Identifier
Values
[1,0] => [1,0] => 1
[1,0,1,0] => [1,1,0,0] => 2
[1,1,0,0] => [1,0,1,0] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,0] => 1
[1,0,1,1,0,0] => [1,1,1,0,0,0] => 3
[1,1,0,0,1,0] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,0] => [1,0,1,0,1,0] => 1
[1,1,1,0,0,0] => [1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
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Description
The number of centered tunnels of a Dyck path.
A tunnel is a pair (a,b) where a is the position of an open parenthesis and b is the position of the matching close parenthesis. If a+b==n then the tunnel is called centered.
Map
inverse promotion
Description
The inverse promotion of a Dyck path.
This is the bijection obtained by applying the inverse of Schützenberger's promotion to the corresponding two rowed standard Young tableau.