10 problems

Let $S_{\pi^{(1)}}$ and $S_{\pi^{(2)}}$ be positroid cells in $Gr^+_{k,n}$ corresponding to coloopless permutations $\pi^{(1)}$ and $\pi^{(2)}$, with … and…

Let $S_{\pi}$ be a loopless $(n-c)$-dimensional cell of $Gr^+_{k+1,n}$ with $c$ connected components, where $c$ is a positive integer. Then $S_{\hat{\pi}}$ is a coloopless…

Let the PBDTP graph $\mathcal G$ represent the irreducible positroid cell $\mathcal S_{\mathcal M}^{\text{\tiny TNN}}\subset Gr^{\text{\tiny TNN}}(k,n)$, and suppose every edge lie…

Let a bipartite graph be equipped with edge weights and formal half-edge variables $z_{U,e}$ satisfying the edge-weight, edge-compatibility, white-vertex, and black-vertex relation…

Let a PBDTP network be a reducible oriented planar network representing a point in an irreducible positroid cell, and suppose that each edge lies on a directed path to the boundary…

Fix a reduced PBDTP graph $\mathcal G$ representing the $|D|$-dimensional irreducible positroid cell…

Let $({\mathcal N},\mathcal O,\mathfrak l)$ be a reducible PBDTP network representing a point…

Universal TP-basis conjecture. For any cell and any TP-basis, every other Plücker variable in the cell can be expressed as a subtraction-free Laurent polynomial in the variables of…

TP-basis mutation-equivalence conjecture. For any positroid cell, all TP-bases are mutation equivalent.

Canonical TP-basis conjecture. For any positroid cell, the canonical TP-basis can be transformed by Plücker mutations into a TP-basis consisting of variables coming from unique pat…