This article introduces an analogue of permutation classes in the context of polyominoes. For both permutation classes and polyomino classes, we present an original way of characterizing them by avoidance constraints (namely, with excluded submatrices) and we discuss how canonical such a description by submatrix-avoidance can be. We provide numerous examples of permutation and polyomino classes which may be defined and studied from the submatrix-avoidance point of view, and conclude with various directions for future research on this topic.

Battaglino, D., Bouvel, M., Frosini, A., Rinaldi, S. (2017). Permutation classes and polyomino classes with excluded submatrices. MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 27(2), 157-183 [10.1017/S0960129515000250].

Permutation classes and polyomino classes with excluded submatrices

Battaglino, Daniela;Bouvel, Mathilde;Rinaldi, Simone
2017-01-01

Abstract

This article introduces an analogue of permutation classes in the context of polyominoes. For both permutation classes and polyomino classes, we present an original way of characterizing them by avoidance constraints (namely, with excluded submatrices) and we discuss how canonical such a description by submatrix-avoidance can be. We provide numerous examples of permutation and polyomino classes which may be defined and studied from the submatrix-avoidance point of view, and conclude with various directions for future research on this topic.
2017
Battaglino, D., Bouvel, M., Frosini, A., Rinaldi, S. (2017). Permutation classes and polyomino classes with excluded submatrices. MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 27(2), 157-183 [10.1017/S0960129515000250].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1035011