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Search: id:A124776
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| A124776 |
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Number of labeled partially ordered sets associated with compositions in standard order. |
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+0
3
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| 1, 1, 1, 2, 1, 9, 3, 6, 1, 28, 54, 60, 4, 36, 12, 24
(list; graph; listen)
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OFFSET
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0,4
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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 labeled respectively
in 12, 24, and 24 ways, so a(11) = 12+24+24 = 60.
..O..*O..*..O
..|..*|..*./|
..O..*O..*O.|
./.\.*|..*|.|
O...O*O.O*O.O
The table starts:
1
1
1 2
1 9 3 6
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CROSSREFS
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Cf. A066099, A124775, A124777, A011782 (row lengths), A001035 (row sums).
Sequence in context: A021460 A090884 A095888 this_sequence A099285 A124905 A021086
Adjacent sequences: A124773 A124774 A124775 this_sequence A124777 A124778 A124779
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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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