Permutation classes and polyomino classes with excluded submatrices

摘要

This article introduces an analogue of permutation classes in the context of polyominoes.rnFor both permutation classes and polyomino classes, we present an original way ofrncharacterizing them by avoidance constraints (namely, with excluded submatrices) and werndiscuss how canonical such a description by submatrix-avoidance can be. We providernnumerous examples of permutation and polyomino classes which may be defined andrnstudied from the submatrix-avoidance point of view, and conclude with various directionsrnfor future research on this topic.