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

0,6

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.

Links

Table of n, a(n) for n=0..15.

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

Adjacent sequences: A124772 A124773 A124774 * A124776 A124777 A124778

Keyword

more,nonn,tabf

Author

Franklin T. Adams-Watters, Nov 06 2006

Status

approved