9 problems

Let $n$ be a positive integer, and let $P$ be a linear polynomial in $x_1,\ldots,x_n$ with positive coefficients. Say that $P$ generates a period 1 seed when it generates a seed of…

Let $\mathcal{A}(X,\mathbf{h},\Lambda,\widetilde{B})$ be a generalized quantum cluster algebra with initial extended cluster $\{X_1,\ldots,X_m\}$. A Laurent polynomial in this clus…

A semicontiguous minor is a minor $M_A^B$ in which only one of $A$ or $B$ is contiguous. Domino-tiling conjecture. Every semicontiguous minor has an associated domino-tiling region…

Let $L$ be the response matrix of a minimal circular planar network with $m$ edges, and call a minor of $L$ noninterlaced when its row and column index sets are noninterlaced. Base…

Let $P=P(x_1,\ldots,x_{n-1})$ be a symmetric polynomial with positive coefficients that generates a period $1$ seed. Symmetric-polynomial classification conjecture. The only possib…

Let $P=P(x_1,\ldots,x_n)$ be a multilinear polynomial with positive coefficients that generates a period $1$ seed. Reversal-symmetry conjecture. … This predicts reversal symmetry f…

Let $P=P(x_1,\cdots,x_{n-1})$ be an irreducible polynomial in the class used to generate the seed $\mathbf{(x,P)}$, and let $P_0$ be the initial exchange polynomial of that seed. A…

Let ${\mathcal A}_\Gamma$ be a graph LP algebra and let $t_{\mathcal S}$ be a seed. Write ${\mathcal L}(t_{\mathcal S})$ for the Laurent polynomial ring associated with this seed.…

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…