Identifier
Identifier
Values
[1] => 6
[1,2] => 18
[2,1] => 12
[1,2,3] => 36
[1,3,2] => 54
[2,1,3] => 36
[2,3,1] => 36
[3,1,2] => 24
[3,2,1] => 36
[1,2,3,4] => 72
[1,2,4,3] => 108
[1,3,2,4] => 108
[1,3,4,2] => 108
[1,4,2,3] => 108
[1,4,3,2] => 162
[2,1,3,4] => 72
[2,1,4,3] => 108
[2,3,1,4] => 36
[2,3,4,1] => 72
[2,4,1,3] => 36
[2,4,3,1] => 108
[3,1,2,4] => 72
[3,1,4,2] => 72
[3,2,1,4] => 36
[3,2,4,1] => 72
[3,4,1,2] => 72
[3,4,2,1] => 108
[4,1,2,3] => 48
[4,1,3,2] => 72
[4,2,1,3] => 72
[4,2,3,1] => 72
[4,3,1,2] => 72
[4,3,2,1] => 108
[1,2,3,4,5] => 144
[1,2,3,5,4] => 216
[1,2,4,3,5] => 216
[1,2,4,5,3] => 216
[1,2,5,3,4] => 216
[1,2,5,4,3] => 324
[1,3,2,4,5] => 216
[1,3,2,5,4] => 108
[1,3,4,2,5] => 216
[1,3,4,5,2] => 216
[1,3,5,2,4] => 216
[1,3,5,4,2] => 324
[1,4,2,3,5] => 216
[1,4,2,5,3] => 108
[1,4,3,2,5] => 324
[1,4,3,5,2] => 324
[1,4,5,2,3] => 216
[1,4,5,3,2] => 324
[1,5,2,3,4] => 216
[1,5,2,4,3] => 108
[1,5,3,2,4] => 324
[1,5,3,4,2] => 324
[1,5,4,2,3] => 324
[1,5,4,3,2] => 486
[2,1,3,4,5] => 144
[2,1,3,5,4] => 216
[2,1,4,3,5] => 216
[2,1,4,5,3] => 216
[2,1,5,3,4] => 216
[2,1,5,4,3] => 324
[2,3,1,4,5] => 72
[2,3,1,5,4] => 108
[2,3,4,1,5] => 72
[2,3,4,5,1] => 144
[2,3,5,1,4] => 72
[2,3,5,4,1] => 216
[2,4,1,3,5] => 72
[2,4,1,5,3] => 108
[2,4,3,1,5] => 108
[2,4,3,5,1] => 216
[2,4,5,1,3] => 72
[2,4,5,3,1] => 216
[2,5,1,3,4] => 72
[2,5,1,4,3] => 108
[2,5,3,1,4] => 108
[2,5,3,4,1] => 216
[2,5,4,1,3] => 108
[2,5,4,3,1] => 324
[3,1,2,4,5] => 144
[3,1,2,5,4] => 216
[3,1,4,2,5] => 72
[3,1,4,5,2] => 144
[3,1,5,2,4] => 72
[3,1,5,4,2] => 216
[3,2,1,4,5] => 72
[3,2,1,5,4] => 108
[3,2,4,1,5] => 72
[3,2,4,5,1] => 144
[3,2,5,1,4] => 72
[3,2,5,4,1] => 216
[3,4,1,2,5] => 72
[3,4,1,5,2] => 72
[3,4,2,1,5] => 108
[3,4,2,5,1] => 216
[3,4,5,1,2] => 144
[3,4,5,2,1] => 216
[3,5,1,2,4] => 72
[3,5,1,4,2] => 72
[3,5,2,1,4] => 108
[3,5,2,4,1] => 216
[3,5,4,1,2] => 216
[3,5,4,2,1] => 324
[4,1,2,3,5] => 144
[4,1,2,5,3] => 144
[4,1,3,2,5] => 72
[4,1,3,5,2] => 144
[4,1,5,2,3] => 144
[4,1,5,3,2] => 216
[4,2,1,3,5] => 72
[4,2,1,5,3] => 72
[4,2,3,1,5] => 72
[4,2,3,5,1] => 144
[4,2,5,1,3] => 144
[4,2,5,3,1] => 216
[4,3,1,2,5] => 72
[4,3,1,5,2] => 72
[4,3,2,1,5] => 108
[4,3,2,5,1] => 216
[4,3,5,1,2] => 144
[4,3,5,2,1] => 216
[4,5,1,2,3] => 144
[4,5,1,3,2] => 72
[4,5,2,1,3] => 216
[4,5,2,3,1] => 216
[4,5,3,1,2] => 216
[4,5,3,2,1] => 324
[5,1,2,3,4] => 96
[5,1,2,4,3] => 144
[5,1,3,2,4] => 144
[5,1,3,4,2] => 144
[5,1,4,2,3] => 144
[5,1,4,3,2] => 216
[5,2,1,3,4] => 144
[5,2,1,4,3] => 72
[5,2,3,1,4] => 144
[5,2,3,4,1] => 144
[5,2,4,1,3] => 144
[5,2,4,3,1] => 216
[5,3,1,2,4] => 144
[5,3,1,4,2] => 72
[5,3,2,1,4] => 216
[5,3,2,4,1] => 216
[5,3,4,1,2] => 144
[5,3,4,2,1] => 216
[5,4,1,2,3] => 144
[5,4,1,3,2] => 72
[5,4,2,1,3] => 216
[5,4,2,3,1] => 216
[5,4,3,1,2] => 216
[5,4,3,2,1] => 324
[1,2,3,4,5,6] => 288
[1,2,3,4,6,5] => 432
[1,2,3,5,4,6] => 432
[1,2,3,5,6,4] => 432
[1,2,3,6,4,5] => 432
[1,2,3,6,5,4] => 648
[1,2,4,3,5,6] => 432
[1,2,4,3,6,5] => 216
[1,2,4,5,3,6] => 432
[1,2,4,5,6,3] => 432
[1,2,4,6,3,5] => 432
[1,2,4,6,5,3] => 648
[1,2,5,3,4,6] => 432
[1,2,5,3,6,4] => 216
[1,2,5,4,3,6] => 648
[1,2,5,4,6,3] => 648
[1,2,5,6,3,4] => 432
[1,2,5,6,4,3] => 648
[1,2,6,3,4,5] => 432
[1,2,6,3,5,4] => 216
[1,2,6,4,3,5] => 648
[1,2,6,4,5,3] => 648
[1,2,6,5,3,4] => 648
[1,2,6,5,4,3] => 972
[1,3,2,4,5,6] => 432
[1,3,2,4,6,5] => 216
[1,3,2,5,4,6] => 216
[1,3,2,5,6,4] => 216
[1,3,2,6,4,5] => 216
[1,3,2,6,5,4] => 324
[1,3,4,2,5,6] => 432
[1,3,4,2,6,5] => 216
[1,3,4,5,2,6] => 432
[1,3,4,5,6,2] => 432
[1,3,4,6,2,5] => 432
[1,3,4,6,5,2] => 648
[1,3,5,2,4,6] => 432
[1,3,5,2,6,4] => 216
[1,3,5,4,2,6] => 648
[1,3,5,4,6,2] => 648
[1,3,5,6,2,4] => 432
[1,3,5,6,4,2] => 648
[1,3,6,2,4,5] => 432
[1,3,6,2,5,4] => 216
[1,3,6,4,2,5] => 648
[1,3,6,4,5,2] => 648
[1,3,6,5,2,4] => 648
[1,3,6,5,4,2] => 972
[1,4,2,3,5,6] => 432
[1,4,2,3,6,5] => 216
[1,4,2,5,3,6] => 216
[1,4,2,5,6,3] => 216
[1,4,2,6,3,5] => 216
[1,4,2,6,5,3] => 324
[1,4,3,2,5,6] => 648
[1,4,3,2,6,5] => 324
[1,4,3,5,2,6] => 648
[1,4,3,5,6,2] => 648
[1,4,3,6,2,5] => 648
[1,4,3,6,5,2] => 324
[1,4,5,2,3,6] => 432
[1,4,5,2,6,3] => 216
[1,4,5,3,2,6] => 648
[1,4,5,3,6,2] => 648
[1,4,5,6,2,3] => 432
[1,4,5,6,3,2] => 648
[1,4,6,2,3,5] => 432
[1,4,6,2,5,3] => 216
[1,4,6,3,2,5] => 648
[1,4,6,3,5,2] => 648
[1,4,6,5,2,3] => 648
[1,4,6,5,3,2] => 972
[1,5,2,3,4,6] => 432
[1,5,2,3,6,4] => 216
[1,5,2,4,3,6] => 216
[1,5,2,4,6,3] => 216
[1,5,2,6,3,4] => 216
[1,5,2,6,4,3] => 324
[1,5,3,2,4,6] => 648
[1,5,3,2,6,4] => 324
[1,5,3,4,2,6] => 648
[1,5,3,4,6,2] => 648
[1,5,3,6,2,4] => 648
[1,5,3,6,4,2] => 324
[1,5,4,2,3,6] => 648
[1,5,4,2,6,3] => 324
[1,5,4,3,2,6] => 972
[1,5,4,3,6,2] => 972
[1,5,4,6,2,3] => 648
[1,5,4,6,3,2] => 972
[1,5,6,2,3,4] => 432
[1,5,6,2,4,3] => 216
[1,5,6,3,2,4] => 648
[1,5,6,3,4,2] => 648
[1,5,6,4,2,3] => 648
[1,5,6,4,3,2] => 972
[1,6,2,3,4,5] => 432
[1,6,2,3,5,4] => 216
[1,6,2,4,3,5] => 216
[1,6,2,4,5,3] => 216
[1,6,2,5,3,4] => 216
[1,6,2,5,4,3] => 324
[1,6,3,2,4,5] => 648
[1,6,3,2,5,4] => 324
[1,6,3,4,2,5] => 648
[1,6,3,4,5,2] => 648
[1,6,3,5,2,4] => 648
[1,6,3,5,4,2] => 324
[1,6,4,2,3,5] => 648
[1,6,4,2,5,3] => 324
[1,6,4,3,2,5] => 972
[1,6,4,3,5,2] => 972
[1,6,4,5,2,3] => 648
[1,6,4,5,3,2] => 972
[1,6,5,2,3,4] => 648
[1,6,5,2,4,3] => 324
[1,6,5,3,2,4] => 972
[1,6,5,3,4,2] => 972
[1,6,5,4,2,3] => 972
[1,6,5,4,3,2] => 1458
[2,1,3,4,5,6] => 288
[2,1,3,4,6,5] => 432
[2,1,3,5,4,6] => 432
[2,1,3,5,6,4] => 432
[2,1,3,6,4,5] => 432
[2,1,3,6,5,4] => 648
[2,1,4,3,5,6] => 432
[2,1,4,3,6,5] => 216
[2,1,4,5,3,6] => 432
[2,1,4,5,6,3] => 432
[2,1,4,6,3,5] => 432
[2,1,4,6,5,3] => 648
[2,1,5,3,4,6] => 432
[2,1,5,3,6,4] => 216
[2,1,5,4,3,6] => 648
[2,1,5,4,6,3] => 648
[2,1,5,6,3,4] => 432
[2,1,5,6,4,3] => 648
[2,1,6,3,4,5] => 432
[2,1,6,3,5,4] => 216
[2,1,6,4,3,5] => 648
[2,1,6,4,5,3] => 648
[2,1,6,5,3,4] => 648
[2,1,6,5,4,3] => 972
[2,3,1,4,5,6] => 144
[2,3,1,4,6,5] => 216
[2,3,1,5,4,6] => 216
[2,3,1,5,6,4] => 216
[2,3,1,6,4,5] => 216
[2,3,1,6,5,4] => 324
[2,3,4,1,5,6] => 144
[2,3,4,1,6,5] => 216
[2,3,4,5,1,6] => 144
[2,3,4,5,6,1] => 288
[2,3,4,6,1,5] => 144
[2,3,4,6,5,1] => 432
[2,3,5,1,4,6] => 144
[2,3,5,1,6,4] => 216
[2,3,5,4,1,6] => 216
[2,3,5,4,6,1] => 432
[2,3,5,6,1,4] => 144
[2,3,5,6,4,1] => 432
[2,3,6,1,4,5] => 144
[2,3,6,1,5,4] => 216
[2,3,6,4,1,5] => 216
[2,3,6,4,5,1] => 432
[2,3,6,5,1,4] => 216
[2,3,6,5,4,1] => 648
[2,4,1,3,5,6] => 144
[2,4,1,3,6,5] => 216
[2,4,1,5,3,6] => 216
[2,4,1,5,6,3] => 216
[2,4,1,6,3,5] => 216
[2,4,1,6,5,3] => 324
[2,4,3,1,5,6] => 216
[2,4,3,1,6,5] => 108
[2,4,3,5,1,6] => 216
[2,4,3,5,6,1] => 432
[2,4,3,6,1,5] => 216
[2,4,3,6,5,1] => 216
[2,4,5,1,3,6] => 144
[2,4,5,1,6,3] => 216
[2,4,5,3,1,6] => 216
[2,4,5,3,6,1] => 432
[2,4,5,6,1,3] => 144
[2,4,5,6,3,1] => 432
[2,4,6,1,3,5] => 144
[2,4,6,1,5,3] => 216
[2,4,6,3,1,5] => 216
[2,4,6,3,5,1] => 432
[2,4,6,5,1,3] => 216
[2,4,6,5,3,1] => 648
[2,5,1,3,4,6] => 144
[2,5,1,3,6,4] => 216
[2,5,1,4,3,6] => 216
[2,5,1,4,6,3] => 216
[2,5,1,6,3,4] => 216
[2,5,1,6,4,3] => 324
[2,5,3,1,4,6] => 216
[2,5,3,1,6,4] => 108
[2,5,3,4,1,6] => 216
[2,5,3,4,6,1] => 432
[2,5,3,6,1,4] => 216
[2,5,3,6,4,1] => 216
[2,5,4,1,3,6] => 216
[2,5,4,1,6,3] => 108
[2,5,4,3,1,6] => 324
[2,5,4,3,6,1] => 648
[2,5,4,6,1,3] => 216
[2,5,4,6,3,1] => 648
[2,5,6,1,3,4] => 144
[2,5,6,1,4,3] => 216
[2,5,6,3,1,4] => 216
[2,5,6,3,4,1] => 432
[2,5,6,4,1,3] => 216
[2,5,6,4,3,1] => 648
[2,6,1,3,4,5] => 144
[2,6,1,3,5,4] => 216
[2,6,1,4,3,5] => 216
[2,6,1,4,5,3] => 216
[2,6,1,5,3,4] => 216
[2,6,1,5,4,3] => 324
[2,6,3,1,4,5] => 216
[2,6,3,1,5,4] => 108
[2,6,3,4,1,5] => 216
[2,6,3,4,5,1] => 432
[2,6,3,5,1,4] => 216
[2,6,3,5,4,1] => 216
[2,6,4,1,3,5] => 216
[2,6,4,1,5,3] => 108
[2,6,4,3,1,5] => 324
[2,6,4,3,5,1] => 648
[2,6,4,5,1,3] => 216
[2,6,4,5,3,1] => 648
[2,6,5,1,3,4] => 216
[2,6,5,1,4,3] => 108
[2,6,5,3,1,4] => 324
[2,6,5,3,4,1] => 648
[2,6,5,4,1,3] => 324
[2,6,5,4,3,1] => 972
[3,1,2,4,5,6] => 288
[3,1,2,4,6,5] => 432
[3,1,2,5,4,6] => 432
[3,1,2,5,6,4] => 432
[3,1,2,6,4,5] => 432
[3,1,2,6,5,4] => 648
[3,1,4,2,5,6] => 144
[3,1,4,2,6,5] => 216
[3,1,4,5,2,6] => 144
[3,1,4,5,6,2] => 288
[3,1,4,6,2,5] => 144
[3,1,4,6,5,2] => 432
[3,1,5,2,4,6] => 144
[3,1,5,2,6,4] => 216
[3,1,5,4,2,6] => 216
[3,1,5,4,6,2] => 432
[3,1,5,6,2,4] => 144
[3,1,5,6,4,2] => 432
[3,1,6,2,4,5] => 144
[3,1,6,2,5,4] => 216
[3,1,6,4,2,5] => 216
[3,1,6,4,5,2] => 432
[3,1,6,5,2,4] => 216
[3,1,6,5,4,2] => 648
[3,2,1,4,5,6] => 144
[3,2,1,4,6,5] => 216
[3,2,1,5,4,6] => 216
[3,2,1,5,6,4] => 216
[3,2,1,6,4,5] => 216
[3,2,1,6,5,4] => 324
[3,2,4,1,5,6] => 144
[3,2,4,1,6,5] => 216
[3,2,4,5,1,6] => 144
[3,2,4,5,6,1] => 288
[3,2,4,6,1,5] => 144
[3,2,4,6,5,1] => 432
[3,2,5,1,4,6] => 144
[3,2,5,1,6,4] => 216
[3,2,5,4,1,6] => 216
[3,2,5,4,6,1] => 432
[3,2,5,6,1,4] => 144
[3,2,5,6,4,1] => 432
[3,2,6,1,4,5] => 144
[3,2,6,1,5,4] => 216
[3,2,6,4,1,5] => 216
[3,2,6,4,5,1] => 432
[3,2,6,5,1,4] => 216
[3,2,6,5,4,1] => 648
[3,4,1,2,5,6] => 144
[3,4,1,2,6,5] => 216
[3,4,1,5,2,6] => 72
[3,4,1,5,6,2] => 144
[3,4,1,6,2,5] => 72
[3,4,1,6,5,2] => 216
[3,4,2,1,5,6] => 216
[3,4,2,1,6,5] => 108
[3,4,2,5,1,6] => 216
[3,4,2,5,6,1] => 432
[3,4,2,6,1,5] => 216
[3,4,2,6,5,1] => 216
[3,4,5,1,2,6] => 144
[3,4,5,1,6,2] => 144
[3,4,5,2,1,6] => 216
[3,4,5,2,6,1] => 432
[3,4,5,6,1,2] => 288
[3,4,5,6,2,1] => 432
[3,4,6,1,2,5] => 144
[3,4,6,1,5,2] => 144
[3,4,6,2,1,5] => 216
[3,4,6,2,5,1] => 432
[3,4,6,5,1,2] => 432
[3,4,6,5,2,1] => 648
[3,5,1,2,4,6] => 144
[3,5,1,2,6,4] => 216
[3,5,1,4,2,6] => 72
[3,5,1,4,6,2] => 144
[3,5,1,6,2,4] => 72
[3,5,1,6,4,2] => 216
[3,5,2,1,4,6] => 216
[3,5,2,1,6,4] => 108
[3,5,2,4,1,6] => 216
[3,5,2,4,6,1] => 432
[3,5,2,6,1,4] => 216
[3,5,2,6,4,1] => 216
[3,5,4,1,2,6] => 216
[3,5,4,1,6,2] => 216
[3,5,4,2,1,6] => 324
[3,5,4,2,6,1] => 648
[3,5,4,6,1,2] => 432
[3,5,4,6,2,1] => 648
[3,5,6,1,2,4] => 144
[3,5,6,1,4,2] => 144
[3,5,6,2,1,4] => 216
[3,5,6,2,4,1] => 432
[3,5,6,4,1,2] => 432
[3,5,6,4,2,1] => 648
[3,6,1,2,4,5] => 144
[3,6,1,2,5,4] => 216
[3,6,1,4,2,5] => 72
[3,6,1,4,5,2] => 144
[3,6,1,5,2,4] => 72
[3,6,1,5,4,2] => 216
[3,6,2,1,4,5] => 216
[3,6,2,1,5,4] => 108
[3,6,2,4,1,5] => 216
[3,6,2,4,5,1] => 432
[3,6,2,5,1,4] => 216
[3,6,2,5,4,1] => 216
[3,6,4,1,2,5] => 216
[3,6,4,1,5,2] => 216
[3,6,4,2,1,5] => 324
[3,6,4,2,5,1] => 648
[3,6,4,5,1,2] => 432
[3,6,4,5,2,1] => 648
[3,6,5,1,2,4] => 216
[3,6,5,1,4,2] => 216
[3,6,5,2,1,4] => 324
[3,6,5,2,4,1] => 648
[3,6,5,4,1,2] => 648
[3,6,5,4,2,1] => 972
[4,1,2,3,5,6] => 288
[4,1,2,3,6,5] => 432
[4,1,2,5,3,6] => 144
[4,1,2,5,6,3] => 288
[4,1,2,6,3,5] => 144
[4,1,2,6,5,3] => 432
[4,1,3,2,5,6] => 144
[4,1,3,2,6,5] => 216
[4,1,3,5,2,6] => 144
[4,1,3,5,6,2] => 288
[4,1,3,6,2,5] => 144
[4,1,3,6,5,2] => 432
[4,1,5,2,3,6] => 144
[4,1,5,2,6,3] => 144
[4,1,5,3,2,6] => 216
[4,1,5,3,6,2] => 432
[4,1,5,6,2,3] => 288
[4,1,5,6,3,2] => 432
[4,1,6,2,3,5] => 144
[4,1,6,2,5,3] => 144
[4,1,6,3,2,5] => 216
[4,1,6,3,5,2] => 432
[4,1,6,5,2,3] => 432
[4,1,6,5,3,2] => 648
[4,2,1,3,5,6] => 144
[4,2,1,3,6,5] => 216
[4,2,1,5,3,6] => 72
[4,2,1,5,6,3] => 144
[4,2,1,6,3,5] => 72
[4,2,1,6,5,3] => 216
[4,2,3,1,5,6] => 144
[4,2,3,1,6,5] => 216
[4,2,3,5,1,6] => 144
[4,2,3,5,6,1] => 288
[4,2,3,6,1,5] => 144
[4,2,3,6,5,1] => 432
[4,2,5,1,3,6] => 144
[4,2,5,1,6,3] => 144
[4,2,5,3,1,6] => 216
[4,2,5,3,6,1] => 432
[4,2,5,6,1,3] => 288
[4,2,5,6,3,1] => 432
[4,2,6,1,3,5] => 144
[4,2,6,1,5,3] => 144
[4,2,6,3,1,5] => 216
[4,2,6,3,5,1] => 432
[4,2,6,5,1,3] => 432
[4,2,6,5,3,1] => 648
[4,3,1,2,5,6] => 144
[4,3,1,2,6,5] => 216
[4,3,1,5,2,6] => 72
[4,3,1,5,6,2] => 144
[4,3,1,6,2,5] => 72
[4,3,1,6,5,2] => 216
[4,3,2,1,5,6] => 216
[4,3,2,1,6,5] => 108
[4,3,2,5,1,6] => 216
[4,3,2,5,6,1] => 432
[4,3,2,6,1,5] => 216
[4,3,2,6,5,1] => 216
[4,3,5,1,2,6] => 144
[4,3,5,1,6,2] => 144
[4,3,5,2,1,6] => 216
[4,3,5,2,6,1] => 432
[4,3,5,6,1,2] => 288
[4,3,5,6,2,1] => 432
[4,3,6,1,2,5] => 144
[4,3,6,1,5,2] => 144
[4,3,6,2,1,5] => 216
[4,3,6,2,5,1] => 432
[4,3,6,5,1,2] => 432
[4,3,6,5,2,1] => 648
[4,5,1,2,3,6] => 144
[4,5,1,2,6,3] => 144
[4,5,1,3,2,6] => 72
[4,5,1,3,6,2] => 144
[4,5,1,6,2,3] => 144
[4,5,1,6,3,2] => 216
[4,5,2,1,3,6] => 216
[4,5,2,1,6,3] => 216
[4,5,2,3,1,6] => 216
[4,5,2,3,6,1] => 432
[4,5,2,6,1,3] => 432
[4,5,2,6,3,1] => 216
[4,5,3,1,2,6] => 216
[4,5,3,1,6,2] => 216
[4,5,3,2,1,6] => 324
[4,5,3,2,6,1] => 648
[4,5,3,6,1,2] => 432
[4,5,3,6,2,1] => 648
[4,5,6,1,2,3] => 288
[4,5,6,1,3,2] => 144
[4,5,6,2,1,3] => 432
[4,5,6,2,3,1] => 432
[4,5,6,3,1,2] => 432
[4,5,6,3,2,1] => 648
[4,6,1,2,3,5] => 144
[4,6,1,2,5,3] => 144
[4,6,1,3,2,5] => 72
[4,6,1,3,5,2] => 144
[4,6,1,5,2,3] => 144
[4,6,1,5,3,2] => 216
[4,6,2,1,3,5] => 216
[4,6,2,1,5,3] => 216
[4,6,2,3,1,5] => 216
[4,6,2,3,5,1] => 432
[4,6,2,5,1,3] => 432
[4,6,2,5,3,1] => 216
[4,6,3,1,2,5] => 216
[4,6,3,1,5,2] => 216
[4,6,3,2,1,5] => 324
[4,6,3,2,5,1] => 648
[4,6,3,5,1,2] => 432
[4,6,3,5,2,1] => 648
[4,6,5,1,2,3] => 432
[4,6,5,1,3,2] => 216
[4,6,5,2,1,3] => 648
[4,6,5,2,3,1] => 648
[4,6,5,3,1,2] => 648
[4,6,5,3,2,1] => 972
[5,1,2,3,4,6] => 288
[5,1,2,3,6,4] => 288
[5,1,2,4,3,6] => 144
[5,1,2,4,6,3] => 288
[5,1,2,6,3,4] => 288
[5,1,2,6,4,3] => 432
[5,1,3,2,4,6] => 144
[5,1,3,2,6,4] => 144
[5,1,3,4,2,6] => 144
[5,1,3,4,6,2] => 288
[5,1,3,6,2,4] => 288
[5,1,3,6,4,2] => 432
[5,1,4,2,3,6] => 144
[5,1,4,2,6,3] => 144
[5,1,4,3,2,6] => 216
[5,1,4,3,6,2] => 432
[5,1,4,6,2,3] => 288
[5,1,4,6,3,2] => 432
[5,1,6,2,3,4] => 288
[5,1,6,2,4,3] => 144
[5,1,6,3,2,4] => 432
[5,1,6,3,4,2] => 432
[5,1,6,4,2,3] => 432
[5,1,6,4,3,2] => 648
[5,2,1,3,4,6] => 144
[5,2,1,3,6,4] => 144
[5,2,1,4,3,6] => 72
[5,2,1,4,6,3] => 144
[5,2,1,6,3,4] => 144
[5,2,1,6,4,3] => 216
[5,2,3,1,4,6] => 144
[5,2,3,1,6,4] => 144
[5,2,3,4,1,6] => 144
[5,2,3,4,6,1] => 288
[5,2,3,6,1,4] => 288
[5,2,3,6,4,1] => 432
[5,2,4,1,3,6] => 144
[5,2,4,1,6,3] => 144
[5,2,4,3,1,6] => 216
[5,2,4,3,6,1] => 432
[5,2,4,6,1,3] => 288
[5,2,4,6,3,1] => 432
[5,2,6,1,3,4] => 288
[5,2,6,1,4,3] => 144
[5,2,6,3,1,4] => 432
[5,2,6,3,4,1] => 432
[5,2,6,4,1,3] => 432
[5,2,6,4,3,1] => 648
[5,3,1,2,4,6] => 144
[5,3,1,2,6,4] => 144
[5,3,1,4,2,6] => 72
[5,3,1,4,6,2] => 144
[5,3,1,6,2,4] => 144
[5,3,1,6,4,2] => 216
[5,3,2,1,4,6] => 216
[5,3,2,1,6,4] => 216
[5,3,2,4,1,6] => 216
[5,3,2,4,6,1] => 432
[5,3,2,6,1,4] => 432
[5,3,2,6,4,1] => 216
[5,3,4,1,2,6] => 144
[5,3,4,1,6,2] => 144
[5,3,4,2,1,6] => 216
[5,3,4,2,6,1] => 432
[5,3,4,6,1,2] => 288
[5,3,4,6,2,1] => 432
[5,3,6,1,2,4] => 288
[5,3,6,1,4,2] => 144
[5,3,6,2,1,4] => 432
[5,3,6,2,4,1] => 432
[5,3,6,4,1,2] => 432
[5,3,6,4,2,1] => 648
[5,4,1,2,3,6] => 144
[5,4,1,2,6,3] => 144
[5,4,1,3,2,6] => 72
[5,4,1,3,6,2] => 144
[5,4,1,6,2,3] => 144
[5,4,1,6,3,2] => 216
[5,4,2,1,3,6] => 216
[5,4,2,1,6,3] => 216
[5,4,2,3,1,6] => 216
[5,4,2,3,6,1] => 432
[5,4,2,6,1,3] => 432
[5,4,2,6,3,1] => 216
[5,4,3,1,2,6] => 216
[5,4,3,1,6,2] => 216
[5,4,3,2,1,6] => 324
[5,4,3,2,6,1] => 648
[5,4,3,6,1,2] => 432
[5,4,3,6,2,1] => 648
[5,4,6,1,2,3] => 288
[5,4,6,1,3,2] => 144
[5,4,6,2,1,3] => 432
[5,4,6,2,3,1] => 432
[5,4,6,3,1,2] => 432
[5,4,6,3,2,1] => 648
[5,6,1,2,3,4] => 288
[5,6,1,2,4,3] => 144
[5,6,1,3,2,4] => 144
[5,6,1,3,4,2] => 144
[5,6,1,4,2,3] => 144
[5,6,1,4,3,2] => 216
[5,6,2,1,3,4] => 432
[5,6,2,1,4,3] => 216
[5,6,2,3,1,4] => 432
[5,6,2,3,4,1] => 432
[5,6,2,4,1,3] => 432
[5,6,2,4,3,1] => 216
[5,6,3,1,2,4] => 432
[5,6,3,1,4,2] => 216
[5,6,3,2,1,4] => 648
[5,6,3,2,4,1] => 648
[5,6,3,4,1,2] => 432
[5,6,3,4,2,1] => 648
[5,6,4,1,2,3] => 432
[5,6,4,1,3,2] => 216
[5,6,4,2,1,3] => 648
[5,6,4,2,3,1] => 648
[5,6,4,3,1,2] => 648
[5,6,4,3,2,1] => 972
[6,1,2,3,4,5] => 192
[6,1,2,3,5,4] => 288
[6,1,2,4,3,5] => 288
[6,1,2,4,5,3] => 288
[6,1,2,5,3,4] => 288
[6,1,2,5,4,3] => 432
[6,1,3,2,4,5] => 288
[6,1,3,2,5,4] => 144
[6,1,3,4,2,5] => 288
[6,1,3,4,5,2] => 288
[6,1,3,5,2,4] => 288
[6,1,3,5,4,2] => 432
[6,1,4,2,3,5] => 288
[6,1,4,2,5,3] => 144
[6,1,4,3,2,5] => 432
[6,1,4,3,5,2] => 432
[6,1,4,5,2,3] => 288
[6,1,4,5,3,2] => 432
[6,1,5,2,3,4] => 288
[6,1,5,2,4,3] => 144
[6,1,5,3,2,4] => 432
[6,1,5,3,4,2] => 432
[6,1,5,4,2,3] => 432
[6,1,5,4,3,2] => 648
[6,2,1,3,4,5] => 288
[6,2,1,3,5,4] => 144
[6,2,1,4,3,5] => 144
[6,2,1,4,5,3] => 144
[6,2,1,5,3,4] => 144
[6,2,1,5,4,3] => 216
[6,2,3,1,4,5] => 288
[6,2,3,1,5,4] => 144
[6,2,3,4,1,5] => 288
[6,2,3,4,5,1] => 288
[6,2,3,5,1,4] => 288
[6,2,3,5,4,1] => 432
[6,2,4,1,3,5] => 288
[6,2,4,1,5,3] => 144
[6,2,4,3,1,5] => 432
[6,2,4,3,5,1] => 432
[6,2,4,5,1,3] => 288
[6,2,4,5,3,1] => 432
[6,2,5,1,3,4] => 288
[6,2,5,1,4,3] => 144
[6,2,5,3,1,4] => 432
[6,2,5,3,4,1] => 432
[6,2,5,4,1,3] => 432
[6,2,5,4,3,1] => 648
[6,3,1,2,4,5] => 288
[6,3,1,2,5,4] => 144
[6,3,1,4,2,5] => 144
[6,3,1,4,5,2] => 144
[6,3,1,5,2,4] => 144
[6,3,1,5,4,2] => 216
[6,3,2,1,4,5] => 432
[6,3,2,1,5,4] => 216
[6,3,2,4,1,5] => 432
[6,3,2,4,5,1] => 432
[6,3,2,5,1,4] => 432
[6,3,2,5,4,1] => 216
[6,3,4,1,2,5] => 288
[6,3,4,1,5,2] => 144
[6,3,4,2,1,5] => 432
[6,3,4,2,5,1] => 432
[6,3,4,5,1,2] => 288
[6,3,4,5,2,1] => 432
[6,3,5,1,2,4] => 288
[6,3,5,1,4,2] => 144
[6,3,5,2,1,4] => 432
[6,3,5,2,4,1] => 432
[6,3,5,4,1,2] => 432
[6,3,5,4,2,1] => 648
[6,4,1,2,3,5] => 288
[6,4,1,2,5,3] => 144
[6,4,1,3,2,5] => 144
[6,4,1,3,5,2] => 144
[6,4,1,5,2,3] => 144
[6,4,1,5,3,2] => 216
[6,4,2,1,3,5] => 432
[6,4,2,1,5,3] => 216
[6,4,2,3,1,5] => 432
[6,4,2,3,5,1] => 432
[6,4,2,5,1,3] => 432
[6,4,2,5,3,1] => 216
[6,4,3,1,2,5] => 432
[6,4,3,1,5,2] => 216
[6,4,3,2,1,5] => 648
[6,4,3,2,5,1] => 648
[6,4,3,5,1,2] => 432
[6,4,3,5,2,1] => 648
[6,4,5,1,2,3] => 288
[6,4,5,1,3,2] => 144
[6,4,5,2,1,3] => 432
[6,4,5,2,3,1] => 432
[6,4,5,3,1,2] => 432
[6,4,5,3,2,1] => 648
[6,5,1,2,3,4] => 288
[6,5,1,2,4,3] => 144
[6,5,1,3,2,4] => 144
[6,5,1,3,4,2] => 144
[6,5,1,4,2,3] => 144
[6,5,1,4,3,2] => 216
[6,5,2,1,3,4] => 432
[6,5,2,1,4,3] => 216
[6,5,2,3,1,4] => 432
[6,5,2,3,4,1] => 432
[6,5,2,4,1,3] => 432
[6,5,2,4,3,1] => 216
[6,5,3,1,2,4] => 432
[6,5,3,1,4,2] => 216
[6,5,3,2,1,4] => 648
[6,5,3,2,4,1] => 648
[6,5,3,4,1,2] => 432
[6,5,3,4,2,1] => 648
[6,5,4,1,2,3] => 432
[6,5,4,1,3,2] => 216
[6,5,4,2,1,3] => 648
[6,5,4,2,3,1] => 648
[6,5,4,3,1,2] => 648
[6,5,4,3,2,1] => 972
click to show generating function       
Description
The shape of the tree associated to a permutation.
A permutation can be mapped to a rooted tree as described on the permutations page, and the statistic is given by $2^w 3^h$ where $w$ is the width St000325The width of the tree associated to a permutation. and $h$ is the height St000308The height of the tree associated to a permutation. of this tree.
Code
def statistic(pi):
    if pi == []: return (0, 0)
    h, w, i, branch, next = 0, 0, len(pi), [0], pi[0]

    while true:
        while next < branch[len(branch)-1]:
            branch.pop()

        current = 0
        w += 1
        while next > current:
            i -= 1
            h = max(h, len(branch))
            if i == 0: return 2^w*3^h
            branch.append(next)
            current, next = next, pi[i]
Created
Dec 11, 2015 at 11:05 by Peter Luschny
Updated
Dec 11, 2015 at 23:41 by Christian Stump