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Search: id:A124777
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| A124777 |
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Number of naturally labeled partially ordered sets associated with compositions in standard order. |
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+0
3
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| 1, 1, 1, 1, 1, 4, 1, 1, 1, 11, 13, 8, 1, 4, 1, 1
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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The standard order of compositions is given by A066099.
The k-th term of the composition is the number of objects with rank k. The rank of an object is one more than the maximum rank of any smaller object in the ordering (1 for a minimal element), or equivalently the size of the largest chain of which the object is the maximal element.
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EXAMPLE
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Composition number 11 is 2,1,1; there are 3 partial orders
associated with this (shown below); these can be naturally labeled
respectively in 1, 4, and 3 ways, so a(11) = 1+4+3 = 8.
..O..*O..*..O
..|..*|..*./|
..O..*O..*O.|
./.\.*|..*|.|
O...O*O.O*O.O
The table starts:
1
1
1 1
1 4 1 1
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CROSSREFS
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Cf. A066099, A124775, A124776, A011782 (row lengths), A006455 (row sums).
Sequence in context: A113196 A037291 A063851 this_sequence A112622 A119591 A010125
Adjacent sequences: A124774 A124775 A124776 this_sequence A124778 A124779 A124780
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KEYWORD
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more,nonn,tabf
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
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