6 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 $({\mathcal N},\mathcal O,\mathfrak l)$ 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…