David Bevan - The permutation class Av(4213,2143)

dmtcs:1309 - Discrete Mathematics & Theoretical Computer Science, April 4, 2017, Vol. 18 no. 2, Permutation Patterns 2015 - https://doi.org/10.46298/dmtcs.1309
The permutation class Av(4213,2143)

Authors: David Bevan

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.

Volume: Vol. 18 no. 2, Permutation Patterns 2015
Section: Permutation Patterns
Published on: April 4, 2017
Accepted on: April 4, 2017
Submitted on: April 3, 2017
Keywords: Mathematics - Combinatorics,05A05, 05A15, 05A16


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