cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Views

Author

Franklin T. Adams-Watters, Nov 06 2006

Keywords

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); 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

Crossrefs

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

A124777 Number of naturally labeled partially ordered sets associated with compositions in standard order.

Original entry on oeis.org

1, 1, 1, 1, 1, 4, 1, 1, 1, 11, 13, 8, 1, 4, 1, 1
Offset: 0

Views

Author

Franklin T. Adams-Watters, Nov 06 2006

Keywords

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); these can be naturally labeled
respectively in 1, 4 and 3 ways, so a(11) = 1+4+3 = 8.
..O..*O..*..O
..|..*|..*./|
..O..*O..*O.|
./.\.*|..*|.|
O...O*O.O*O.O
The table starts:
1
1
1 1
1 4 1 1

Crossrefs

Cf. A066099, A124775, A124776, A011782 (row lengths), A006455 (row sums).
Showing 1-2 of 2 results.

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