4 problems

Fix a realizable chirotope $\chi\in\{-1,1\}^{\binom{n}{3}}$. Let $\operatorname{Dr}^\chi_{3,n}$ be the chirotopal Dressian, consisting of the $\chi$-tropical Plücker vectors, and l…

Let $\mathcal S_{k,n}$ denote the possibly infinite cluster complex of the Grassmannian $\operatorname{Gr}(k,n)$. Let $\operatorname{TGr}_0^+(k,n)$ denote its positive tropicalizat…

Let $\operatorname{TGr}_0(k,n)$ denote the characteristic-zero tropical Grassmannian, let $\operatorname{Dr}(k,n)$ denote the Dressian, and let $\mathcal I_{n,k}$ be the Plücker id…

Weighted-tree tropical Grassmannian conjecture. For $m\geq 5$, one has