6 problems

Let $M$ be a cyclic partial multiplication matrix containing $\ell$ non-empty cells. A coil is a permutation represented by a cyclic sequence of points following the cycle of non-e…

Let $M$ be a finite matrix defining a grid class $\operatorname{Grid}(M)$, and let $G(M)$ be the bipartite graph whose vertices represent the rows and columns of $M$, with an edge…

Let $M$ be a finite matrix whose entries specify the monotone permutation classes placed in the cells of a grid, and let $\operatorname{Grid}(M)$ denote the resulting grid class. A…

A monotone grid class is a permutation class defined by a finite grid whose nonempty cells contain monotone permutations. Huczynska–Vatter's conjecture. Every monotone grid class i…

Fine-set conjecture. For every one-column grid class ${\mathcal G}^{\mathbf{v}}$, the set

Finite-basis conjecture for monotone grid classes. Every monotone grid class has a finite basis. The source notes that only limited cases are known, including skew-merged permutati…