Permutation classes and polyomino classes with excluded submatrices. (3rd July 2015)

• Record Type: Journal Article
• Authors: BATTAGLINO, DANIELA; BOUVEL, MATHILDE; FROSINI, ANDREA; RINALDI, SIMONE
• Is Part Of: Mathematical structures in computer science. Volume 27:Number 2(2017)
• Page Start: 157
• Page End: 183
• Publication Date: 2015-07-03
• Subjects: Computer science -- Mathematics -- Periodicals; 004.015105
• DOI: 10.1017/S0960129515000250
• Languages: English
• ISSNs: 0960-1295

Abstract

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.