Superpatterns and Generalizations of Layered Permutations

Presenters/Authors

Daniel Gray, Georgia Southern UniversityFollow
Matthew R. Just, Georgia Southern UniversityFollow
Hua Wang, Georgia Southern UniversityFollow

Document Type

Presentation

Presentation Date

10-17-2015

Abstract or Description

In the study of permutation patterns, superpatterns are permutations that contain many patterns at least once. For a set P of permutations, we say that a permutation σ is a P -superpattern if it contains every permutation in P , and we denote by sp(P ) the shortest length of all P -superpatterns. When P is the set of layered permutations of length k, it has been shown that sp(P ) = Θ(k log(k)). The notion of superpatterns can be extended naturally to words. In this talk, we explore some generalizations of layered permutations to ‘layered words’ and seek to find shortest lengths for superpatterns containing these sets.

Sponsorship/Conference/Institution

Midwestern Conference on Combinatorics and Combinatorial Computing (MCCCC)

Location

Charleston, SC

Recommended Citation

Gray, Daniel, Matthew R. Just, Hua Wang. 2015. "Superpatterns and Generalizations of Layered Permutations." Department of Mathematical Sciences Faculty Presentations. Presentation 111.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/111