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Search: id:A124775
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| A124775 |
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Number of unlabeled partially ordered sets associated with compositions in standard order. |
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+0
3
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| 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 3, 1, 2, 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), so a(11) = 3.
..O..*O..*..O
..|..*|..*./|
..O..*O..*O.|
./.\.*|..*|.|
O...O*O.O*O.O
The table starts:
1
1
1 1
1 2 1 1
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CROSSREFS
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Cf. A066099, A124776, A124777, A011782 (row lengths), A000112 (row sums).
Sequence in context: A057001 A084097 A122867 this_sequence A140075 A099555 A124530
Adjacent sequences: A124772 A124773 A124774 this_sequence A124776 A124777 A124778
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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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