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Dense Packing of Patterns in a Permutation

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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.

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Correspondence to Henrik Eriksson.

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Received January 2, 2007

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Eriksson, H., Eriksson, K., Linusson, S. et al. Dense Packing of Patterns in a Permutation. Ann. Comb. 11, 459–470 (2007). https://doi.org/10.1007/s00026-007-0329-7

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  • DOI: https://doi.org/10.1007/s00026-007-0329-7

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