Identifier
Identifier
Values
[1] => 1
[1,2] => 1
[2,1] => 2
[1,2,3] => 1
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 4
[3,1,2] => 4
[3,2,1] => 6
[1,2,3,4] => 1
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 4
[1,4,2,3] => 4
[1,4,3,2] => 6
[2,1,3,4] => 2
[2,1,4,3] => 4
[2,3,1,4] => 4
[2,3,4,1] => 8
[2,4,1,3] => 8
[2,4,3,1] => 12
[3,1,2,4] => 4
[3,1,4,2] => 8
[3,2,1,4] => 6
[3,2,4,1] => 12
[3,4,1,2] => 14
[3,4,2,1] => 18
[4,1,2,3] => 8
[4,1,3,2] => 12
[4,2,1,3] => 12
[4,2,3,1] => 20
[4,3,1,2] => 18
[4,3,2,1] => 24
[1,2,3,4,5] => 1
[1,2,3,5,4] => 2
[1,2,4,3,5] => 2
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 6
[1,3,2,4,5] => 2
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 8
[1,3,5,2,4] => 8
[1,3,5,4,2] => 12
[1,4,2,3,5] => 4
[1,4,2,5,3] => 8
[1,4,3,2,5] => 6
[1,4,3,5,2] => 12
[1,4,5,2,3] => 14
[1,4,5,3,2] => 18
[1,5,2,3,4] => 8
[1,5,2,4,3] => 12
[1,5,3,2,4] => 12
[1,5,3,4,2] => 20
[1,5,4,2,3] => 18
[1,5,4,3,2] => 24
[2,1,3,4,5] => 2
[2,1,3,5,4] => 4
[2,1,4,3,5] => 4
[2,1,4,5,3] => 8
[2,1,5,3,4] => 8
[2,1,5,4,3] => 12
[2,3,1,4,5] => 4
[2,3,1,5,4] => 8
[2,3,4,1,5] => 8
[2,3,4,5,1] => 16
[2,3,5,1,4] => 16
[2,3,5,4,1] => 24
[2,4,1,3,5] => 8
[2,4,1,5,3] => 16
[2,4,3,1,5] => 12
[2,4,3,5,1] => 24
[2,4,5,1,3] => 28
[2,4,5,3,1] => 36
[2,5,1,3,4] => 16
[2,5,1,4,3] => 24
[2,5,3,1,4] => 24
[2,5,3,4,1] => 40
[2,5,4,1,3] => 36
[2,5,4,3,1] => 48
[3,1,2,4,5] => 4
[3,1,2,5,4] => 8
[3,1,4,2,5] => 8
[3,1,4,5,2] => 16
[3,1,5,2,4] => 16
[3,1,5,4,2] => 24
[3,2,1,4,5] => 6
[3,2,1,5,4] => 12
[3,2,4,1,5] => 12
[3,2,4,5,1] => 24
[3,2,5,1,4] => 24
[3,2,5,4,1] => 36
[3,4,1,2,5] => 14
[3,4,1,5,2] => 28
[3,4,2,1,5] => 18
[3,4,2,5,1] => 36
[3,4,5,1,2] => 46
[3,4,5,2,1] => 54
[3,5,1,2,4] => 28
[3,5,1,4,2] => 44
[3,5,2,1,4] => 36
[3,5,2,4,1] => 60
[3,5,4,1,2] => 60
[3,5,4,2,1] => 72
[4,1,2,3,5] => 8
[4,1,2,5,3] => 16
[4,1,3,2,5] => 12
[4,1,3,5,2] => 24
[4,1,5,2,3] => 28
[4,1,5,3,2] => 36
[4,2,1,3,5] => 12
[4,2,1,5,3] => 24
[4,2,3,1,5] => 20
[4,2,3,5,1] => 40
[4,2,5,1,3] => 44
[4,2,5,3,1] => 60
[4,3,1,2,5] => 18
[4,3,1,5,2] => 36
[4,3,2,1,5] => 24
[4,3,2,5,1] => 48
[4,3,5,1,2] => 60
[4,3,5,2,1] => 72
[4,5,1,2,3] => 46
[4,5,1,3,2] => 60
[4,5,2,1,3] => 60
[4,5,2,3,1] => 88
[4,5,3,1,2] => 78
[4,5,3,2,1] => 96
[5,1,2,3,4] => 16
[5,1,2,4,3] => 24
[5,1,3,2,4] => 24
[5,1,3,4,2] => 40
[5,1,4,2,3] => 36
[5,1,4,3,2] => 48
[5,2,1,3,4] => 24
[5,2,1,4,3] => 36
[5,2,3,1,4] => 40
[5,2,3,4,1] => 68
[5,2,4,1,3] => 60
[5,2,4,3,1] => 84
[5,3,1,2,4] => 36
[5,3,1,4,2] => 60
[5,3,2,1,4] => 48
[5,3,2,4,1] => 84
[5,3,4,1,2] => 88
[5,3,4,2,1] => 108
[5,4,1,2,3] => 54
[5,4,1,3,2] => 72
[5,4,2,1,3] => 72
[5,4,2,3,1] => 108
[5,4,3,1,2] => 96
[5,4,3,2,1] => 120
[1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => 2
[1,2,3,5,4,6] => 2
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 6
[1,2,4,3,5,6] => 2
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 4
[1,2,4,5,6,3] => 8
[1,2,4,6,3,5] => 8
[1,2,4,6,5,3] => 12
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 8
[1,2,5,4,3,6] => 6
[1,2,5,4,6,3] => 12
[1,2,5,6,3,4] => 14
[1,2,5,6,4,3] => 18
[1,2,6,3,4,5] => 8
[1,2,6,3,5,4] => 12
[1,2,6,4,3,5] => 12
[1,2,6,4,5,3] => 20
[1,2,6,5,3,4] => 18
[1,2,6,5,4,3] => 24
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 4
[1,3,2,5,6,4] => 8
[1,3,2,6,4,5] => 8
[1,3,2,6,5,4] => 12
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 8
[1,3,4,5,2,6] => 8
[1,3,4,5,6,2] => 16
[1,3,4,6,2,5] => 16
[1,3,4,6,5,2] => 24
[1,3,5,2,4,6] => 8
[1,3,5,2,6,4] => 16
[1,3,5,4,2,6] => 12
[1,3,5,4,6,2] => 24
[1,3,5,6,2,4] => 28
[1,3,5,6,4,2] => 36
[1,3,6,2,4,5] => 16
[1,3,6,2,5,4] => 24
[1,3,6,4,2,5] => 24
[1,3,6,4,5,2] => 40
[1,3,6,5,2,4] => 36
[1,3,6,5,4,2] => 48
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 8
[1,4,2,5,3,6] => 8
[1,4,2,5,6,3] => 16
[1,4,2,6,3,5] => 16
[1,4,2,6,5,3] => 24
[1,4,3,2,5,6] => 6
[1,4,3,2,6,5] => 12
[1,4,3,5,2,6] => 12
[1,4,3,5,6,2] => 24
[1,4,3,6,2,5] => 24
[1,4,3,6,5,2] => 36
[1,4,5,2,3,6] => 14
[1,4,5,2,6,3] => 28
[1,4,5,3,2,6] => 18
[1,4,5,3,6,2] => 36
[1,4,5,6,2,3] => 46
[1,4,5,6,3,2] => 54
[1,4,6,2,3,5] => 28
[1,4,6,2,5,3] => 44
[1,4,6,3,2,5] => 36
[1,4,6,3,5,2] => 60
[1,4,6,5,2,3] => 60
[1,4,6,5,3,2] => 72
[1,5,2,3,4,6] => 8
[1,5,2,3,6,4] => 16
[1,5,2,4,3,6] => 12
[1,5,2,4,6,3] => 24
[1,5,2,6,3,4] => 28
[1,5,2,6,4,3] => 36
[1,5,3,2,4,6] => 12
[1,5,3,2,6,4] => 24
[1,5,3,4,2,6] => 20
[1,5,3,4,6,2] => 40
[1,5,3,6,2,4] => 44
[1,5,3,6,4,2] => 60
[1,5,4,2,3,6] => 18
[1,5,4,2,6,3] => 36
[1,5,4,3,2,6] => 24
[1,5,4,3,6,2] => 48
[1,5,4,6,2,3] => 60
[1,5,4,6,3,2] => 72
[1,5,6,2,3,4] => 46
[1,5,6,2,4,3] => 60
[1,5,6,3,2,4] => 60
[1,5,6,3,4,2] => 88
[1,5,6,4,2,3] => 78
[1,5,6,4,3,2] => 96
[1,6,2,3,4,5] => 16
[1,6,2,3,5,4] => 24
[1,6,2,4,3,5] => 24
[1,6,2,4,5,3] => 40
[1,6,2,5,3,4] => 36
[1,6,2,5,4,3] => 48
[1,6,3,2,4,5] => 24
[1,6,3,2,5,4] => 36
[1,6,3,4,2,5] => 40
[1,6,3,4,5,2] => 68
[1,6,3,5,2,4] => 60
[1,6,3,5,4,2] => 84
[1,6,4,2,3,5] => 36
[1,6,4,2,5,3] => 60
[1,6,4,3,2,5] => 48
[1,6,4,3,5,2] => 84
[1,6,4,5,2,3] => 88
[1,6,4,5,3,2] => 108
[1,6,5,2,3,4] => 54
[1,6,5,2,4,3] => 72
[1,6,5,3,2,4] => 72
[1,6,5,3,4,2] => 108
[1,6,5,4,2,3] => 96
[1,6,5,4,3,2] => 120
[2,1,3,4,5,6] => 2
[2,1,3,4,6,5] => 4
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 8
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 12
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 8
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 16
[2,1,4,6,3,5] => 16
[2,1,4,6,5,3] => 24
[2,1,5,3,4,6] => 8
[2,1,5,3,6,4] => 16
[2,1,5,4,3,6] => 12
[2,1,5,4,6,3] => 24
[2,1,5,6,3,4] => 28
[2,1,5,6,4,3] => 36
[2,1,6,3,4,5] => 16
[2,1,6,3,5,4] => 24
[2,1,6,4,3,5] => 24
[2,1,6,4,5,3] => 40
[2,1,6,5,3,4] => 36
[2,1,6,5,4,3] => 48
[2,3,1,4,5,6] => 4
[2,3,1,4,6,5] => 8
[2,3,1,5,4,6] => 8
[2,3,1,5,6,4] => 16
[2,3,1,6,4,5] => 16
[2,3,1,6,5,4] => 24
[2,3,4,1,5,6] => 8
[2,3,4,1,6,5] => 16
[2,3,4,5,1,6] => 16
[2,3,4,5,6,1] => 32
[2,3,4,6,1,5] => 32
[2,3,4,6,5,1] => 48
[2,3,5,1,4,6] => 16
[2,3,5,1,6,4] => 32
[2,3,5,4,1,6] => 24
[2,3,5,4,6,1] => 48
[2,3,5,6,1,4] => 56
[2,3,5,6,4,1] => 72
[2,3,6,1,4,5] => 32
[2,3,6,1,5,4] => 48
[2,3,6,4,1,5] => 48
[2,3,6,4,5,1] => 80
[2,3,6,5,1,4] => 72
[2,3,6,5,4,1] => 96
[2,4,1,3,5,6] => 8
[2,4,1,3,6,5] => 16
[2,4,1,5,3,6] => 16
[2,4,1,5,6,3] => 32
[2,4,1,6,3,5] => 32
[2,4,1,6,5,3] => 48
[2,4,3,1,5,6] => 12
[2,4,3,1,6,5] => 24
[2,4,3,5,1,6] => 24
[2,4,3,5,6,1] => 48
[2,4,3,6,1,5] => 48
[2,4,3,6,5,1] => 72
[2,4,5,1,3,6] => 28
[2,4,5,1,6,3] => 56
[2,4,5,3,1,6] => 36
[2,4,5,3,6,1] => 72
[2,4,5,6,1,3] => 92
[2,4,5,6,3,1] => 108
[2,4,6,1,3,5] => 56
[2,4,6,1,5,3] => 88
[2,4,6,3,1,5] => 72
[2,4,6,3,5,1] => 120
[2,4,6,5,1,3] => 120
[2,4,6,5,3,1] => 144
[2,5,1,3,4,6] => 16
[2,5,1,3,6,4] => 32
[2,5,1,4,3,6] => 24
[2,5,1,4,6,3] => 48
[2,5,1,6,3,4] => 56
[2,5,1,6,4,3] => 72
[2,5,3,1,4,6] => 24
[2,5,3,1,6,4] => 48
[2,5,3,4,1,6] => 40
[2,5,3,4,6,1] => 80
[2,5,3,6,1,4] => 88
[2,5,3,6,4,1] => 120
[2,5,4,1,3,6] => 36
[2,5,4,1,6,3] => 72
[2,5,4,3,1,6] => 48
[2,5,4,3,6,1] => 96
[2,5,4,6,1,3] => 120
[2,5,4,6,3,1] => 144
[2,5,6,1,3,4] => 92
[2,5,6,1,4,3] => 120
[2,5,6,3,1,4] => 120
[2,5,6,3,4,1] => 176
[2,5,6,4,1,3] => 156
[2,5,6,4,3,1] => 192
[2,6,1,3,4,5] => 32
[2,6,1,3,5,4] => 48
[2,6,1,4,3,5] => 48
[2,6,1,4,5,3] => 80
[2,6,1,5,3,4] => 72
[2,6,1,5,4,3] => 96
[2,6,3,1,4,5] => 48
[2,6,3,1,5,4] => 72
[2,6,3,4,1,5] => 80
[2,6,3,4,5,1] => 136
[2,6,3,5,1,4] => 120
[2,6,3,5,4,1] => 168
[2,6,4,1,3,5] => 72
[2,6,4,1,5,3] => 120
[2,6,4,3,1,5] => 96
[2,6,4,3,5,1] => 168
[2,6,4,5,1,3] => 176
[2,6,4,5,3,1] => 216
[2,6,5,1,3,4] => 108
[2,6,5,1,4,3] => 144
[2,6,5,3,1,4] => 144
[2,6,5,3,4,1] => 216
[2,6,5,4,1,3] => 192
[2,6,5,4,3,1] => 240
[3,1,2,4,5,6] => 4
[3,1,2,4,6,5] => 8
[3,1,2,5,4,6] => 8
[3,1,2,5,6,4] => 16
[3,1,2,6,4,5] => 16
[3,1,2,6,5,4] => 24
[3,1,4,2,5,6] => 8
[3,1,4,2,6,5] => 16
[3,1,4,5,2,6] => 16
[3,1,4,5,6,2] => 32
[3,1,4,6,2,5] => 32
[3,1,4,6,5,2] => 48
[3,1,5,2,4,6] => 16
[3,1,5,2,6,4] => 32
[3,1,5,4,2,6] => 24
[3,1,5,4,6,2] => 48
[3,1,5,6,2,4] => 56
[3,1,5,6,4,2] => 72
[3,1,6,2,4,5] => 32
[3,1,6,2,5,4] => 48
[3,1,6,4,2,5] => 48
[3,1,6,4,5,2] => 80
[3,1,6,5,2,4] => 72
[3,1,6,5,4,2] => 96
[3,2,1,4,5,6] => 6
[3,2,1,4,6,5] => 12
[3,2,1,5,4,6] => 12
[3,2,1,5,6,4] => 24
[3,2,1,6,4,5] => 24
[3,2,1,6,5,4] => 36
[3,2,4,1,5,6] => 12
[3,2,4,1,6,5] => 24
[3,2,4,5,1,6] => 24
[3,2,4,5,6,1] => 48
[3,2,4,6,1,5] => 48
[3,2,4,6,5,1] => 72
[3,2,5,1,4,6] => 24
[3,2,5,1,6,4] => 48
[3,2,5,4,1,6] => 36
[3,2,5,4,6,1] => 72
[3,2,5,6,1,4] => 84
[3,2,5,6,4,1] => 108
[3,2,6,1,4,5] => 48
[3,2,6,1,5,4] => 72
[3,2,6,4,1,5] => 72
[3,2,6,4,5,1] => 120
[3,2,6,5,1,4] => 108
[3,2,6,5,4,1] => 144
[3,4,1,2,5,6] => 14
[3,4,1,2,6,5] => 28
[3,4,1,5,2,6] => 28
[3,4,1,5,6,2] => 56
[3,4,1,6,2,5] => 56
[3,4,1,6,5,2] => 84
[3,4,2,1,5,6] => 18
[3,4,2,1,6,5] => 36
[3,4,2,5,1,6] => 36
[3,4,2,5,6,1] => 72
[3,4,2,6,1,5] => 72
[3,4,2,6,5,1] => 108
[3,4,5,1,2,6] => 46
[3,4,5,1,6,2] => 92
[3,4,5,2,1,6] => 54
[3,4,5,2,6,1] => 108
[3,4,5,6,1,2] => 146
[3,4,5,6,2,1] => 162
[3,4,6,1,2,5] => 92
[3,4,6,1,5,2] => 148
[3,4,6,2,1,5] => 108
[3,4,6,2,5,1] => 180
[3,4,6,5,1,2] => 192
[3,4,6,5,2,1] => 216
[3,5,1,2,4,6] => 28
[3,5,1,2,6,4] => 56
[3,5,1,4,2,6] => 44
[3,5,1,4,6,2] => 88
[3,5,1,6,2,4] => 100
[3,5,1,6,4,2] => 132
[3,5,2,1,4,6] => 36
[3,5,2,1,6,4] => 72
[3,5,2,4,1,6] => 60
[3,5,2,4,6,1] => 120
[3,5,2,6,1,4] => 132
[3,5,2,6,4,1] => 180
[3,5,4,1,2,6] => 60
[3,5,4,1,6,2] => 120
[3,5,4,2,1,6] => 72
[3,5,4,2,6,1] => 144
[3,5,4,6,1,2] => 192
[3,5,4,6,2,1] => 216
[3,5,6,1,2,4] => 152
[3,5,6,1,4,2] => 208
[3,5,6,2,1,4] => 180
[3,5,6,2,4,1] => 264
[3,5,6,4,1,2] => 252
[3,5,6,4,2,1] => 288
[3,6,1,2,4,5] => 56
[3,6,1,2,5,4] => 84
[3,6,1,4,2,5] => 88
[3,6,1,4,5,2] => 148
[3,6,1,5,2,4] => 132
[3,6,1,5,4,2] => 180
[3,6,2,1,4,5] => 72
[3,6,2,1,5,4] => 108
[3,6,2,4,1,5] => 120
[3,6,2,4,5,1] => 204
[3,6,2,5,1,4] => 180
[3,6,2,5,4,1] => 252
[3,6,4,1,2,5] => 120
[3,6,4,1,5,2] => 204
[3,6,4,2,1,5] => 144
[3,6,4,2,5,1] => 252
[3,6,4,5,1,2] => 284
[3,6,4,5,2,1] => 324
[3,6,5,1,2,4] => 180
[3,6,5,1,4,2] => 252
[3,6,5,2,1,4] => 216
[3,6,5,2,4,1] => 324
[3,6,5,4,1,2] => 312
[3,6,5,4,2,1] => 360
[4,1,2,3,5,6] => 8
[4,1,2,3,6,5] => 16
[4,1,2,5,3,6] => 16
[4,1,2,5,6,3] => 32
[4,1,2,6,3,5] => 32
[4,1,2,6,5,3] => 48
[4,1,3,2,5,6] => 12
[4,1,3,2,6,5] => 24
[4,1,3,5,2,6] => 24
[4,1,3,5,6,2] => 48
[4,1,3,6,2,5] => 48
[4,1,3,6,5,2] => 72
[4,1,5,2,3,6] => 28
[4,1,5,2,6,3] => 56
[4,1,5,3,2,6] => 36
[4,1,5,3,6,2] => 72
[4,1,5,6,2,3] => 92
[4,1,5,6,3,2] => 108
[4,1,6,2,3,5] => 56
[4,1,6,2,5,3] => 88
[4,1,6,3,2,5] => 72
[4,1,6,3,5,2] => 120
[4,1,6,5,2,3] => 120
[4,1,6,5,3,2] => 144
[4,2,1,3,5,6] => 12
[4,2,1,3,6,5] => 24
[4,2,1,5,3,6] => 24
[4,2,1,5,6,3] => 48
[4,2,1,6,3,5] => 48
[4,2,1,6,5,3] => 72
[4,2,3,1,5,6] => 20
[4,2,3,1,6,5] => 40
[4,2,3,5,1,6] => 40
[4,2,3,5,6,1] => 80
[4,2,3,6,1,5] => 80
[4,2,3,6,5,1] => 120
[4,2,5,1,3,6] => 44
[4,2,5,1,6,3] => 88
[4,2,5,3,1,6] => 60
[4,2,5,3,6,1] => 120
[4,2,5,6,1,3] => 148
[4,2,5,6,3,1] => 180
[4,2,6,1,3,5] => 88
[4,2,6,1,5,3] => 136
[4,2,6,3,1,5] => 120
[4,2,6,3,5,1] => 200
[4,2,6,5,1,3] => 192
[4,2,6,5,3,1] => 240
[4,3,1,2,5,6] => 18
[4,3,1,2,6,5] => 36
[4,3,1,5,2,6] => 36
[4,3,1,5,6,2] => 72
[4,3,1,6,2,5] => 72
[4,3,1,6,5,2] => 108
[4,3,2,1,5,6] => 24
[4,3,2,1,6,5] => 48
[4,3,2,5,1,6] => 48
[4,3,2,5,6,1] => 96
[4,3,2,6,1,5] => 96
[4,3,2,6,5,1] => 144
[4,3,5,1,2,6] => 60
[4,3,5,1,6,2] => 120
[4,3,5,2,1,6] => 72
[4,3,5,2,6,1] => 144
[4,3,5,6,1,2] => 192
[4,3,5,6,2,1] => 216
[4,3,6,1,2,5] => 120
[4,3,6,1,5,2] => 192
[4,3,6,2,1,5] => 144
[4,3,6,2,5,1] => 240
[4,3,6,5,1,2] => 252
[4,3,6,5,2,1] => 288
[4,5,1,2,3,6] => 46
[4,5,1,2,6,3] => 92
[4,5,1,3,2,6] => 60
[4,5,1,3,6,2] => 120
[4,5,1,6,2,3] => 152
[4,5,1,6,3,2] => 180
[4,5,2,1,3,6] => 60
[4,5,2,1,6,3] => 120
[4,5,2,3,1,6] => 88
[4,5,2,3,6,1] => 176
[4,5,2,6,1,3] => 208
[4,5,2,6,3,1] => 264
[4,5,3,1,2,6] => 78
[4,5,3,1,6,2] => 156
[4,5,3,2,1,6] => 96
[4,5,3,2,6,1] => 192
[4,5,3,6,1,2] => 252
[4,5,3,6,2,1] => 288
[4,5,6,1,2,3] => 230
[4,5,6,1,3,2] => 276
[4,5,6,2,1,3] => 276
[4,5,6,2,3,1] => 368
[4,5,6,3,1,2] => 330
[4,5,6,3,2,1] => 384
[4,6,1,2,3,5] => 92
[4,6,1,2,5,3] => 148
[4,6,1,3,2,5] => 120
[4,6,1,3,5,2] => 204
[4,6,1,5,2,3] => 208
[4,6,1,5,3,2] => 252
[4,6,2,1,3,5] => 120
[4,6,2,1,5,3] => 192
[4,6,2,3,1,5] => 176
[4,6,2,3,5,1] => 304
[4,6,2,5,1,3] => 296
[4,6,2,5,3,1] => 384
[4,6,3,1,2,5] => 156
[4,6,3,1,5,2] => 264
[4,6,3,2,1,5] => 192
[4,6,3,2,5,1] => 336
[4,6,3,5,1,2] => 372
[4,6,3,5,2,1] => 432
[4,6,5,1,2,3] => 276
[4,6,5,1,3,2] => 336
[4,6,5,2,1,3] => 336
[4,6,5,2,3,1] => 456
[4,6,5,3,1,2] => 408
[4,6,5,3,2,1] => 480
[5,1,2,3,4,6] => 16
[5,1,2,3,6,4] => 32
[5,1,2,4,3,6] => 24
[5,1,2,4,6,3] => 48
[5,1,2,6,3,4] => 56
[5,1,2,6,4,3] => 72
[5,1,3,2,4,6] => 24
[5,1,3,2,6,4] => 48
[5,1,3,4,2,6] => 40
[5,1,3,4,6,2] => 80
[5,1,3,6,2,4] => 88
[5,1,3,6,4,2] => 120
[5,1,4,2,3,6] => 36
[5,1,4,2,6,3] => 72
[5,1,4,3,2,6] => 48
[5,1,4,3,6,2] => 96
[5,1,4,6,2,3] => 120
[5,1,4,6,3,2] => 144
[5,1,6,2,3,4] => 92
[5,1,6,2,4,3] => 120
[5,1,6,3,2,4] => 120
[5,1,6,3,4,2] => 176
[5,1,6,4,2,3] => 156
[5,1,6,4,3,2] => 192
[5,2,1,3,4,6] => 24
[5,2,1,3,6,4] => 48
[5,2,1,4,3,6] => 36
[5,2,1,4,6,3] => 72
[5,2,1,6,3,4] => 84
[5,2,1,6,4,3] => 108
[5,2,3,1,4,6] => 40
[5,2,3,1,6,4] => 80
[5,2,3,4,1,6] => 68
[5,2,3,4,6,1] => 136
[5,2,3,6,1,4] => 148
[5,2,3,6,4,1] => 204
[5,2,4,1,3,6] => 60
[5,2,4,1,6,3] => 120
[5,2,4,3,1,6] => 84
[5,2,4,3,6,1] => 168
[5,2,4,6,1,3] => 204
[5,2,4,6,3,1] => 252
[5,2,6,1,3,4] => 148
[5,2,6,1,4,3] => 192
[5,2,6,3,1,4] => 204
[5,2,6,3,4,1] => 304
[5,2,6,4,1,3] => 264
[5,2,6,4,3,1] => 336
[5,3,1,2,4,6] => 36
[5,3,1,2,6,4] => 72
[5,3,1,4,2,6] => 60
[5,3,1,4,6,2] => 120
[5,3,1,6,2,4] => 132
[5,3,1,6,4,2] => 180
[5,3,2,1,4,6] => 48
[5,3,2,1,6,4] => 96
[5,3,2,4,1,6] => 84
[5,3,2,4,6,1] => 168
[5,3,2,6,1,4] => 180
[5,3,2,6,4,1] => 252
[5,3,4,1,2,6] => 88
[5,3,4,1,6,2] => 176
[5,3,4,2,1,6] => 108
[5,3,4,2,6,1] => 216
[5,3,4,6,1,2] => 284
[5,3,4,6,2,1] => 324
[5,3,6,1,2,4] => 208
[5,3,6,1,4,2] => 296
[5,3,6,2,1,4] => 252
[5,3,6,2,4,1] => 384
[5,3,6,4,1,2] => 372
[5,3,6,4,2,1] => 432
[5,4,1,2,3,6] => 54
[5,4,1,2,6,3] => 108
[5,4,1,3,2,6] => 72
[5,4,1,3,6,2] => 144
[5,4,1,6,2,3] => 180
[5,4,1,6,3,2] => 216
[5,4,2,1,3,6] => 72
[5,4,2,1,6,3] => 144
[5,4,2,3,1,6] => 108
[5,4,2,3,6,1] => 216
[5,4,2,6,1,3] => 252
[5,4,2,6,3,1] => 324
[5,4,3,1,2,6] => 96
[5,4,3,1,6,2] => 192
[5,4,3,2,1,6] => 120
[5,4,3,2,6,1] => 240
[5,4,3,6,1,2] => 312
[5,4,3,6,2,1] => 360
[5,4,6,1,2,3] => 276
[5,4,6,1,3,2] => 336
[5,4,6,2,1,3] => 336
[5,4,6,2,3,1] => 456
[5,4,6,3,1,2] => 408
[5,4,6,3,2,1] => 480
[5,6,1,2,3,4] => 146
[5,6,1,2,4,3] => 192
[5,6,1,3,2,4] => 192
[5,6,1,3,4,2] => 284
[5,6,1,4,2,3] => 252
[5,6,1,4,3,2] => 312
[5,6,2,1,3,4] => 192
[5,6,2,1,4,3] => 252
[5,6,2,3,1,4] => 284
[5,6,2,3,4,1] => 436
[5,6,2,4,1,3] => 372
[5,6,2,4,3,1] => 492
[5,6,3,1,2,4] => 252
[5,6,3,1,4,2] => 372
[5,6,3,2,1,4] => 312
[5,6,3,2,4,1] => 492
[5,6,3,4,1,2] => 488
[5,6,3,4,2,1] => 576
[5,6,4,1,2,3] => 330
[5,6,4,1,3,2] => 408
[5,6,4,2,1,3] => 408
[5,6,4,2,3,1] => 564
[5,6,4,3,1,2] => 504
[5,6,4,3,2,1] => 600
[6,1,2,3,4,5] => 32
[6,1,2,3,5,4] => 48
[6,1,2,4,3,5] => 48
[6,1,2,4,5,3] => 80
[6,1,2,5,3,4] => 72
[6,1,2,5,4,3] => 96
[6,1,3,2,4,5] => 48
[6,1,3,2,5,4] => 72
[6,1,3,4,2,5] => 80
[6,1,3,4,5,2] => 136
[6,1,3,5,2,4] => 120
[6,1,3,5,4,2] => 168
[6,1,4,2,3,5] => 72
[6,1,4,2,5,3] => 120
[6,1,4,3,2,5] => 96
[6,1,4,3,5,2] => 168
[6,1,4,5,2,3] => 176
[6,1,4,5,3,2] => 216
[6,1,5,2,3,4] => 108
[6,1,5,2,4,3] => 144
[6,1,5,3,2,4] => 144
[6,1,5,3,4,2] => 216
[6,1,5,4,2,3] => 192
[6,1,5,4,3,2] => 240
[6,2,1,3,4,5] => 48
[6,2,1,3,5,4] => 72
[6,2,1,4,3,5] => 72
[6,2,1,4,5,3] => 120
[6,2,1,5,3,4] => 108
[6,2,1,5,4,3] => 144
[6,2,3,1,4,5] => 80
[6,2,3,1,5,4] => 120
[6,2,3,4,1,5] => 136
[6,2,3,4,5,1] => 232
[6,2,3,5,1,4] => 204
[6,2,3,5,4,1] => 288
[6,2,4,1,3,5] => 120
[6,2,4,1,5,3] => 200
[6,2,4,3,1,5] => 168
[6,2,4,3,5,1] => 296
[6,2,4,5,1,3] => 304
[6,2,4,5,3,1] => 384
[6,2,5,1,3,4] => 180
[6,2,5,1,4,3] => 240
[6,2,5,3,1,4] => 252
[6,2,5,3,4,1] => 384
[6,2,5,4,1,3] => 336
[6,2,5,4,3,1] => 432
[6,3,1,2,4,5] => 72
[6,3,1,2,5,4] => 108
[6,3,1,4,2,5] => 120
[6,3,1,4,5,2] => 204
[6,3,1,5,2,4] => 180
[6,3,1,5,4,2] => 252
[6,3,2,1,4,5] => 96
[6,3,2,1,5,4] => 144
[6,3,2,4,1,5] => 168
[6,3,2,4,5,1] => 288
[6,3,2,5,1,4] => 252
[6,3,2,5,4,1] => 360
[6,3,4,1,2,5] => 176
[6,3,4,1,5,2] => 304
[6,3,4,2,1,5] => 216
[6,3,4,2,5,1] => 384
[6,3,4,5,1,2] => 436
[6,3,4,5,2,1] => 504
[6,3,5,1,2,4] => 264
[6,3,5,1,4,2] => 384
[6,3,5,2,1,4] => 324
[6,3,5,2,4,1] => 504
[6,3,5,4,1,2] => 492
[6,3,5,4,2,1] => 576
[6,4,1,2,3,5] => 108
[6,4,1,2,5,3] => 180
[6,4,1,3,2,5] => 144
[6,4,1,3,5,2] => 252
[6,4,1,5,2,3] => 264
[6,4,1,5,3,2] => 324
[6,4,2,1,3,5] => 144
[6,4,2,1,5,3] => 240
[6,4,2,3,1,5] => 216
[6,4,2,3,5,1] => 384
[6,4,2,5,1,3] => 384
[6,4,2,5,3,1] => 504
[6,4,3,1,2,5] => 192
[6,4,3,1,5,2] => 336
[6,4,3,2,1,5] => 240
[6,4,3,2,5,1] => 432
[6,4,3,5,1,2] => 492
[6,4,3,5,2,1] => 576
[6,4,5,1,2,3] => 368
[6,4,5,1,3,2] => 456
[6,4,5,2,1,3] => 456
[6,4,5,2,3,1] => 632
[6,4,5,3,1,2] => 564
[6,4,5,3,2,1] => 672
[6,5,1,2,3,4] => 162
[6,5,1,2,4,3] => 216
[6,5,1,3,2,4] => 216
[6,5,1,3,4,2] => 324
[6,5,1,4,2,3] => 288
[6,5,1,4,3,2] => 360
[6,5,2,1,3,4] => 216
[6,5,2,1,4,3] => 288
[6,5,2,3,1,4] => 324
[6,5,2,3,4,1] => 504
[6,5,2,4,1,3] => 432
[6,5,2,4,3,1] => 576
[6,5,3,1,2,4] => 288
[6,5,3,1,4,2] => 432
[6,5,3,2,1,4] => 360
[6,5,3,2,4,1] => 576
[6,5,3,4,1,2] => 576
[6,5,3,4,2,1] => 684
[6,5,4,1,2,3] => 384
[6,5,4,1,3,2] => 480
[6,5,4,2,1,3] => 480
[6,5,4,2,3,1] => 672
[6,5,4,3,1,2] => 600
[6,5,4,3,2,1] => 720
click to show generating function       
Description
The number of elements less than or equal to the given element in Bruhat order.
Code
def statistic(pi):
    return len([y for y in Permutations(pi.size()) if y.bruhat_lequal(pi)])
Created
Jun 15, 2013 at 13:19 by Chris Berg
Updated
Apr 01, 2015 at 21:31 by Martin Rubey