Identifier
Values
[1,0] => [1,1,0,0] => {{1,2}} => 2
[1,0,1,0] => [1,1,0,1,0,0] => {{1,3},{2}} => 5
[1,1,0,0] => [1,1,1,0,0,0] => {{1,2,3}} => 3
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => {{1,4},{2},{3}} => 9
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => {{1,3,4},{2}} => 6
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => {{1,4},{2,3}} => 7
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => {{1,2,4},{3}} => 7
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}} => 4
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}} => 14
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}} => 10
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}} => 11
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}} => 11
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}} => 7
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}} => 12
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}} => 8
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}} => 12
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}} => 12
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}} => 8
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}} => 9
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}} => 9
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}} => 9
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => 5
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}} => 20
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}} => 15
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}} => 16
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}} => 16
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}} => 11
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}} => 17
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}} => 12
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}} => 17
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}} => 17
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}} => 12
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}} => 13
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}} => 13
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}} => 13
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}} => 8
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}} => 18
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}} => 13
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}} => 14
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}} => 14
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}} => 9
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}} => 18
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}} => 13
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}} => 18
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}} => 18
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}} => 13
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}} => 14
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}} => 14
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}} => 14
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}} => 9
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}} => 15
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}} => 10
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}} => 15
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}} => 15
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}} => 10
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}} => 15
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}} => 15
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}} => 15
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}} => 10
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}} => 11
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}} => 11
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}} => 11
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}} => 11
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => 6
[] => [1,0] => {{1}} => 1
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Description
Sum of the maximal elements of the blocks of a set partition.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.