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

Author

Franklin T. Adams-Watters, Nov 06 2006

Keywords

• more
• nonn
• tabf

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.

Examples

			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).