Simple permutations: Decidability and unavoidable substructures

Authors:
Robert Brignall;Nik Rukuc;Vincent Vatter
Affiliations:
University of St Andrews, School of Mathematics and Statistics, St Andrews, Fife, KY16 9SS, UK;University of St Andrews, School of Mathematics and Statistics, St Andrews, Fife, KY16 9SS, UK;University of St Andrews, School of Mathematics and Statistics, St Andrews, Fife, KY16 9SS, UK
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

We prove that it is decidable whether a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains an alternation or oscillation of length k.