Identifier
Values
[1,0] => [1,0] => [1,0] => 0
[1,0,1,0] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,0,0] => [1,1,0,0] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[1,0,1,1,0,0] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,1,0,0,1,0] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,1,1,0,0,0] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
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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
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.