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Search: id:A136094
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| A136094 |
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a(n) is the shortest substring containing all the permutations of {1,...,n} as (not necessarily adjacent) substrings. |
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2
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| 1, 121, 1232123, 123412314213, 123454321234543212345, 1234565432123456543212345654321, 1234567654321234567654321234567654321234567
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In case of a tie we pick the earliest example.
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REFERENCES
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P. J. Koutas and T. C. Hu, Shortest String Containing All Permutations, Discrete Mathematics, Vol. 11, 1975, pp. 125-132.
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LINKS
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Hu, T. C. and Koutas, P. J., Shortest Substing.
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EXAMPLE
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a(4)=1234321234321 because it contains all the permutation 1234((1234)321234321), 1243((12)3(43)21234321), 1324((1)2(3)4321(2)3(4)321), 1342((1)2(34)3(2)1234321), 1423, 1432, 2134, 2143, 2314, etc. The brackets indicate where the permutation is present.
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CROSSREFS
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Adjacent sequences: A136091 A136092 A136093 this_sequence A136095 A136096 A136097
Sequence in context: A135825 A082215 A123179 this_sequence A053885 A068490 A077735
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KEYWORD
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nonn
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AUTHOR
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Aniruddha Das (hi.annie.pal(AT)gmail.com), May 10 2008
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), May 16 2008
a(4) corrected from 1234321234321 to 123412314213 by Bridget Tenner (bridget(AT)math.depaul.edu), Apr 21 2009, who also confirms a(1), a(2), a(3) and a(5).
The entries a(6) and a(7) should be checked! - N. J. A. Sloane, May 08 2009
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