7 problems

Let $\mathcal{A}_{n,k,2}$ be the $m=2$ amplituhedron, and let $\operatorname{Trop}^+{\rm Gr}(k+1,n)$ denote the positive tropical Grassmannian. A regular positroidal subdivision is…

Define a cyclical one gap for a one-column tableau in $\operatorname{SSYT}(k,[n])$ as having entries either of the form $[i_1,i_2]\cup[i_3,i_4]$, with $i_1\leq i_2<i_3-1$,…

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…

A positroidal triangulation or dissection of the amplituhedron is a collection of positroid cells whose full-dimensional images form the corresponding subdivision. Previously const…

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

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…