A124777 -id:A124777 - cp's OEIS frontend

A124775 Number of unlabeled partially ordered sets associated with compositions in standard order.

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 3, 1, 2, 1, 1

Offset: 0

Franklin T. Adams-Watters, Nov 06 2006

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.

			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

Cf. A066099, A124776, A124777, A011782 (row lengths), A000112 (row sums).

A124776 Number of labeled partially ordered sets associated with compositions in standard order.

Original entry on oeis.org

1, 1, 1, 2, 1, 9, 3, 6, 1, 28, 54, 60, 4, 36, 12, 24

Offset: 0

Franklin T. Adams-Watters, Nov 06 2006

The standard order of compositions is given by A066099.

			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

Cf. A066099, A124775, A124777, A011782 (row lengths), A001035 (row sums).

cp's OEIS Frontend

A124775 Number of unlabeled partially ordered sets associated with compositions in standard order.

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