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Ars Combinatoria

  • Research article

Shape and Pattern Containment of Separable Permutations

Andrew Crites1, Greta Panova2, Gregory S.Warrington3
1Dept. of Mathematics, University of Washington, Seattle, WA 98195,
2Dept. of Mathematics, University of California, Los Angeles Los Angeles, CA $0095
3Dept. of Mathematics and Statistics, University of Vermont, Burlington, VT 05401,
  • Published: 31/07/2016

Abstract

A word has a shape determined by its image under the Robinson-Schensted-Knuth correspondence. We show that when a word \(w\) contains a separable (i.e., \(3142\)- and \(2413\)-avoiding) permutation \(\sigma\) as a pattern, the shape of \(w\) contains the shape of \(\sigma\). As an application, we exhibit lower bounds for the lengths of supersequences of sets containing separable permutations.

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Citation
Andrew Crites, Greta Panova, Gregory S.Warrington. Shape and Pattern Containment of Separable Permutations[J], Ars Combinatoria, Volume 128. 103-116. .