Vol. 9, No. 5, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
Note on superpatterns

Daniel Gray and Hua Wang

Vol. 9 (2016), No. 5, 797–804
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 k2e2. 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