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A321162
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Maximum number of unbordered conjugates for a binary word of length n.
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1
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1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 9, 9, 10, 10, 11, 12, 12, 12, 13, 13, 14, 14, 15, 16, 16, 16, 17, 17, 18, 18, 19
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Two words are conjugate if one is a cyclic shift of the other, such as "enlist" and "listen". A word w is bordered if it has a nonempty prefix that is also a suffix (and not equal to w), such as the word "entanglement". Harju and Nowotka show that for length-n binary words, at most n/2 unbordered conjugates are possible.
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LINKS
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EXAMPLE
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For n = 10, the word 0000101101 has 10 distinct conjugates, but only 4 of them are unbordered: {0000101101, 1011010000, 1101000010, 0100001011}. This is maximum for n = 10.
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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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EXTENSIONS
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STATUS
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approved
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