, Volume 11, Issue 3-4, pp 459-470

Dense Packing of Patterns in a Permutation

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Abstract.

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

Received January 2, 2007