture. The complex…

A linear LP algebra is an LP algebra whose exchange polynomials are linear in the relevant cluster variables, allowing the coefficients and constant terms described in the paper. F…

Let ${\mathcal A}_\Gamma$ be a graph LP algebra and let $t_{\mathcal S}$ be a seed. Write ${\mathcal L}(t_{\mathcal S})$ for the Laurent polynomial ring associated with this seed.…