## Albert, Michael and Brignall, Robert - $2\times 2$ monotone grid classes are finitely based

dmtcs:1325 - Discrete Mathematics & Theoretical Computer Science, February 11, 2016, Vol. 18 no. 2, Permutation Patterns 2015
$2\times 2$ monotone grid classes are finitely based

Authors: Albert, Michael and Brignall, Robert

In this note, we prove that all $2 \times 2$ 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 $2 \times 2$ (generalized) grid classes having two monotone cells in the same row.

Volume: Vol. 18 no. 2, Permutation Patterns 2015
Section: Permutation Patterns
Published on: February 11, 2016
Submitted on: February 11, 2016
Keywords: Mathematics - Combinatorics,05A05