Vol. 9, No. 5, 2016

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Note on superpatterns

Daniel Gray and Hua Wang

Vol. 9 (2016), No. 5, 797–804

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.

superpatterns, colored permutations
Mathematical Subject Classification 2010
Primary: 05A05
Received: 1 May 2015
Revised: 10 September 2015
Accepted: 17 September 2015
Published: 25 August 2016

Communicated by Joshua Cooper
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