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Search: id:A115622
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| A115622 |
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Signature of partitions in Mathematica order. |
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+0
5
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| 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 4, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 5, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 3, 2, 2, 4, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 4, 1, 3, 1, 3, 2, 5, 1, 7, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 4, 1, 2, 1, 2, 2, 2
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The signature of a partition is a partition consisting of the repetition factors of the original partition. E.g. [4,4,3,1,1] = [4^2,3^1,1^2], so the repetition factors are 2,1,2, making the signature [2,2,1] = [2^2,1].
The sum (or order) of the signature is the number of parts of the original partition, and the number of parts of the signature is the number of distinct parts of the original partition.
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EXAMPLE
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[1]; [1], [2]; [1], [1,1], [3]; [1], [1,1], [2], [2,1], [4]; ...
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CROSSREFS
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Cf. A080577, A115624, A115621, part counts A115623, row counts A000070.
Sequence in context: A115621 A077565 A115561 this_sequence A108886 A140886 A001492
Adjacent sequences: A115619 A115620 A115621 this_sequence A115623 A115624 A115625
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KEYWORD
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nonn,tabf
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 25 2006
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