Annals of Combinatorics

, Volume 11, Issue 3, pp 459–470

Dense Packing of Patterns in a Permutation

  • Henrik Eriksson
  • Kimmo Eriksson
  • Svante Linusson
  • Johan Wästlund
Article

DOI: 10.1007/s00026-007-0329-7

Cite this article as:
Eriksson, H., Eriksson, K., Linusson, S. et al. Ann. Comb. (2007) 11: 459. doi:10.1007/s00026-007-0329-7

Abstract.

We study the length Lk of the shortest permutation containing all patterns of length k. We establish the bounds e−2k2Lk ≤ (2/3 + o(1))k2. We also prove that as k → ∞, there are permutations of length (1/4 + o(1))k2 containing almost all patterns of length k.

AMS Subject Classification:

05A05 05D40 

Keywords:

pattern containment permutation statistic 

Copyright information

© Birkhaueser 2007

Authors and Affiliations

  • Henrik Eriksson
    • 1
  • Kimmo Eriksson
    • 2
  • Svante Linusson
    • 3
  • Johan Wästlund
    • 4
  1. 1.NADAKTHStockholmSweden
  2. 2.IMAMälardalens högskolaVästeråsSweden
  3. 3.Department of MathematicsKTHStockholmSweden
  4. 4.MaILinköpings universitetLinköpingSweden

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