5 problems

Let $T \in \operatorname{SSYT}(2,[n])$ have $m$ columns. Let $(S_1,\ldots,S_m)$ be the unique unordered $m$-tuple of pairwise weakly separated one-column tableaux whose union is…

Let $T \in \operatorname{SSYT}(k,[n])$ be a tableau with no frozen factors. Write $T=S^{\cup r}$ with $r$ maximal, where $S=\underline{T}$ has no further common frozen factor. A po…

Consider regular positroidal subdivisions $\{\Gamma_{\pi}\}$ and $\{\Gamma_{\pi'}\}$ of $\Delta_{k+1,n}$ and corresponding subdivisions $\{Z_{\hat{\pi}}\}$ and $\{Z_{\hat{\pi'}}\}$…

Let $\operatorname{Trop}^+Gr_{k+1,n}$ be the positive tropical Grassmannian, whose cones carry their natural partial order. Positive tropical Grassmannian fan conjecture. The regul…

A regular positroidal subdivision of $\mathcal{A}_{n,k,2}$ is a positroidal dissection of the form $\{S_{\hat{\pi}}\}$, where $\{S_{\pi}\}$ is a regular positroidal subdivision of…