Note on superpatterns

Gray, Daniel; Wang, Hua

doi:10.2140/involve.2016.9.797

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Note on superpatterns

Daniel Gray and Hua Wang

Vol. 9 (2016), No. 5, 797–804

DOI: 10.2140/involve.2016.9.797

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 $k^{2} ∕ e^{2}$ . 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.

Keywords

superpatterns, colored permutations

Mathematical Subject Classification 2010

Primary: 05A05

Milestones

Received: 1 May 2015

Revised: 10 September 2015

Accepted: 17 September 2015

Published: 25 August 2016

Communicated by Joshua Cooper

Authors

Daniel Gray
Department of Mathematics University of Florida Gainesville, FL 32611 United States

Hua Wang
Department of Mathematical Sciences Georgia Southern University Statesboro, GA 30460 United States

Vol. 9, No. 5, 2016