Substitution-closed pattern classes

Authors:
M. D. Atkinson;N. Ruškuc;Rebecca Smith
Affiliations:
Department of Computer Science, University of Otago, New Zealand;School of Mathematics and Statistics, University of St. Andrews, UK;Department of Mathematics, SUNY Brockport, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 7
Cited 0

On the closure of graphs under substitution

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Extension of hereditary classes with substitutions

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A Characterization of Domination Reducible Graphs

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All minimal prime extensions of hereditary classes of graphs

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Simple permutations: Decidability and unavoidable substructures

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Simple permutations and algebraic generating functions

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Decomposing simple permutations, with enumerative consequences

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Abstract

The substitution closure of a pattern class is the class of all permutations obtained by repeated substitution. The principal pattern classes (those defined by a single restriction) whose substitution closure can be defined by a finite number of restrictions are classified by listing them as a set of explicit families.