Dense Packing of Patterns in a Permutation
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- Eriksson, H., Eriksson, K., Linusson, S. et al. Ann. Comb. (2007) 11: 459. doi:10.1007/s00026-007-0329-7
We study the length Lk of the shortest permutation containing all patterns of length k. We establish the bounds e−2k2 < Lk ≤ (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.