The permutation class Av(4213,2143)

We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its left. We use this characterisation to establis...

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Bibliographic Details
Published inDiscrete mathematics and theoretical computer science Vol. 18 no. 2, Permutation...; no. Permutation Patterns
Main Author Bevan, David
Format Journal Article
LanguageEnglish
Published Discrete Mathematics & Theoretical Computer Science 04.04.2017
Subjects
05a05, 05a15, 05a16
mathematics - combinatorics
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Summary:We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its left. We use this characterisation to establish the generating function enumerating these permutations. We also investigate the properties of a typical large permutation in the class and prove that if a large permutation that avoids 4213 and 2143 is chosen uniformly at random, then it is more likely than not to avoid 2413 as well.
ISSN:1365-8050
1365-8050
DOI:10.46298/dmtcs.1309