Decomposing simple permutations, with enumerative consequences

Authors:
Robert Brignall;Sophie Huczynska;Vincent Vatter
Affiliations:
University of Bristol, Department of Mathematics, Royal Fort Annexe University Walk, Bristol, England, UK;University of St Andrews Mathematical Institute, School of Mathematics and Statistics, North Haugh St Andrews, Fife, Scotland, UK;University of St Andrews Mathematical Institute, School of Mathematics and Statistics, North Haugh St Andrews, Fife, Scotland, UK
Venue:
Combinatorica
Year:
2008

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Abstract

We prove that every sufficiently long simple permutation contains two long almost disjoint simple subsequences, and then we show how this result has enumerative consequences. For example, it implies that, for any r, the number of permutations with at most r copies of 132 has an algebraic generating function (this was previously proved, constructively, by Bóna and (independently) Mansour and Vainshtein).