Identifier
Values
[1] => [1,0] => [1,0] => [1,0] => 0
[1,2] => [1,0,1,0] => [1,1,0,0] => [1,1,0,0] => 0
[2,1] => [1,1,0,0] => [1,0,1,0] => [1,0,1,0] => 1
[1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,1,1,0,0,0] => 0
[1,3,2] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[2,3,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 0
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0] => 4
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 3
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[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] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 6
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[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] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 6
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 5
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 2
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 4
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 6
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 10
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 12
[1,2,3,6,4,7,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 12
[1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,2,4,6,3,7,5] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,2,4,6,5,7,3] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[1,2,5,3,6,4,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,2,5,3,6,7,4] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
>>> Load all 178 entries. <<<
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,3,4,6,2,7,5] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 9
[1,3,4,6,5,2,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,3,4,6,5,7,2] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 9
[1,3,5,2,6,4,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,4,2,5,6,3,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,4,2,6,3,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,4,2,6,5,3,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,4,3,6,2,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,4,3,6,5,2,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,4,5,2,6,3,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,4,5,2,6,7,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[1,4,5,3,6,2,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,4,5,3,6,7,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
[2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,4,6,3,5,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[2,1,4,6,5,3,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[2,3,1,6,4,7,5] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[2,3,1,6,5,7,4] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[2,3,4,6,1,5,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10
[2,3,4,6,5,1,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10
[2,3,5,1,4,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[2,3,5,1,6,4,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[2,3,5,4,1,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[2,3,5,4,6,1,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[2,4,1,5,3,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,1,6,3,5,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[2,4,1,6,5,3,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[2,4,3,5,1,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,3,6,1,5,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[2,4,3,6,5,1,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[2,4,5,1,6,3,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[2,4,5,3,1,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[2,4,5,3,6,1,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[3,1,4,5,2,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[3,2,4,5,1,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[3,4,1,5,2,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[3,4,1,5,6,2,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[3,4,2,5,1,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[3,4,2,5,6,1,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[3,5,1,2,6,4,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[3,5,1,4,6,2,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[3,5,2,1,6,4,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[3,5,2,4,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[3,5,4,1,6,2,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[3,5,4,2,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[4,1,5,2,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[4,1,5,3,6,2,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[4,2,5,1,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[4,2,5,3,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[4,3,5,1,6,2,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[4,3,5,2,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
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
Cori-Le Borgne involution
Description
The Cori-Le Borgne involution on Dyck paths.
Append an additional down step to the Dyck path and consider its (literal) reversal. The image of the involution is then the unique rotation of this word which is a Dyck word followed by an additional down step. Alternatively, it is the composite $\zeta\circ\mathrm{rev}\circ\zeta^{(-1)}$, where $\zeta$ is Mp00030zeta map.
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.
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.