Identifier
Identifier
Values
[1,2] => 2
[2,1] => 1
[1,2,3] => 6
[1,3,2] => 2
[2,1,3] => 3
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 24
[1,2,4,3] => 6
[1,3,2,4] => 8
[1,3,4,2] => 4
[1,4,2,3] => 6
[1,4,3,2] => 2
[2,1,3,4] => 12
[2,1,4,3] => 3
[2,3,1,4] => 8
[2,3,4,1] => 6
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 8
[3,1,4,2] => 4
[3,2,1,4] => 4
[3,2,4,1] => 3
[3,4,1,2] => 4
[3,4,2,1] => 2
[4,1,2,3] => 6
[4,1,3,2] => 2
[4,2,1,3] => 3
[4,2,3,1] => 2
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 120
[1,2,3,5,4] => 24
[1,2,4,3,5] => 30
[1,2,4,5,3] => 12
[1,2,5,3,4] => 24
[1,2,5,4,3] => 6
[1,3,2,4,5] => 40
[1,3,2,5,4] => 8
[1,3,4,2,5] => 20
[1,3,4,5,2] => 12
[1,3,5,2,4] => 8
[1,3,5,4,2] => 4
[1,4,2,3,5] => 30
[1,4,2,5,3] => 12
[1,4,3,2,5] => 10
[1,4,3,5,2] => 6
[1,4,5,2,3] => 12
[1,4,5,3,2] => 4
[1,5,2,3,4] => 24
[1,5,2,4,3] => 6
[1,5,3,2,4] => 8
[1,5,3,4,2] => 4
[1,5,4,2,3] => 6
[1,5,4,3,2] => 2
[2,1,3,4,5] => 60
[2,1,3,5,4] => 12
[2,1,4,3,5] => 15
[2,1,4,5,3] => 6
[2,1,5,3,4] => 12
[2,1,5,4,3] => 3
[2,3,1,4,5] => 40
[2,3,1,5,4] => 8
[2,3,4,1,5] => 30
[2,3,4,5,1] => 24
[2,3,5,1,4] => 8
[2,3,5,4,1] => 6
[2,4,1,3,5] => 15
[2,4,1,5,3] => 6
[2,4,3,1,5] => 10
[2,4,3,5,1] => 8
[2,4,5,1,3] => 6
[2,4,5,3,1] => 4
[2,5,1,3,4] => 12
[2,5,1,4,3] => 3
[2,5,3,1,4] => 8
[2,5,3,4,1] => 6
[2,5,4,1,3] => 3
[2,5,4,3,1] => 2
[3,1,2,4,5] => 40
[3,1,2,5,4] => 8
[3,1,4,2,5] => 20
[3,1,4,5,2] => 12
[3,1,5,2,4] => 8
[3,1,5,4,2] => 4
[3,2,1,4,5] => 20
[3,2,1,5,4] => 4
[3,2,4,1,5] => 15
[3,2,4,5,1] => 12
[3,2,5,1,4] => 4
[3,2,5,4,1] => 3
[3,4,1,2,5] => 20
[3,4,1,5,2] => 12
[3,4,2,1,5] => 10
[3,4,2,5,1] => 8
[3,4,5,1,2] => 12
[3,4,5,2,1] => 6
[3,5,1,2,4] => 8
[3,5,1,4,2] => 4
[3,5,2,1,4] => 4
[3,5,2,4,1] => 3
[3,5,4,1,2] => 4
[3,5,4,2,1] => 2
[4,1,2,3,5] => 30
[4,1,2,5,3] => 12
[4,1,3,2,5] => 10
[4,1,3,5,2] => 6
[4,1,5,2,3] => 12
[4,1,5,3,2] => 4
[4,2,1,3,5] => 15
[4,2,1,5,3] => 6
[4,2,3,1,5] => 10
[4,2,3,5,1] => 8
[4,2,5,1,3] => 6
[4,2,5,3,1] => 4
[4,3,1,2,5] => 10
[4,3,1,5,2] => 6
[4,3,2,1,5] => 5
[4,3,2,5,1] => 4
[4,3,5,1,2] => 6
[4,3,5,2,1] => 3
[4,5,1,2,3] => 12
[4,5,1,3,2] => 4
[4,5,2,1,3] => 6
[4,5,2,3,1] => 4
[4,5,3,1,2] => 4
[4,5,3,2,1] => 2
[5,1,2,3,4] => 24
[5,1,2,4,3] => 6
[5,1,3,2,4] => 8
[5,1,3,4,2] => 4
[5,1,4,2,3] => 6
[5,1,4,3,2] => 2
[5,2,1,3,4] => 12
[5,2,1,4,3] => 3
[5,2,3,1,4] => 8
[5,2,3,4,1] => 6
[5,2,4,1,3] => 3
[5,2,4,3,1] => 2
[5,3,1,2,4] => 8
[5,3,1,4,2] => 4
[5,3,2,1,4] => 4
[5,3,2,4,1] => 3
[5,3,4,1,2] => 4
[5,3,4,2,1] => 2
[5,4,1,2,3] => 6
[5,4,1,3,2] => 2
[5,4,2,1,3] => 3
[5,4,2,3,1] => 2
[5,4,3,1,2] => 2
[5,4,3,2,1] => 1
[1,2,3,4,5,6] => 720
[1,2,3,4,6,5] => 120
[1,2,3,5,4,6] => 144
[1,2,3,5,6,4] => 48
[1,2,3,6,4,5] => 120
[1,2,3,6,5,4] => 24
[1,2,4,3,5,6] => 180
[1,2,4,3,6,5] => 30
[1,2,4,5,3,6] => 72
[1,2,4,5,6,3] => 36
[1,2,4,6,3,5] => 30
[1,2,4,6,5,3] => 12
[1,2,5,3,4,6] => 144
[1,2,5,3,6,4] => 48
[1,2,5,4,3,6] => 36
[1,2,5,4,6,3] => 18
[1,2,5,6,3,4] => 48
[1,2,5,6,4,3] => 12
[1,2,6,3,4,5] => 120
[1,2,6,3,5,4] => 24
[1,2,6,4,3,5] => 30
[1,2,6,4,5,3] => 12
[1,2,6,5,3,4] => 24
[1,2,6,5,4,3] => 6
[1,3,2,4,5,6] => 240
[1,3,2,4,6,5] => 40
[1,3,2,5,4,6] => 48
[1,3,2,5,6,4] => 16
[1,3,2,6,4,5] => 40
[1,3,2,6,5,4] => 8
[1,3,4,2,5,6] => 120
[1,3,4,2,6,5] => 20
[1,3,4,5,2,6] => 72
[1,3,4,5,6,2] => 48
[1,3,4,6,2,5] => 20
[1,3,4,6,5,2] => 12
[1,3,5,2,4,6] => 48
[1,3,5,2,6,4] => 16
[1,3,5,4,2,6] => 24
[1,3,5,4,6,2] => 16
[1,3,5,6,2,4] => 16
[1,3,5,6,4,2] => 8
[1,3,6,2,4,5] => 40
[1,3,6,2,5,4] => 8
[1,3,6,4,2,5] => 20
[1,3,6,4,5,2] => 12
[1,3,6,5,2,4] => 8
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 180
[1,4,2,3,6,5] => 30
[1,4,2,5,3,6] => 72
[1,4,2,5,6,3] => 36
[1,4,2,6,3,5] => 30
[1,4,2,6,5,3] => 12
[1,4,3,2,5,6] => 60
[1,4,3,2,6,5] => 10
[1,4,3,5,2,6] => 36
[1,4,3,5,6,2] => 24
[1,4,3,6,2,5] => 10
[1,4,3,6,5,2] => 6
[1,4,5,2,3,6] => 72
[1,4,5,2,6,3] => 36
[1,4,5,3,2,6] => 24
[1,4,5,3,6,2] => 16
[1,4,5,6,2,3] => 36
[1,4,5,6,3,2] => 12
[1,4,6,2,3,5] => 30
[1,4,6,2,5,3] => 12
[1,4,6,3,2,5] => 10
[1,4,6,3,5,2] => 6
[1,4,6,5,2,3] => 12
[1,4,6,5,3,2] => 4
[1,5,2,3,4,6] => 144
[1,5,2,3,6,4] => 48
[1,5,2,4,3,6] => 36
[1,5,2,4,6,3] => 18
[1,5,2,6,3,4] => 48
[1,5,2,6,4,3] => 12
[1,5,3,2,4,6] => 48
[1,5,3,2,6,4] => 16
[1,5,3,4,2,6] => 24
[1,5,3,4,6,2] => 16
[1,5,3,6,2,4] => 16
[1,5,3,6,4,2] => 8
[1,5,4,2,3,6] => 36
[1,5,4,2,6,3] => 18
[1,5,4,3,2,6] => 12
[1,5,4,3,6,2] => 8
[1,5,4,6,2,3] => 18
[1,5,4,6,3,2] => 6
[1,5,6,2,3,4] => 48
[1,5,6,2,4,3] => 12
[1,5,6,3,2,4] => 16
[1,5,6,3,4,2] => 8
[1,5,6,4,2,3] => 12
[1,5,6,4,3,2] => 4
[1,6,2,3,4,5] => 120
[1,6,2,3,5,4] => 24
[1,6,2,4,3,5] => 30
[1,6,2,4,5,3] => 12
[1,6,2,5,3,4] => 24
[1,6,2,5,4,3] => 6
[1,6,3,2,4,5] => 40
[1,6,3,2,5,4] => 8
[1,6,3,4,2,5] => 20
[1,6,3,4,5,2] => 12
[1,6,3,5,2,4] => 8
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 30
[1,6,4,2,5,3] => 12
[1,6,4,3,2,5] => 10
[1,6,4,3,5,2] => 6
[1,6,4,5,2,3] => 12
[1,6,4,5,3,2] => 4
[1,6,5,2,3,4] => 24
[1,6,5,2,4,3] => 6
[1,6,5,3,2,4] => 8
[1,6,5,3,4,2] => 4
[1,6,5,4,2,3] => 6
[1,6,5,4,3,2] => 2
[2,1,3,4,5,6] => 360
[2,1,3,4,6,5] => 60
[2,1,3,5,4,6] => 72
[2,1,3,5,6,4] => 24
[2,1,3,6,4,5] => 60
[2,1,3,6,5,4] => 12
[2,1,4,3,5,6] => 90
[2,1,4,3,6,5] => 15
[2,1,4,5,3,6] => 36
[2,1,4,5,6,3] => 18
[2,1,4,6,3,5] => 15
[2,1,4,6,5,3] => 6
[2,1,5,3,4,6] => 72
[2,1,5,3,6,4] => 24
[2,1,5,4,3,6] => 18
[2,1,5,4,6,3] => 9
[2,1,5,6,3,4] => 24
[2,1,5,6,4,3] => 6
[2,1,6,3,4,5] => 60
[2,1,6,3,5,4] => 12
[2,1,6,4,3,5] => 15
[2,1,6,4,5,3] => 6
[2,1,6,5,3,4] => 12
[2,1,6,5,4,3] => 3
[2,3,1,4,5,6] => 240
[2,3,1,4,6,5] => 40
[2,3,1,5,4,6] => 48
[2,3,1,5,6,4] => 16
[2,3,1,6,4,5] => 40
[2,3,1,6,5,4] => 8
[2,3,4,1,5,6] => 180
[2,3,4,1,6,5] => 30
[2,3,4,5,1,6] => 144
[2,3,4,5,6,1] => 120
[2,3,4,6,1,5] => 30
[2,3,4,6,5,1] => 24
[2,3,5,1,4,6] => 48
[2,3,5,1,6,4] => 16
[2,3,5,4,1,6] => 36
[2,3,5,4,6,1] => 30
[2,3,5,6,1,4] => 16
[2,3,5,6,4,1] => 12
[2,3,6,1,4,5] => 40
[2,3,6,1,5,4] => 8
[2,3,6,4,1,5] => 30
[2,3,6,4,5,1] => 24
[2,3,6,5,1,4] => 8
[2,3,6,5,4,1] => 6
[2,4,1,3,5,6] => 90
[2,4,1,3,6,5] => 15
[2,4,1,5,3,6] => 36
[2,4,1,5,6,3] => 18
[2,4,1,6,3,5] => 15
[2,4,1,6,5,3] => 6
[2,4,3,1,5,6] => 60
[2,4,3,1,6,5] => 10
[2,4,3,5,1,6] => 48
[2,4,3,5,6,1] => 40
[2,4,3,6,1,5] => 10
[2,4,3,6,5,1] => 8
[2,4,5,1,3,6] => 36
[2,4,5,1,6,3] => 18
[2,4,5,3,1,6] => 24
[2,4,5,3,6,1] => 20
[2,4,5,6,1,3] => 18
[2,4,5,6,3,1] => 12
[2,4,6,1,3,5] => 15
[2,4,6,1,5,3] => 6
[2,4,6,3,1,5] => 10
[2,4,6,3,5,1] => 8
[2,4,6,5,1,3] => 6
[2,4,6,5,3,1] => 4
[2,5,1,3,4,6] => 72
[2,5,1,3,6,4] => 24
[2,5,1,4,3,6] => 18
[2,5,1,4,6,3] => 9
[2,5,1,6,3,4] => 24
[2,5,1,6,4,3] => 6
[2,5,3,1,4,6] => 48
[2,5,3,1,6,4] => 16
[2,5,3,4,1,6] => 36
[2,5,3,4,6,1] => 30
[2,5,3,6,1,4] => 16
[2,5,3,6,4,1] => 12
[2,5,4,1,3,6] => 18
[2,5,4,1,6,3] => 9
[2,5,4,3,1,6] => 12
[2,5,4,3,6,1] => 10
[2,5,4,6,1,3] => 9
[2,5,4,6,3,1] => 6
[2,5,6,1,3,4] => 24
[2,5,6,1,4,3] => 6
[2,5,6,3,1,4] => 16
[2,5,6,3,4,1] => 12
[2,5,6,4,1,3] => 6
[2,5,6,4,3,1] => 4
[2,6,1,3,4,5] => 60
[2,6,1,3,5,4] => 12
[2,6,1,4,3,5] => 15
[2,6,1,4,5,3] => 6
[2,6,1,5,3,4] => 12
[2,6,1,5,4,3] => 3
[2,6,3,1,4,5] => 40
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 30
[2,6,3,4,5,1] => 24
[2,6,3,5,1,4] => 8
[2,6,3,5,4,1] => 6
[2,6,4,1,3,5] => 15
[2,6,4,1,5,3] => 6
[2,6,4,3,1,5] => 10
[2,6,4,3,5,1] => 8
[2,6,4,5,1,3] => 6
[2,6,4,5,3,1] => 4
[2,6,5,1,3,4] => 12
[2,6,5,1,4,3] => 3
[2,6,5,3,1,4] => 8
[2,6,5,3,4,1] => 6
[2,6,5,4,1,3] => 3
[2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => 240
[3,1,2,4,6,5] => 40
[3,1,2,5,4,6] => 48
[3,1,2,5,6,4] => 16
[3,1,2,6,4,5] => 40
[3,1,2,6,5,4] => 8
[3,1,4,2,5,6] => 120
[3,1,4,2,6,5] => 20
[3,1,4,5,2,6] => 72
[3,1,4,5,6,2] => 48
[3,1,4,6,2,5] => 20
[3,1,4,6,5,2] => 12
[3,1,5,2,4,6] => 48
[3,1,5,2,6,4] => 16
[3,1,5,4,2,6] => 24
[3,1,5,4,6,2] => 16
[3,1,5,6,2,4] => 16
[3,1,5,6,4,2] => 8
[3,1,6,2,4,5] => 40
[3,1,6,2,5,4] => 8
[3,1,6,4,2,5] => 20
[3,1,6,4,5,2] => 12
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 4
[3,2,1,4,5,6] => 120
[3,2,1,4,6,5] => 20
[3,2,1,5,4,6] => 24
[3,2,1,5,6,4] => 8
[3,2,1,6,4,5] => 20
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 90
[3,2,4,1,6,5] => 15
[3,2,4,5,1,6] => 72
[3,2,4,5,6,1] => 60
[3,2,4,6,1,5] => 15
[3,2,4,6,5,1] => 12
[3,2,5,1,4,6] => 24
[3,2,5,1,6,4] => 8
[3,2,5,4,1,6] => 18
[3,2,5,4,6,1] => 15
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 6
[3,2,6,1,4,5] => 20
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 15
[3,2,6,4,5,1] => 12
[3,2,6,5,1,4] => 4
[3,2,6,5,4,1] => 3
[3,4,1,2,5,6] => 120
[3,4,1,2,6,5] => 20
[3,4,1,5,2,6] => 72
[3,4,1,5,6,2] => 48
[3,4,1,6,2,5] => 20
[3,4,1,6,5,2] => 12
[3,4,2,1,5,6] => 60
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 48
[3,4,2,5,6,1] => 40
[3,4,2,6,1,5] => 10
[3,4,2,6,5,1] => 8
[3,4,5,1,2,6] => 72
[3,4,5,1,6,2] => 48
[3,4,5,2,1,6] => 36
[3,4,5,2,6,1] => 30
[3,4,5,6,1,2] => 48
[3,4,5,6,2,1] => 24
[3,4,6,1,2,5] => 20
[3,4,6,1,5,2] => 12
[3,4,6,2,1,5] => 10
[3,4,6,2,5,1] => 8
[3,4,6,5,1,2] => 12
[3,4,6,5,2,1] => 6
[3,5,1,2,4,6] => 48
[3,5,1,2,6,4] => 16
[3,5,1,4,2,6] => 24
[3,5,1,4,6,2] => 16
[3,5,1,6,2,4] => 16
[3,5,1,6,4,2] => 8
[3,5,2,1,4,6] => 24
[3,5,2,1,6,4] => 8
[3,5,2,4,1,6] => 18
[3,5,2,4,6,1] => 15
[3,5,2,6,1,4] => 8
[3,5,2,6,4,1] => 6
[3,5,4,1,2,6] => 24
[3,5,4,1,6,2] => 16
[3,5,4,2,1,6] => 12
[3,5,4,2,6,1] => 10
[3,5,4,6,1,2] => 16
[3,5,4,6,2,1] => 8
[3,5,6,1,2,4] => 16
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 6
[3,5,6,4,1,2] => 8
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 40
[3,6,1,2,5,4] => 8
[3,6,1,4,2,5] => 20
[3,6,1,4,5,2] => 12
[3,6,1,5,2,4] => 8
[3,6,1,5,4,2] => 4
[3,6,2,1,4,5] => 20
[3,6,2,1,5,4] => 4
[3,6,2,4,1,5] => 15
[3,6,2,4,5,1] => 12
[3,6,2,5,1,4] => 4
[3,6,2,5,4,1] => 3
[3,6,4,1,2,5] => 20
[3,6,4,1,5,2] => 12
[3,6,4,2,1,5] => 10
[3,6,4,2,5,1] => 8
[3,6,4,5,1,2] => 12
[3,6,4,5,2,1] => 6
[3,6,5,1,2,4] => 8
[3,6,5,1,4,2] => 4
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 3
[3,6,5,4,1,2] => 4
[3,6,5,4,2,1] => 2
[4,1,2,3,5,6] => 180
[4,1,2,3,6,5] => 30
[4,1,2,5,3,6] => 72
[4,1,2,5,6,3] => 36
[4,1,2,6,3,5] => 30
[4,1,2,6,5,3] => 12
[4,1,3,2,5,6] => 60
[4,1,3,2,6,5] => 10
[4,1,3,5,2,6] => 36
[4,1,3,5,6,2] => 24
[4,1,3,6,2,5] => 10
[4,1,3,6,5,2] => 6
[4,1,5,2,3,6] => 72
[4,1,5,2,6,3] => 36
[4,1,5,3,2,6] => 24
[4,1,5,3,6,2] => 16
[4,1,5,6,2,3] => 36
[4,1,5,6,3,2] => 12
[4,1,6,2,3,5] => 30
[4,1,6,2,5,3] => 12
[4,1,6,3,2,5] => 10
[4,1,6,3,5,2] => 6
[4,1,6,5,2,3] => 12
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 90
[4,2,1,3,6,5] => 15
[4,2,1,5,3,6] => 36
[4,2,1,5,6,3] => 18
[4,2,1,6,3,5] => 15
[4,2,1,6,5,3] => 6
[4,2,3,1,5,6] => 60
[4,2,3,1,6,5] => 10
[4,2,3,5,1,6] => 48
[4,2,3,5,6,1] => 40
[4,2,3,6,1,5] => 10
[4,2,3,6,5,1] => 8
[4,2,5,1,3,6] => 36
[4,2,5,1,6,3] => 18
[4,2,5,3,1,6] => 24
[4,2,5,3,6,1] => 20
[4,2,5,6,1,3] => 18
[4,2,5,6,3,1] => 12
[4,2,6,1,3,5] => 15
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 10
[4,2,6,3,5,1] => 8
[4,2,6,5,1,3] => 6
[4,2,6,5,3,1] => 4
[4,3,1,2,5,6] => 60
[4,3,1,2,6,5] => 10
[4,3,1,5,2,6] => 36
[4,3,1,5,6,2] => 24
[4,3,1,6,2,5] => 10
[4,3,1,6,5,2] => 6
[4,3,2,1,5,6] => 30
[4,3,2,1,6,5] => 5
[4,3,2,5,1,6] => 24
[4,3,2,5,6,1] => 20
[4,3,2,6,1,5] => 5
[4,3,2,6,5,1] => 4
[4,3,5,1,2,6] => 36
[4,3,5,1,6,2] => 24
[4,3,5,2,1,6] => 18
[4,3,5,2,6,1] => 15
[4,3,5,6,1,2] => 24
[4,3,5,6,2,1] => 12
[4,3,6,1,2,5] => 10
[4,3,6,1,5,2] => 6
[4,3,6,2,1,5] => 5
[4,3,6,2,5,1] => 4
[4,3,6,5,1,2] => 6
[4,3,6,5,2,1] => 3
[4,5,1,2,3,6] => 72
[4,5,1,2,6,3] => 36
[4,5,1,3,2,6] => 24
[4,5,1,3,6,2] => 16
[4,5,1,6,2,3] => 36
[4,5,1,6,3,2] => 12
[4,5,2,1,3,6] => 36
[4,5,2,1,6,3] => 18
[4,5,2,3,1,6] => 24
[4,5,2,3,6,1] => 20
[4,5,2,6,1,3] => 18
[4,5,2,6,3,1] => 12
[4,5,3,1,2,6] => 24
[4,5,3,1,6,2] => 16
[4,5,3,2,1,6] => 12
[4,5,3,2,6,1] => 10
[4,5,3,6,1,2] => 16
[4,5,3,6,2,1] => 8
[4,5,6,1,2,3] => 36
[4,5,6,1,3,2] => 12
[4,5,6,2,1,3] => 18
[4,5,6,2,3,1] => 12
[4,5,6,3,1,2] => 12
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 30
[4,6,1,2,5,3] => 12
[4,6,1,3,2,5] => 10
[4,6,1,3,5,2] => 6
[4,6,1,5,2,3] => 12
[4,6,1,5,3,2] => 4
[4,6,2,1,3,5] => 15
[4,6,2,1,5,3] => 6
[4,6,2,3,1,5] => 10
[4,6,2,3,5,1] => 8
[4,6,2,5,1,3] => 6
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 10
[4,6,3,1,5,2] => 6
[4,6,3,2,1,5] => 5
[4,6,3,2,5,1] => 4
[4,6,3,5,1,2] => 6
[4,6,3,5,2,1] => 3
[4,6,5,1,2,3] => 12
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 6
[4,6,5,2,3,1] => 4
[4,6,5,3,1,2] => 4
[4,6,5,3,2,1] => 2
[5,1,2,3,4,6] => 144
[5,1,2,3,6,4] => 48
[5,1,2,4,3,6] => 36
[5,1,2,4,6,3] => 18
[5,1,2,6,3,4] => 48
[5,1,2,6,4,3] => 12
[5,1,3,2,4,6] => 48
[5,1,3,2,6,4] => 16
[5,1,3,4,2,6] => 24
[5,1,3,4,6,2] => 16
[5,1,3,6,2,4] => 16
[5,1,3,6,4,2] => 8
[5,1,4,2,3,6] => 36
[5,1,4,2,6,3] => 18
[5,1,4,3,2,6] => 12
[5,1,4,3,6,2] => 8
[5,1,4,6,2,3] => 18
[5,1,4,6,3,2] => 6
[5,1,6,2,3,4] => 48
[5,1,6,2,4,3] => 12
[5,1,6,3,2,4] => 16
[5,1,6,3,4,2] => 8
[5,1,6,4,2,3] => 12
[5,1,6,4,3,2] => 4
[5,2,1,3,4,6] => 72
[5,2,1,3,6,4] => 24
[5,2,1,4,3,6] => 18
[5,2,1,4,6,3] => 9
[5,2,1,6,3,4] => 24
[5,2,1,6,4,3] => 6
[5,2,3,1,4,6] => 48
[5,2,3,1,6,4] => 16
[5,2,3,4,1,6] => 36
[5,2,3,4,6,1] => 30
[5,2,3,6,1,4] => 16
[5,2,3,6,4,1] => 12
[5,2,4,1,3,6] => 18
[5,2,4,1,6,3] => 9
[5,2,4,3,1,6] => 12
[5,2,4,3,6,1] => 10
[5,2,4,6,1,3] => 9
[5,2,4,6,3,1] => 6
[5,2,6,1,3,4] => 24
[5,2,6,1,4,3] => 6
[5,2,6,3,1,4] => 16
[5,2,6,3,4,1] => 12
[5,2,6,4,1,3] => 6
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 48
[5,3,1,2,6,4] => 16
[5,3,1,4,2,6] => 24
[5,3,1,4,6,2] => 16
[5,3,1,6,2,4] => 16
[5,3,1,6,4,2] => 8
[5,3,2,1,4,6] => 24
[5,3,2,1,6,4] => 8
[5,3,2,4,1,6] => 18
[5,3,2,4,6,1] => 15
[5,3,2,6,1,4] => 8
[5,3,2,6,4,1] => 6
[5,3,4,1,2,6] => 24
[5,3,4,1,6,2] => 16
[5,3,4,2,1,6] => 12
[5,3,4,2,6,1] => 10
[5,3,4,6,1,2] => 16
[5,3,4,6,2,1] => 8
[5,3,6,1,2,4] => 16
[5,3,6,1,4,2] => 8
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 6
[5,3,6,4,1,2] => 8
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 36
[5,4,1,2,6,3] => 18
[5,4,1,3,2,6] => 12
[5,4,1,3,6,2] => 8
[5,4,1,6,2,3] => 18
[5,4,1,6,3,2] => 6
[5,4,2,1,3,6] => 18
[5,4,2,1,6,3] => 9
[5,4,2,3,1,6] => 12
[5,4,2,3,6,1] => 10
[5,4,2,6,1,3] => 9
[5,4,2,6,3,1] => 6
[5,4,3,1,2,6] => 12
[5,4,3,1,6,2] => 8
[5,4,3,2,1,6] => 6
[5,4,3,2,6,1] => 5
[5,4,3,6,1,2] => 8
[5,4,3,6,2,1] => 4
[5,4,6,1,2,3] => 18
[5,4,6,1,3,2] => 6
[5,4,6,2,1,3] => 9
[5,4,6,2,3,1] => 6
[5,4,6,3,1,2] => 6
[5,4,6,3,2,1] => 3
[5,6,1,2,3,4] => 48
[5,6,1,2,4,3] => 12
[5,6,1,3,2,4] => 16
[5,6,1,3,4,2] => 8
[5,6,1,4,2,3] => 12
[5,6,1,4,3,2] => 4
[5,6,2,1,3,4] => 24
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 16
[5,6,2,3,4,1] => 12
[5,6,2,4,1,3] => 6
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 16
[5,6,3,1,4,2] => 8
[5,6,3,2,1,4] => 8
[5,6,3,2,4,1] => 6
[5,6,3,4,1,2] => 8
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 12
[5,6,4,1,3,2] => 4
[5,6,4,2,1,3] => 6
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 4
[5,6,4,3,2,1] => 2
[6,1,2,3,4,5] => 120
[6,1,2,3,5,4] => 24
[6,1,2,4,3,5] => 30
[6,1,2,4,5,3] => 12
[6,1,2,5,3,4] => 24
[6,1,2,5,4,3] => 6
[6,1,3,2,4,5] => 40
[6,1,3,2,5,4] => 8
[6,1,3,4,2,5] => 20
[6,1,3,4,5,2] => 12
[6,1,3,5,2,4] => 8
[6,1,3,5,4,2] => 4
[6,1,4,2,3,5] => 30
[6,1,4,2,5,3] => 12
[6,1,4,3,2,5] => 10
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 12
[6,1,4,5,3,2] => 4
[6,1,5,2,3,4] => 24
[6,1,5,2,4,3] => 6
[6,1,5,3,2,4] => 8
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 6
[6,1,5,4,3,2] => 2
[6,2,1,3,4,5] => 60
[6,2,1,3,5,4] => 12
[6,2,1,4,3,5] => 15
[6,2,1,4,5,3] => 6
[6,2,1,5,3,4] => 12
[6,2,1,5,4,3] => 3
[6,2,3,1,4,5] => 40
[6,2,3,1,5,4] => 8
[6,2,3,4,1,5] => 30
[6,2,3,4,5,1] => 24
[6,2,3,5,1,4] => 8
[6,2,3,5,4,1] => 6
[6,2,4,1,3,5] => 15
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 10
[6,2,4,3,5,1] => 8
[6,2,4,5,1,3] => 6
[6,2,4,5,3,1] => 4
[6,2,5,1,3,4] => 12
[6,2,5,1,4,3] => 3
[6,2,5,3,1,4] => 8
[6,2,5,3,4,1] => 6
[6,2,5,4,1,3] => 3
[6,2,5,4,3,1] => 2
[6,3,1,2,4,5] => 40
[6,3,1,2,5,4] => 8
[6,3,1,4,2,5] => 20
[6,3,1,4,5,2] => 12
[6,3,1,5,2,4] => 8
[6,3,1,5,4,2] => 4
[6,3,2,1,4,5] => 20
[6,3,2,1,5,4] => 4
[6,3,2,4,1,5] => 15
[6,3,2,4,5,1] => 12
[6,3,2,5,1,4] => 4
[6,3,2,5,4,1] => 3
[6,3,4,1,2,5] => 20
[6,3,4,1,5,2] => 12
[6,3,4,2,1,5] => 10
[6,3,4,2,5,1] => 8
[6,3,4,5,1,2] => 12
[6,3,4,5,2,1] => 6
[6,3,5,1,2,4] => 8
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 4
[6,3,5,2,4,1] => 3
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 2
[6,4,1,2,3,5] => 30
[6,4,1,2,5,3] => 12
[6,4,1,3,2,5] => 10
[6,4,1,3,5,2] => 6
[6,4,1,5,2,3] => 12
[6,4,1,5,3,2] => 4
[6,4,2,1,3,5] => 15
[6,4,2,1,5,3] => 6
[6,4,2,3,1,5] => 10
[6,4,2,3,5,1] => 8
[6,4,2,5,1,3] => 6
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 10
[6,4,3,1,5,2] => 6
[6,4,3,2,1,5] => 5
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 6
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 12
[6,4,5,1,3,2] => 4
[6,4,5,2,1,3] => 6
[6,4,5,2,3,1] => 4
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 2
[6,5,1,2,3,4] => 24
[6,5,1,2,4,3] => 6
[6,5,1,3,2,4] => 8
[6,5,1,3,4,2] => 4
[6,5,1,4,2,3] => 6
[6,5,1,4,3,2] => 2
[6,5,2,1,3,4] => 12
[6,5,2,1,4,3] => 3
[6,5,2,3,1,4] => 8
[6,5,2,3,4,1] => 6
[6,5,2,4,1,3] => 3
[6,5,2,4,3,1] => 2
[6,5,3,1,2,4] => 8
[6,5,3,1,4,2] => 4
[6,5,3,2,1,4] => 4
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 2
[6,5,4,2,1,3] => 3
[6,5,4,2,3,1] => 2
[6,5,4,3,1,2] => 2
[6,5,4,3,2,1] => 1
click to show generating function       
Description
The number of parking functions that give the same permutation.
A parking function $(a_1,...,a_n)$ is give the preferences of parking spots of $n$ cars entering a one-way street. Once the cars have parked, the order of cars gives a permutation of $\{1,..,n\}$. This statistic records the number of parking functions that yield the same permutation of cars.
Code
from collections import defaultdict
@cached_function 
def PF_to_Perms(n):
    out = defaultdict(list)
    for pf in ParkingFunctions(n):
        out[pf.parking_permutation()].append(pf)
    return out


def statistic(pi):
    return len(PF_to_Perms(len(pi))[pi])


Created
Jan 26, 2019 at 13:10 by Raman Sanyal
Updated
Jan 26, 2019 at 13:10 by Raman Sanyal