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A124775
Number of unlabeled partially ordered sets associated with compositions in standard order.
2
1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 3, 1, 2, 1, 1
OFFSET
0,6
COMMENTS
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.
EXAMPLE
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
CROSSREFS
Cf. A066099, A124776, A124777, A011782 (row lengths), A000112 (row sums).
Sequence in context: A349574 A168377 A122867 * A140075 A099555 A262082
KEYWORD
more,nonn,tabf
AUTHOR
STATUS
approved