Title

Note on Superpatterns

Document Type

Article

Publication Date

8-25-2016

Publication Title

Involve

DOI

10.2140/involve.2016.9.797

ISSN

1944-4176

Abstract

Given a set P of permutations, a P-superpattern is a permutation that contains every permutation in P as a pattern. The study of the minimum length of a superpattern has been of interest. For P being the set of all permutations of a given length, bounds on the minimum length have been improved over the years, and the minimum length is conjectured to be asymptotic with k2/e2. Similar questions have been considered for the set of layered permutations. We consider superpatterns with respect to packing colored permutations or multiple copies of permutations. Some simple but interesting observations will be presented. We also propose a few questions.

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