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Permutation classes and polyomino classes with excluded submatrices

Published online by Cambridge University Press:  03 July 2015

DANIELA BATTAGLINO ,
MATHILDE BOUVEL ,
ANDREA FROSINI  and
SIMONE RINALDI
DANIELA BATTAGLINO
Affiliation:
Dipartimento di Ingegneria dell'Informazione e Scienza Matematiche, Via Roma, 56, 53100, Siena, Italy Email: battaglino3@unisi.it, rinaldi@unisi.it
MATHILDE BOUVEL
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland Email: mathilde.bouvel@math.uzh.ch
ANDREA FROSINI
Affiliation:
Dipartimento di Matematica e Informatica, viale Morgagni 67, 50134, Firenze, Italy Email: andrea.frosini@unifi.it
SIMONE RINALDI
Affiliation:
Dipartimento di Ingegneria dell'Informazione e Scienza Matematiche, Via Roma, 56, 53100, Siena, Italy Email: battaglino3@unisi.it, rinaldi@unisi.it
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 2: Special Issue: XIV ICTCS , February 2017 , pp. 157 - 183
Copyright
Copyright © Cambridge University Press 2015 

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