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Permutations Containing Many Patterns
M.H. Albert1, Micah Coleman2, Ryan Flynn2, and Imre Leader3
1Department of Computer Science, University of Otago, PO Box 56, Dunedin, New Zealand
2Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
mcoleman@math.ufl.edu, ryflynn@ufl.edu
3Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB2 1TN, U.K.
Annals of Combinatorics 11 (3-4) p.265-270 September, 2007
AMS Subject Classification: 05A05, 05A16, 05D40
It is shown that the maximum number of patterns that can occur in a permutation of length n is asymptotically 2n. This significantly improves a previous result of Coleman.
Keywords: permutation patterns, probabilistic counting


1. M. Coleman, An answer to a question by Wilf on packing distinct patterns in a permutation, Electron. J. Combin. 11 (1) (2004) #N8.

2. H. Eriksson, K. Eriksson, S. Linusson, and J. W¨astlund, Dense packing of patterns in a permutation, Ann. Combin., to appear, http://www.i3s.unice.fr/fpsac/FPSAC02/articles.html.