Identifier
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,0,1,0] => 1
[1,1,0,0] => [2,1] => [2,1] => [1,1,0,0] => 0
[1,0,1,1,0,0] => [1,3,2] => [2,3,1] => [1,1,0,1,0,0] => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,0] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [3,5,2,4,1,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [3,6,2,4,5,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [2,1,4,3,7,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [3,2,5,4,1,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [3,2,6,4,5,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [2,1,6,3,4,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [2,1,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [3,2,6,1,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [3,2,7,1,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [3,2,1,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [3,2,1,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [4,2,3,6,1,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,2,3,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [4,2,3,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [4,2,3,1,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [5,2,3,4,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [5,2,3,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [5,2,3,7,1,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [6,2,3,7,1,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [5,2,3,1,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [4,2,6,1,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [4,2,7,1,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [5,2,7,1,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [6,2,7,1,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [5,2,1,4,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [4,2,1,6,3,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [4,2,1,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
>>> Load all 135 entries. <<<
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [5,2,1,7,3,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [1,3,2,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [4,2,1,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [2,4,3,1,6,5,7] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [2,4,3,1,7,5,6] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [2,5,3,4,7,1,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [2,5,3,4,1,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 12
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [2,6,3,4,5,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [2,6,3,4,7,1,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [5,1,3,4,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [4,1,3,6,2,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [4,1,3,7,2,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [5,1,3,7,2,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [2,5,3,1,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [4,1,3,2,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [3,1,6,2,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [3,1,7,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [3,1,2,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [4,1,6,2,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [4,1,7,2,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [5,1,7,2,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [2,5,1,4,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [3,1,2,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [3,1,2,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [2,4,1,3,7,5,6] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
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
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
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.