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Search: id:A115621
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| A115621 |
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Signature of partitions in Abramowitz and Stegun order. |
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+0
10
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| 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 4, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 5, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 3, 2, 2, 1, 4, 6, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 5, 7, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 1, 1, 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. [1,1,3,4,4] = [1^2,3^1,4^2], so the repetition factors are 2,1,2, making the signature [1,2,2] = [1,2^2].
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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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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[1]; [1], [2]; [1], [1,1], [3]; [1], [1,1], [2], [1,2], [4]; ...
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CROSSREFS
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Cf. A036036, A113787, A115622, part counts A103921, row counts A000070.
Sequence in context: A137844 A079229 A160267 this_sequence A077565 A115561 A115622
Adjacent sequences: A115618 A115619 A115620 this_sequence A115622 A115623 A115624
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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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