16 problems

Let $[1\dots n]$ be labeled cyclically, and let a non-crossing family be a family of pairwise non-crossing $k$-subsets, where non-crossing means that no chord with endpoints in…

Move-connectivity conjecture. If

A normal plabic graph is a plabic graph whose boundary vertices are black of degree $1$, whose internal black vertices have degree $3$, and in which no two vertices of the same col…

Let $(G,\mathbf{D})$ be a tangle admitting a brushing, with $\dim\Pi_G=km$ and positive intersection number $\operatorname{IN}_m(G)>0$. Let $F_{\widehat{(G,\mathbf{D})}}$ be the as…

Fix a positive integer $m$, and let $G$ be a plabic graph of type $(k,n)$ with $\dim\Pi_G=km$. Let $T_G$ denote the associated family of $k$-planes. Intersection-number-zero criter…

Let $(G,\mathbf{D})$ be a dominant solvable plabic tangle, where $G$ has $n$ outer boundary vertices and inner disks $D^{(1)},\dots,D^{(\ell)}$, and let $m$-VRCs denote the associa…

Let $G$ be a plabic graph, and let $rG$ denote any rotation of $G$. Its associated Newton–Okounkov body is denoted by $\Delta_G$. Rotation invariance conjecture. All rotations of a…

Let $G(\mathbf w,f)$ and $G(\mathbf w',f')$ be affine plabic fences, with restricted move equivalence defined using the relevant affine plabic-fence moves. Affine plabic-fence clas…

Let $G$ and $G'$ be connected simple plabic graphs whose quivers $Q_G$ and $Q_{G'}$ are mutation equivalent. Let $L^{\operatorname{plab}}_G$ and $L^{\operatorname{plab}}_{G'}$ be t…

Let $G$ be a plabic graph with $\operatorname{c}(G)$ connected components and $n$ interior faces. Let $L^{\operatorname{plab}}_G$ be its associated plabic graph link, and let…

Let $G$ be a planar bicoloured PBDTP graph, and let its edges carry the geometric signature. Form the associated sign matrix by assigning the corresponding geometric-signature sign…

Let $G$ be a reduced plabic graph, and let $\Sigma_G^S$ and $\Sigma_G^T$ denote respectively its source and target seeds. A quasi-cluster transformation is the relevant equivalence…

The source concerns open positroid varieties and the cluster structures determined by relabeled plabic graphs. For a relabeled graph $G^\rho$ and an ordinary plabic graph $H$ with…

Let $\mathcal{A}$ be the set of vertices of a generic convex $n$-gon, and let $\Upsigma_{\mathcal{A},k}$ be the associated higher associahedron. The generic polygon invariance conj…

Let $k$ and $n$ be positive integers with $n=2k$. For a bipartite $(k,2k)$-plabic graph $G$, let $G^{\operatorname{op}}$ be the graph obtained from $G$ by a $180^\circ$ rotation fo…

Let $P$ and $P'$ be plabic graphs, and associate to each its quiver. Two plabic graphs are move equivalent when they are related by local moves and changes of the colors of boundar…