Geodesic
$2\times 2$ monotone grid classes are finitely based
Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2.

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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. 
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     author = {Albert, Michael and Brignall, Robert},
     title = {$2\times 2$ monotone grid classes are finitely based},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2015-2016},
     doi = {10.46298/dmtcs.1325},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1325/}
}
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Albert, Michael; Brignall, Robert. $2\times 2$ monotone grid classes are finitely based. Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2. doi : 10.46298/dmtcs.1325. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1325/

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