English

Permutation classes and polyomino classes with excluded submatrices

Combinatorics 2015-07-08 v2

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.

Keywords

Cite

@article{arxiv.1402.2260,
  title  = {Permutation classes and polyomino classes with excluded submatrices},
  author = {Daniela Battaglino and Mathilde Bouvel and Andrea Frosini and Simone Rinaldi},
  journal= {arXiv preprint arXiv:1402.2260},
  year   = {2015}
}

Comments

Second version taking into account referees' suggestions, and correcting some inaccuracies of the first version

R2 v1 2026-06-22T03:05:05.040Z