Identifier
Values
[1,0] => [1,0] => 0
[1,0,1,0] => [1,0,1,0] => 1
[1,1,0,0] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [1,0,1,0,1,0] => 2
[1,0,1,1,0,0] => [1,0,1,0,1,0] => 2
[1,1,0,0,1,0] => [1,0,1,0,1,0] => 2
[1,1,0,1,0,0] => [1,0,1,0,1,0] => 2
[1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
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 number of upper interactions of a Dyck path.
An upper interaction in a Dyck path is defined as the occurrence of a factor $A^{k}$$B^{k}$ for any ${k ≥ 1}$, where ${A}$ is a down-step and ${B}$ is a up-step.
Map
peeling map
Description
Send a Dyck path to its peeled Dyck path.