Identifier
Values
[1,1] => [1,0,1,0] => {{1},{2}} => {{1},{2}} => 1
[2] => [1,1,0,0] => {{1,2}} => {{1,2}} => 0
[1,1,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => {{1},{2},{3}} => 3
[1,2] => [1,0,1,1,0,0] => {{1},{2,3}} => {{1,3},{2}} => 0
[2,1] => [1,1,0,0,1,0] => {{1,2},{3}} => {{1,2},{3}} => 1
[3] => [1,1,1,0,0,0] => {{1,2,3}} => {{1,2,3}} => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => 6
[1,1,2] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => {{1,4},{2},{3}} => 1
[1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => {{1,3},{2},{4}} => 2
[1,3] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1,3},{2,4}} => 1
[2,1,1] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => {{1,2},{3},{4}} => 3
[2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2,4},{3}} => 0
[3,1] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => {{1,2,3},{4}} => 1
[4] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}} => {{1,2,3,4}} => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => 10
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => {{1,5},{2},{3},{4}} => 3
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => {{1,4},{2},{3},{5}} => 4
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1,4},{2,5},{3}} => 1
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => {{1,3},{2},{4},{5}} => 5
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,3},{2,5},{4}} => 2
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1,3},{2,4},{5}} => 3
[1,4] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,3,5},{2,4}} => 0
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}} => 6
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => {{1,2,5},{3},{4}} => 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1,2,4},{3},{5}} => 2
[2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,4},{3,5}} => 1
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => {{1,2,3},{4},{5}} => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2,3,5},{4}} => 0
[4,1] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => {{1,2,3,4},{5}} => 1
[5] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => {{1,2,3,4,5}} => 0
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => 15
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => {{1,6},{2},{3},{4},{5}} => 6
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => {{1,5},{2},{3},{4},{6}} => 7
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => {{1,5},{2,6},{3},{4}} => 2
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => {{1,4},{2},{3},{5},{6}} => 8
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,4},{2,6},{3},{5}} => 3
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1,4},{2,5},{3},{6}} => 4
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,4},{2,5},{3,6}} => 3
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => 9
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1,3},{2,6},{4},{5}} => 4
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1,3},{2,5},{4},{6}} => 5
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,6},{2,5},{4}} => 0
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1,3},{2,4},{5},{6}} => 6
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,6},{2,4},{5}} => 1
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1,3,5},{2,4},{6}} => 2
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,3,5},{2,4,6}} => 1
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6}} => 10
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => {{1,2,6},{3},{4},{5}} => 3
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => {{1,2,5},{3},{4},{6}} => 4
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2,5},{3,6},{4}} => 1
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1,2,4},{3},{5},{6}} => 5
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4},{3,6},{5}} => 2
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2,4},{3,5},{6}} => 3
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,6},{3,5}} => 0
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => {{1,2,3},{4},{5},{6}} => 6
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => {{1,2,3,6},{4},{5}} => 1
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1,2,3,5},{4},{6}} => 2
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5},{4,6}} => 1
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => {{1,2,3,4},{5},{6}} => 3
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2,3,4,6},{5}} => 0
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => {{1,2,3,4,5},{6}} => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}} => 0
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => 21
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 10
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => {{1,6},{2},{3},{4},{5},{7}} => 11
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => {{1,6},{2,7},{3},{4},{5}} => 4
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}} => 12
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,5},{2,7},{3},{4},{6}} => 5
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => {{1,5},{2,6},{3},{4},{7}} => 6
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1,5},{2,6},{3,7},{4}} => 3
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}} => 13
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1,4},{2,7},{3},{5},{6}} => 6
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1,4},{2,6},{3},{5},{7}} => 7
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4},{2,6},{3,7},{5}} => 4
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => {{1,4},{2,5},{3},{6},{7}} => 8
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4},{2,5},{3,7},{6}} => 5
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1,4},{2,5},{3,6},{7}} => 6
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,4,7},{2,5},{3,6}} => 1
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}} => 14
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1,3},{2,7},{4},{5},{6}} => 7
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1,3},{2,6},{4},{5},{7}} => 8
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,3,7},{2,6},{4},{5}} => 1
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1,3},{2,5},{4},{6},{7}} => 9
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,7},{2,5},{4},{6}} => 2
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,6},{2,5},{4},{7}} => 3
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,6},{2,5},{4,7}} => 2
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => {{1,3},{2,4},{5},{6},{7}} => 10
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,3,7},{2,4},{5},{6}} => 3
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,6},{2,4},{5},{7}} => 4
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,6},{2,4,7},{5}} => 1
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1,3,5},{2,4},{6},{7}} => 5
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,5},{2,4,7},{6}} => 2
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1,3,5},{2,4,6},{7}} => 3
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,3,5,7},{2,4,6}} => 0
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => {{1,2},{3},{4},{5},{6},{7}} => 15
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => {{1,2,7},{3},{4},{5},{6}} => 6
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => {{1,2,6},{3},{4},{5},{7}} => 7
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => {{1,2,6},{3,7},{4},{5}} => 2
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => {{1,2,5},{3},{4},{6},{7}} => 8
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2,5},{3,7},{4},{6}} => 3
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => {{1,2,5},{3,6},{4},{7}} => 4
>>> Load all 131 entries. <<<
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,5},{3,6},{4,7}} => 3
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => 9
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2,4},{3,7},{5},{6}} => 4
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4},{3,6},{5},{7}} => 5
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,7},{3,6},{5}} => 0
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1,2,4},{3,5},{6},{7}} => 6
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,7},{3,5},{6}} => 1
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,6},{3,5},{7}} => 2
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,6},{3,5,7}} => 1
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7}} => 10
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => {{1,2,3,7},{4},{5},{6}} => 3
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => {{1,2,3,6},{4},{5},{7}} => 4
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => {{1,2,3,6},{4,7},{5}} => 1
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => 5
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5},{4,7},{6}} => 2
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5},{4,6},{7}} => 3
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,7},{4,6}} => 0
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7}} => 6
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => {{1,2,3,4,7},{5},{6}} => 1
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4,6},{5},{7}} => 2
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6},{5,7}} => 1
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => {{1,2,3,4,5},{6},{7}} => 3
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5,7},{6}} => 0
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => {{1,2,3,4,5,6},{7}} => 1
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}} => 0
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,8},{5,7}} => 0
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7},{6,8}} => 1
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => 0
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => {{1,2,3,4,5,6,7},{8}} => 1
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}} => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The lcs statistic of a set partition.
Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$.
According to [1, Definition 3], a lcs (left-closer-smaller) of $S$ is given by a pair $i > j$ such that $j = \operatorname{max} B_b$ and $i \in B_a$ for $a > b$.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
dual major index to intertwining number
Description
A bijection sending the dual major index of a set partition to its intertwining number.
More precisely, St000493The los statistic of a set partition.$(P) = $St000490The intertwining number of a set partition.$(\phi(P))$ for all set partitions $P$.
This is the inverse of Mp00171intertwining number to dual major index.