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A342474
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Minimal length of a permutation containing every permutation of length n as a pattern.
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0
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OFFSET
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1,2
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COMMENTS
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These permutations are sometimes called "superpatterns".
A upper bound is ceiling((n^2+1)/2), see Engen and Vatter. A simple lower bound is n^2/e^2, which has been improved to 1.000076 n^2/e^2 by Chroman, Kwan, and Singhal.
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LINKS
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EXAMPLE
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For n=3, the permutation 25314 contains all 6 permutations of length 3, but no shorter permutation does, so a(3)=5.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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