Identifier
Values
[1,0] => [1] => [1,0] => [1,0] => 0
[1,0,1,0] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,0,0] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,1,0,0,1,0] => [2,1,3] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,1,0,1,0,0] => [2,3,1] => [1,1,0,1,0,0] => [1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => [3,2,1] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [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] => [1,2,4,3] => [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] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [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] => [2,1,4,3] => [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] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [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] => [1,2,3,5,4] => [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] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [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] => [2,1,3,5,4] => [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] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [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] => [1,2,3,4,6,5] => [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] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [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
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [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] => [2,1,3,4,6,5] => [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] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [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] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
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Description
Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. Then the statistic gives the vector space dimension of the second Ext-group between X and the regular module.
For the first 196 values, the statistic also gives the number of indecomposable non-projective modules $X$ such that $\tau(X)$ has codominant dimension equal to one and projective dimension equal to one.
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.