$2× 2$ monotone grid classes are finitely based - Michael Albert; Robert Brignall (Discrete Mathematics & Theoretical Computer Science, 2016)
In this note, we prove that all $2 × 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a slightly more general result about certain $2 × 2$ (generalized) grid classes having two monotone cells in the same row.