#### Title

Plane Binary Trees and Superpatterns for Layered Permutations

#### Document Type

Presentation

#### Publication Date

3-5-2016

#### Abstract

Let P be a set of permutation patterns. If τ is a permutation that contains every element of P as a pattern, then we say that τ is a P -superpattern. Since Arratia coined the term in 1999, there have been several investigations into the length of the shortest Sk-superpattern, where Sk is the set of permutations of length k. Here, we will construct superpatterns for layered permutations of length k and explore an interesting connection between this set of superpatterns and plane binary trees on k vertices.

#### Sponsorship/Conference/Institution

Spring Southeastern Sectional Meeting of the American Mathematical Society (AMS)

#### Location

Athens, GA

#### Recommended Citation

Gray, Daniel.
2016.
"Plane Binary Trees and Superpatterns for Layered Permutations."
*Mathematical Sciences Faculty Presentations*.
Presentation 109.

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/109