The first few most recent pending statistics:

Identifier
Values
[1] => 1
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 1
[1,2,4,3] => 6
[1,3,2,4] => 6
[1,3,4,2] => 8
[1,4,2,3] => 8
[1,4,3,2] => 6
[2,1,3,4] => 6
[2,1,4,3] => 9
[2,3,1,4] => 8
[2,3,4,1] => 9
[2,4,1,3] => 9
[2,4,3,1] => 8
[3,1,2,4] => 8
[3,1,4,2] => 9
[3,2,1,4] => 6
[3,2,4,1] => 8
[3,4,1,2] => 9
[3,4,2,1] => 9
[4,1,2,3] => 9
[4,1,3,2] => 8
[4,2,1,3] => 8
[4,2,3,1] => 6
[4,3,1,2] => 9
[4,3,2,1] => 9
[1,2,3,4,5] => 1
[1,2,3,5,4] => 10
[1,2,4,3,5] => 10
[1,2,4,5,3] => 20
[1,2,5,3,4] => 20
[1,2,5,4,3] => 10
[1,3,2,4,5] => 10
[1,3,2,5,4] => 45
[1,3,4,2,5] => 20
[1,3,4,5,2] => 45
[1,3,5,2,4] => 45
[1,3,5,4,2] => 20
[1,4,2,3,5] => 20
[1,4,2,5,3] => 45
[1,4,3,2,5] => 10
[1,4,3,5,2] => 20
[1,4,5,2,3] => 45
[1,4,5,3,2] => 45
[1,5,2,3,4] => 45
[1,5,2,4,3] => 20
[1,5,3,2,4] => 20
[1,5,3,4,2] => 10
[1,5,4,2,3] => 45
[1,5,4,3,2] => 45
[2,1,3,4,5] => 10
[2,1,3,5,4] => 45
[2,1,4,3,5] => 45
[2,1,4,5,3] => 44
[2,1,5,3,4] => 44
[2,1,5,4,3] => 45
[2,3,1,4,5] => 20
[2,3,1,5,4] => 44
[2,3,4,1,5] => 45
[2,3,4,5,1] => 44
[2,3,5,1,4] => 44
[2,3,5,4,1] => 45
[2,4,1,3,5] => 45
[2,4,1,5,3] => 44
[2,4,3,1,5] => 20
[2,4,3,5,1] => 45
[2,4,5,1,3] => 44
[2,4,5,3,1] => 44
[2,5,1,3,4] => 44
[2,5,1,4,3] => 45
[2,5,3,1,4] => 45
[2,5,3,4,1] => 20
[2,5,4,1,3] => 44
[2,5,4,3,1] => 44
[3,1,2,4,5] => 20
[3,1,2,5,4] => 44
[3,1,4,2,5] => 45
[3,1,4,5,2] => 44
[3,1,5,2,4] => 44
[3,1,5,4,2] => 45
[3,2,1,4,5] => 10
[3,2,1,5,4] => 45
[3,2,4,1,5] => 20
[3,2,4,5,1] => 45
[3,2,5,1,4] => 45
[3,2,5,4,1] => 20
[3,4,1,2,5] => 45
[3,4,1,5,2] => 44
[3,4,2,1,5] => 45
[3,4,2,5,1] => 44
[3,4,5,1,2] => 44
[3,4,5,2,1] => 44
[3,5,1,2,4] => 44
[3,5,1,4,2] => 45
[3,5,2,1,4] => 44
[3,5,2,4,1] => 45
[3,5,4,1,2] => 44
[3,5,4,2,1] => 44
[4,1,2,3,5] => 45
[4,1,2,5,3] => 44
[4,1,3,2,5] => 20
[4,1,3,5,2] => 45
[4,1,5,2,3] => 44
[4,1,5,3,2] => 44
[4,2,1,3,5] => 20
[4,2,1,5,3] => 45
[4,2,3,1,5] => 10
[4,2,3,5,1] => 20
[4,2,5,1,3] => 45
[4,2,5,3,1] => 45
[4,3,1,2,5] => 45
[4,3,1,5,2] => 44
[4,3,2,1,5] => 45
[4,3,2,5,1] => 44
[4,3,5,1,2] => 44
[4,3,5,2,1] => 44
[4,5,1,2,3] => 44
[4,5,1,3,2] => 44
[4,5,2,1,3] => 44
[4,5,2,3,1] => 44
[4,5,3,1,2] => 45
[4,5,3,2,1] => 45
[5,1,2,3,4] => 44
[5,1,2,4,3] => 45
[5,1,3,2,4] => 45
[5,1,3,4,2] => 20
[5,1,4,2,3] => 44
[5,1,4,3,2] => 44
[5,2,1,3,4] => 45
[5,2,1,4,3] => 20
[5,2,3,1,4] => 20
[5,2,3,4,1] => 10
[5,2,4,1,3] => 45
[5,2,4,3,1] => 45
[5,3,1,2,4] => 44
[5,3,1,4,2] => 45
[5,3,2,1,4] => 44
[5,3,2,4,1] => 45
[5,3,4,1,2] => 44
[5,3,4,2,1] => 44
[5,4,1,2,3] => 44
[5,4,1,3,2] => 44
[5,4,2,1,3] => 44
[5,4,2,3,1] => 44
[5,4,3,1,2] => 45
[5,4,3,2,1] => 45
[1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => 15
[1,2,3,5,4,6] => 15
[1,2,3,5,6,4] => 40
[1,2,3,6,4,5] => 40
[1,2,3,6,5,4] => 15
[1,2,4,3,5,6] => 15
[1,2,4,3,6,5] => 135
[1,2,4,5,3,6] => 40
[1,2,4,5,6,3] => 135
[1,2,4,6,3,5] => 135
[1,2,4,6,5,3] => 40
[1,2,5,3,4,6] => 40
[1,2,5,3,6,4] => 135
[1,2,5,4,3,6] => 15
[1,2,5,4,6,3] => 40
[1,2,5,6,3,4] => 135
[1,2,5,6,4,3] => 135
[1,2,6,3,4,5] => 135
[1,2,6,3,5,4] => 40
[1,2,6,4,3,5] => 40
[1,2,6,4,5,3] => 15
[1,2,6,5,3,4] => 135
[1,2,6,5,4,3] => 135
[1,3,2,4,5,6] => 15
[1,3,2,4,6,5] => 135
[1,3,2,5,4,6] => 135
[1,3,2,5,6,4] => 264
[1,3,2,6,4,5] => 264
[1,3,2,6,5,4] => 135
[1,3,4,2,5,6] => 40
[1,3,4,2,6,5] => 264
[1,3,4,5,2,6] => 135
[1,3,4,5,6,2] => 264
[1,3,4,6,2,5] => 264
[1,3,4,6,5,2] => 135
[1,3,5,2,4,6] => 135
[1,3,5,2,6,4] => 264
[1,3,5,4,2,6] => 40
[1,3,5,4,6,2] => 135
[1,3,5,6,2,4] => 264
[1,3,5,6,4,2] => 264
[1,3,6,2,4,5] => 264
[1,3,6,2,5,4] => 135
[1,3,6,4,2,5] => 135
[1,3,6,4,5,2] => 40
[1,3,6,5,2,4] => 264
[1,3,6,5,4,2] => 264
[1,4,2,3,5,6] => 40
[1,4,2,3,6,5] => 264
[1,4,2,5,3,6] => 135
[1,4,2,5,6,3] => 264
[1,4,2,6,3,5] => 264
[1,4,2,6,5,3] => 135
[1,4,3,2,5,6] => 15
[1,4,3,2,6,5] => 135
[1,4,3,5,2,6] => 40
[1,4,3,5,6,2] => 135
[1,4,3,6,2,5] => 135
[1,4,3,6,5,2] => 40
[1,4,5,2,3,6] => 135
[1,4,5,2,6,3] => 264
[1,4,5,3,2,6] => 135
[1,4,5,3,6,2] => 264
[1,4,5,6,2,3] => 264
[1,4,5,6,3,2] => 264
[1,4,6,2,3,5] => 264
[1,4,6,2,5,3] => 135
[1,4,6,3,2,5] => 264
[1,4,6,3,5,2] => 135
[1,4,6,5,2,3] => 264
[1,4,6,5,3,2] => 264
[1,5,2,3,4,6] => 135
[1,5,2,3,6,4] => 264
[1,5,2,4,3,6] => 40
[1,5,2,4,6,3] => 135
[1,5,2,6,3,4] => 264
[1,5,2,6,4,3] => 264
[1,5,3,2,4,6] => 40
[1,5,3,2,6,4] => 135
[1,5,3,4,2,6] => 15
[1,5,3,4,6,2] => 40
[1,5,3,6,2,4] => 135
[1,5,3,6,4,2] => 135
[1,5,4,2,3,6] => 135
[1,5,4,2,6,3] => 264
[1,5,4,3,2,6] => 135
[1,5,4,3,6,2] => 264
[1,5,4,6,2,3] => 264
[1,5,4,6,3,2] => 264
[1,5,6,2,3,4] => 264
[1,5,6,2,4,3] => 264
[1,5,6,3,2,4] => 264
[1,5,6,3,4,2] => 264
[1,5,6,4,2,3] => 135
[1,5,6,4,3,2] => 135
[1,6,2,3,4,5] => 264
[1,6,2,3,5,4] => 135
[1,6,2,4,3,5] => 135
[1,6,2,4,5,3] => 40
[1,6,2,5,3,4] => 264
[1,6,2,5,4,3] => 264
[1,6,3,2,4,5] => 135
[1,6,3,2,5,4] => 40
[1,6,3,4,2,5] => 40
[1,6,3,4,5,2] => 15
[1,6,3,5,2,4] => 135
[1,6,3,5,4,2] => 135
[1,6,4,2,3,5] => 264
[1,6,4,2,5,3] => 135
[1,6,4,3,2,5] => 264
[1,6,4,3,5,2] => 135
[1,6,4,5,2,3] => 264
[1,6,4,5,3,2] => 264
[1,6,5,2,3,4] => 264
[1,6,5,2,4,3] => 264
[1,6,5,3,2,4] => 264
[1,6,5,3,4,2] => 264
[1,6,5,4,2,3] => 135
[1,6,5,4,3,2] => 135
[2,1,3,4,5,6] => 15
[2,1,3,4,6,5] => 135
[2,1,3,5,4,6] => 135
[2,1,3,5,6,4] => 264
[2,1,3,6,4,5] => 264
[2,1,3,6,5,4] => 135
[2,1,4,3,5,6] => 135
[2,1,4,3,6,5] => 265
[2,1,4,5,3,6] => 264
[2,1,4,5,6,3] => 265
[2,1,4,6,3,5] => 265
[2,1,4,6,5,3] => 264
[2,1,5,3,4,6] => 264
[2,1,5,3,6,4] => 265
[2,1,5,4,3,6] => 135
[2,1,5,4,6,3] => 264
[2,1,5,6,3,4] => 265
[2,1,5,6,4,3] => 265
[2,1,6,3,4,5] => 265
[2,1,6,3,5,4] => 264
[2,1,6,4,3,5] => 264
[2,1,6,4,5,3] => 135
[2,1,6,5,3,4] => 265
[2,1,6,5,4,3] => 265
[2,3,1,4,5,6] => 40
[2,3,1,4,6,5] => 264
[2,3,1,5,4,6] => 264
[2,3,1,5,6,4] => 265
[2,3,1,6,4,5] => 265
[2,3,1,6,5,4] => 264
[2,3,4,1,5,6] => 135
[2,3,4,1,6,5] => 265
[2,3,4,5,1,6] => 264
[2,3,4,5,6,1] => 265
[2,3,4,6,1,5] => 265
[2,3,4,6,5,1] => 264
[2,3,5,1,4,6] => 264
[2,3,5,1,6,4] => 265
[2,3,5,4,1,6] => 135
[2,3,5,4,6,1] => 264
[2,3,5,6,1,4] => 265
[2,3,5,6,4,1] => 265
[2,3,6,1,4,5] => 265
[2,3,6,1,5,4] => 264
[2,3,6,4,1,5] => 264
[2,3,6,4,5,1] => 135
[2,3,6,5,1,4] => 265
[2,3,6,5,4,1] => 265
[2,4,1,3,5,6] => 135
[2,4,1,3,6,5] => 265
[2,4,1,5,3,6] => 264
[2,4,1,5,6,3] => 265
[2,4,1,6,3,5] => 265
[2,4,1,6,5,3] => 264
[2,4,3,1,5,6] => 40
[2,4,3,1,6,5] => 264
[2,4,3,5,1,6] => 135
[2,4,3,5,6,1] => 264
[2,4,3,6,1,5] => 264
[2,4,3,6,5,1] => 135
[2,4,5,1,3,6] => 264
[2,4,5,1,6,3] => 265
[2,4,5,3,1,6] => 264
[2,4,5,3,6,1] => 265
[2,4,5,6,1,3] => 265
[2,4,5,6,3,1] => 265
[2,4,6,1,3,5] => 265
[2,4,6,1,5,3] => 264
[2,4,6,3,1,5] => 265
[2,4,6,3,5,1] => 264
[2,4,6,5,1,3] => 265
[2,4,6,5,3,1] => 265
[2,5,1,3,4,6] => 264
[2,5,1,3,6,4] => 265
[2,5,1,4,3,6] => 135
[2,5,1,4,6,3] => 264
[2,5,1,6,3,4] => 265
[2,5,1,6,4,3] => 265
[2,5,3,1,4,6] => 135
[2,5,3,1,6,4] => 264
[2,5,3,4,1,6] => 40
[2,5,3,4,6,1] => 135
[2,5,3,6,1,4] => 264
[2,5,3,6,4,1] => 264
[2,5,4,1,3,6] => 264
[2,5,4,1,6,3] => 265
[2,5,4,3,1,6] => 264
[2,5,4,3,6,1] => 265
[2,5,4,6,1,3] => 265
[2,5,4,6,3,1] => 265
[2,5,6,1,3,4] => 265
[2,5,6,1,4,3] => 265
[2,5,6,3,1,4] => 265
[2,5,6,3,4,1] => 265
[2,5,6,4,1,3] => 264
[2,5,6,4,3,1] => 264
[2,6,1,3,4,5] => 265
[2,6,1,3,5,4] => 264
[2,6,1,4,3,5] => 264
[2,6,1,4,5,3] => 135
[2,6,1,5,3,4] => 265
[2,6,1,5,4,3] => 265
[2,6,3,1,4,5] => 264
[2,6,3,1,5,4] => 135
[2,6,3,4,1,5] => 135
[2,6,3,4,5,1] => 40
[2,6,3,5,1,4] => 264
[2,6,3,5,4,1] => 264
[2,6,4,1,3,5] => 265
[2,6,4,1,5,3] => 264
[2,6,4,3,1,5] => 265
[2,6,4,3,5,1] => 264
[2,6,4,5,1,3] => 265
[2,6,4,5,3,1] => 265
[2,6,5,1,3,4] => 265
[2,6,5,1,4,3] => 265
[2,6,5,3,1,4] => 265
[2,6,5,3,4,1] => 265
[2,6,5,4,1,3] => 264
[2,6,5,4,3,1] => 264
[3,1,2,4,5,6] => 40
[3,1,2,4,6,5] => 264
[3,1,2,5,4,6] => 264
[3,1,2,5,6,4] => 265
[3,1,2,6,4,5] => 265
[3,1,2,6,5,4] => 264
[3,1,4,2,5,6] => 135
[3,1,4,2,6,5] => 265
[3,1,4,5,2,6] => 264
[3,1,4,5,6,2] => 265
[3,1,4,6,2,5] => 265
[3,1,4,6,5,2] => 264
[3,1,5,2,4,6] => 264
[3,1,5,2,6,4] => 265
[3,1,5,4,2,6] => 135
[3,1,5,4,6,2] => 264
[3,1,5,6,2,4] => 265
[3,1,5,6,4,2] => 265
[3,1,6,2,4,5] => 265
[3,1,6,2,5,4] => 264
[3,1,6,4,2,5] => 264
[3,1,6,4,5,2] => 135
[3,1,6,5,2,4] => 265
[3,1,6,5,4,2] => 265
[3,2,1,4,5,6] => 15
[3,2,1,4,6,5] => 135
[3,2,1,5,4,6] => 135
[3,2,1,5,6,4] => 264
[3,2,1,6,4,5] => 264
[3,2,1,6,5,4] => 135
[3,2,4,1,5,6] => 40
[3,2,4,1,6,5] => 264
[3,2,4,5,1,6] => 135
[3,2,4,5,6,1] => 264
[3,2,4,6,1,5] => 264
[3,2,4,6,5,1] => 135
[3,2,5,1,4,6] => 135
[3,2,5,1,6,4] => 264
[3,2,5,4,1,6] => 40
[3,2,5,4,6,1] => 135
[3,2,5,6,1,4] => 264
[3,2,5,6,4,1] => 264
[3,2,6,1,4,5] => 264
[3,2,6,1,5,4] => 135
[3,2,6,4,1,5] => 135
[3,2,6,4,5,1] => 40
[3,2,6,5,1,4] => 264
[3,2,6,5,4,1] => 264
[3,4,1,2,5,6] => 135
[3,4,1,2,6,5] => 265
[3,4,1,5,2,6] => 264
[3,4,1,5,6,2] => 265
[3,4,1,6,2,5] => 265
[3,4,1,6,5,2] => 264
[3,4,2,1,5,6] => 135
[3,4,2,1,6,5] => 265
[3,4,2,5,1,6] => 264
[3,4,2,5,6,1] => 265
[3,4,2,6,1,5] => 265
[3,4,2,6,5,1] => 264
[3,4,5,1,2,6] => 264
[3,4,5,1,6,2] => 265
[3,4,5,2,1,6] => 264
[3,4,5,2,6,1] => 265
[3,4,5,6,1,2] => 265
[3,4,5,6,2,1] => 265
[3,4,6,1,2,5] => 265
[3,4,6,1,5,2] => 264
[3,4,6,2,1,5] => 265
[3,4,6,2,5,1] => 264
[3,4,6,5,1,2] => 265
[3,4,6,5,2,1] => 265
[3,5,1,2,4,6] => 264
[3,5,1,2,6,4] => 265
[3,5,1,4,2,6] => 135
[3,5,1,4,6,2] => 264
[3,5,1,6,2,4] => 265
[3,5,1,6,4,2] => 265
[3,5,2,1,4,6] => 264
[3,5,2,1,6,4] => 265
[3,5,2,4,1,6] => 135
[3,5,2,4,6,1] => 264
[3,5,2,6,1,4] => 265
[3,5,2,6,4,1] => 265
[3,5,4,1,2,6] => 264
[3,5,4,1,6,2] => 265
[3,5,4,2,1,6] => 264
[3,5,4,2,6,1] => 265
[3,5,4,6,1,2] => 265
[3,5,4,6,2,1] => 265
[3,5,6,1,2,4] => 265
[3,5,6,1,4,2] => 265
[3,5,6,2,1,4] => 265
[3,5,6,2,4,1] => 265
[3,5,6,4,1,2] => 264
[3,5,6,4,2,1] => 264
[3,6,1,2,4,5] => 265
[3,6,1,2,5,4] => 264
[3,6,1,4,2,5] => 264
[3,6,1,4,5,2] => 135
[3,6,1,5,2,4] => 265
[3,6,1,5,4,2] => 265
[3,6,2,1,4,5] => 265
[3,6,2,1,5,4] => 264
[3,6,2,4,1,5] => 264
[3,6,2,4,5,1] => 135
[3,6,2,5,1,4] => 265
[3,6,2,5,4,1] => 265
[3,6,4,1,2,5] => 265
[3,6,4,1,5,2] => 264
[3,6,4,2,1,5] => 265
[3,6,4,2,5,1] => 264
[3,6,4,5,1,2] => 265
[3,6,4,5,2,1] => 265
[3,6,5,1,2,4] => 265
[3,6,5,1,4,2] => 265
[3,6,5,2,1,4] => 265
[3,6,5,2,4,1] => 265
[3,6,5,4,1,2] => 264
[3,6,5,4,2,1] => 264
[4,1,2,3,5,6] => 135
[4,1,2,3,6,5] => 265
[4,1,2,5,3,6] => 264
[4,1,2,5,6,3] => 265
[4,1,2,6,3,5] => 265
[4,1,2,6,5,3] => 264
[4,1,3,2,5,6] => 40
[4,1,3,2,6,5] => 264
[4,1,3,5,2,6] => 135
[4,1,3,5,6,2] => 264
[4,1,3,6,2,5] => 264
[4,1,3,6,5,2] => 135
[4,1,5,2,3,6] => 264
[4,1,5,2,6,3] => 265
[4,1,5,3,2,6] => 264
[4,1,5,3,6,2] => 265
[4,1,5,6,2,3] => 265
[4,1,5,6,3,2] => 265
[4,1,6,2,3,5] => 265
[4,1,6,2,5,3] => 264
[4,1,6,3,2,5] => 265
[4,1,6,3,5,2] => 264
[4,1,6,5,2,3] => 265
[4,1,6,5,3,2] => 265
[4,2,1,3,5,6] => 40
[4,2,1,3,6,5] => 264
[4,2,1,5,3,6] => 135
[4,2,1,5,6,3] => 264
[4,2,1,6,3,5] => 264
[4,2,1,6,5,3] => 135
[4,2,3,1,5,6] => 15
[4,2,3,1,6,5] => 135
[4,2,3,5,1,6] => 40
[4,2,3,5,6,1] => 135
[4,2,3,6,1,5] => 135
[4,2,3,6,5,1] => 40
[4,2,5,1,3,6] => 135
[4,2,5,1,6,3] => 264
[4,2,5,3,1,6] => 135
[4,2,5,3,6,1] => 264
[4,2,5,6,1,3] => 264
[4,2,5,6,3,1] => 264
[4,2,6,1,3,5] => 264
[4,2,6,1,5,3] => 135
[4,2,6,3,1,5] => 264
[4,2,6,3,5,1] => 135
[4,2,6,5,1,3] => 264
[4,2,6,5,3,1] => 264
[4,3,1,2,5,6] => 135
[4,3,1,2,6,5] => 265
[4,3,1,5,2,6] => 264
[4,3,1,5,6,2] => 265
[4,3,1,6,2,5] => 265
[4,3,1,6,5,2] => 264
[4,3,2,1,5,6] => 135
[4,3,2,1,6,5] => 265
[4,3,2,5,1,6] => 264
[4,3,2,5,6,1] => 265
[4,3,2,6,1,5] => 265
[4,3,2,6,5,1] => 264
[4,3,5,1,2,6] => 264
[4,3,5,1,6,2] => 265
[4,3,5,2,1,6] => 264
[4,3,5,2,6,1] => 265
[4,3,5,6,1,2] => 265
[4,3,5,6,2,1] => 265
[4,3,6,1,2,5] => 265
[4,3,6,1,5,2] => 264
[4,3,6,2,1,5] => 265
[4,3,6,2,5,1] => 264
[4,3,6,5,1,2] => 265
[4,3,6,5,2,1] => 265
[4,5,1,2,3,6] => 264
[4,5,1,2,6,3] => 265
[4,5,1,3,2,6] => 264
[4,5,1,3,6,2] => 265
[4,5,1,6,2,3] => 265
[4,5,1,6,3,2] => 265
[4,5,2,1,3,6] => 264
[4,5,2,1,6,3] => 265
[4,5,2,3,1,6] => 264
[4,5,2,3,6,1] => 265
[4,5,2,6,1,3] => 265
[4,5,2,6,3,1] => 265
[4,5,3,1,2,6] => 135
[4,5,3,1,6,2] => 264
[4,5,3,2,1,6] => 135
[4,5,3,2,6,1] => 264
[4,5,3,6,1,2] => 264
[4,5,3,6,2,1] => 264
[4,5,6,1,2,3] => 265
[4,5,6,1,3,2] => 265
[4,5,6,2,1,3] => 265
[4,5,6,2,3,1] => 265
[4,5,6,3,1,2] => 265
[4,5,6,3,2,1] => 265
[4,6,1,2,3,5] => 265
[4,6,1,2,5,3] => 264
[4,6,1,3,2,5] => 265
[4,6,1,3,5,2] => 264
[4,6,1,5,2,3] => 265
[4,6,1,5,3,2] => 265
[4,6,2,1,3,5] => 265
[4,6,2,1,5,3] => 264
[4,6,2,3,1,5] => 265
[4,6,2,3,5,1] => 264
[4,6,2,5,1,3] => 265
[4,6,2,5,3,1] => 265
[4,6,3,1,2,5] => 264
[4,6,3,1,5,2] => 135
[4,6,3,2,1,5] => 264
[4,6,3,2,5,1] => 135
[4,6,3,5,1,2] => 264
[4,6,3,5,2,1] => 264
[4,6,5,1,2,3] => 265
[4,6,5,1,3,2] => 265
[4,6,5,2,1,3] => 265
[4,6,5,2,3,1] => 265
[4,6,5,3,1,2] => 265
[4,6,5,3,2,1] => 265
[5,1,2,3,4,6] => 264
[5,1,2,3,6,4] => 265
[5,1,2,4,3,6] => 135
[5,1,2,4,6,3] => 264
[5,1,2,6,3,4] => 265
[5,1,2,6,4,3] => 265
[5,1,3,2,4,6] => 135
[5,1,3,2,6,4] => 264
[5,1,3,4,2,6] => 40
[5,1,3,4,6,2] => 135
[5,1,3,6,2,4] => 264
[5,1,3,6,4,2] => 264
[5,1,4,2,3,6] => 264
[5,1,4,2,6,3] => 265
[5,1,4,3,2,6] => 264
[5,1,4,3,6,2] => 265
[5,1,4,6,2,3] => 265
[5,1,4,6,3,2] => 265
[5,1,6,2,3,4] => 265
[5,1,6,2,4,3] => 265
[5,1,6,3,2,4] => 265
[5,1,6,3,4,2] => 265
[5,1,6,4,2,3] => 264
[5,1,6,4,3,2] => 264
[5,2,1,3,4,6] => 135
[5,2,1,3,6,4] => 264
[5,2,1,4,3,6] => 40
[5,2,1,4,6,3] => 135
[5,2,1,6,3,4] => 264
[5,2,1,6,4,3] => 264
[5,2,3,1,4,6] => 40
[5,2,3,1,6,4] => 135
[5,2,3,4,1,6] => 15
[5,2,3,4,6,1] => 40
[5,2,3,6,1,4] => 135
[5,2,3,6,4,1] => 135
[5,2,4,1,3,6] => 135
[5,2,4,1,6,3] => 264
[5,2,4,3,1,6] => 135
[5,2,4,3,6,1] => 264
[5,2,4,6,1,3] => 264
[5,2,4,6,3,1] => 264
[5,2,6,1,3,4] => 264
[5,2,6,1,4,3] => 264
[5,2,6,3,1,4] => 264
[5,2,6,3,4,1] => 264
[5,2,6,4,1,3] => 135
[5,2,6,4,3,1] => 135
[5,3,1,2,4,6] => 264
[5,3,1,2,6,4] => 265
[5,3,1,4,2,6] => 135
[5,3,1,4,6,2] => 264
[5,3,1,6,2,4] => 265
[5,3,1,6,4,2] => 265
[5,3,2,1,4,6] => 264
[5,3,2,1,6,4] => 265
[5,3,2,4,1,6] => 135
[5,3,2,4,6,1] => 264
[5,3,2,6,1,4] => 265
[5,3,2,6,4,1] => 265
[5,3,4,1,2,6] => 264
[5,3,4,1,6,2] => 265
[5,3,4,2,1,6] => 264
[5,3,4,2,6,1] => 265
[5,3,4,6,1,2] => 265
[5,3,4,6,2,1] => 265
[5,3,6,1,2,4] => 265
[5,3,6,1,4,2] => 265
[5,3,6,2,1,4] => 265
[5,3,6,2,4,1] => 265
[5,3,6,4,1,2] => 264
[5,3,6,4,2,1] => 264
[5,4,1,2,3,6] => 264
[5,4,1,2,6,3] => 265
[5,4,1,3,2,6] => 264
[5,4,1,3,6,2] => 265
[5,4,1,6,2,3] => 265
[5,4,1,6,3,2] => 265
[5,4,2,1,3,6] => 264
[5,4,2,1,6,3] => 265
[5,4,2,3,1,6] => 264
[5,4,2,3,6,1] => 265
[5,4,2,6,1,3] => 265
[5,4,2,6,3,1] => 265
[5,4,3,1,2,6] => 135
[5,4,3,1,6,2] => 264
[5,4,3,2,1,6] => 135
[5,4,3,2,6,1] => 264
[5,4,3,6,1,2] => 264
[5,4,3,6,2,1] => 264
[5,4,6,1,2,3] => 265
[5,4,6,1,3,2] => 265
[5,4,6,2,1,3] => 265
[5,4,6,2,3,1] => 265
[5,4,6,3,1,2] => 265
[5,4,6,3,2,1] => 265
[5,6,1,2,3,4] => 265
[5,6,1,2,4,3] => 265
[5,6,1,3,2,4] => 265
[5,6,1,3,4,2] => 265
[5,6,1,4,2,3] => 264
[5,6,1,4,3,2] => 264
[5,6,2,1,3,4] => 265
[5,6,2,1,4,3] => 265
[5,6,2,3,1,4] => 265
[5,6,2,3,4,1] => 265
[5,6,2,4,1,3] => 264
[5,6,2,4,3,1] => 264
[5,6,3,1,2,4] => 264
[5,6,3,1,4,2] => 264
[5,6,3,2,1,4] => 264
[5,6,3,2,4,1] => 264
[5,6,3,4,1,2] => 135
[5,6,3,4,2,1] => 135
[5,6,4,1,2,3] => 265
[5,6,4,1,3,2] => 265
[5,6,4,2,1,3] => 265
[5,6,4,2,3,1] => 265
[5,6,4,3,1,2] => 265
[5,6,4,3,2,1] => 265
[6,1,2,3,4,5] => 265
[6,1,2,3,5,4] => 264
[6,1,2,4,3,5] => 264
[6,1,2,4,5,3] => 135
[6,1,2,5,3,4] => 265
[6,1,2,5,4,3] => 265
[6,1,3,2,4,5] => 264
[6,1,3,2,5,4] => 135
[6,1,3,4,2,5] => 135
[6,1,3,4,5,2] => 40
[6,1,3,5,2,4] => 264
[6,1,3,5,4,2] => 264
[6,1,4,2,3,5] => 265
[6,1,4,2,5,3] => 264
[6,1,4,3,2,5] => 265
[6,1,4,3,5,2] => 264
[6,1,4,5,2,3] => 265
[6,1,4,5,3,2] => 265
[6,1,5,2,3,4] => 265
[6,1,5,2,4,3] => 265
[6,1,5,3,2,4] => 265
[6,1,5,3,4,2] => 265
[6,1,5,4,2,3] => 264
[6,1,5,4,3,2] => 264
[6,2,1,3,4,5] => 264
[6,2,1,3,5,4] => 135
[6,2,1,4,3,5] => 135
[6,2,1,4,5,3] => 40
[6,2,1,5,3,4] => 264
[6,2,1,5,4,3] => 264
[6,2,3,1,4,5] => 135
[6,2,3,1,5,4] => 40
[6,2,3,4,1,5] => 40
[6,2,3,4,5,1] => 15
[6,2,3,5,1,4] => 135
[6,2,3,5,4,1] => 135
[6,2,4,1,3,5] => 264
[6,2,4,1,5,3] => 135
[6,2,4,3,1,5] => 264
[6,2,4,3,5,1] => 135
[6,2,4,5,1,3] => 264
[6,2,4,5,3,1] => 264
[6,2,5,1,3,4] => 264
[6,2,5,1,4,3] => 264
[6,2,5,3,1,4] => 264
[6,2,5,3,4,1] => 264
[6,2,5,4,1,3] => 135
[6,2,5,4,3,1] => 135
[6,3,1,2,4,5] => 265
[6,3,1,2,5,4] => 264
[6,3,1,4,2,5] => 264
[6,3,1,4,5,2] => 135
[6,3,1,5,2,4] => 265
[6,3,1,5,4,2] => 265
[6,3,2,1,4,5] => 265
[6,3,2,1,5,4] => 264
[6,3,2,4,1,5] => 264
[6,3,2,4,5,1] => 135
[6,3,2,5,1,4] => 265
[6,3,2,5,4,1] => 265
[6,3,4,1,2,5] => 265
[6,3,4,1,5,2] => 264
[6,3,4,2,1,5] => 265
[6,3,4,2,5,1] => 264
[6,3,4,5,1,2] => 265
[6,3,4,5,2,1] => 265
[6,3,5,1,2,4] => 265
[6,3,5,1,4,2] => 265
[6,3,5,2,1,4] => 265
[6,3,5,2,4,1] => 265
[6,3,5,4,1,2] => 264
[6,3,5,4,2,1] => 264
[6,4,1,2,3,5] => 265
[6,4,1,2,5,3] => 264
[6,4,1,3,2,5] => 265
[6,4,1,3,5,2] => 264
[6,4,1,5,2,3] => 265
[6,4,1,5,3,2] => 265
[6,4,2,1,3,5] => 265
[6,4,2,1,5,3] => 264
[6,4,2,3,1,5] => 265
[6,4,2,3,5,1] => 264
[6,4,2,5,1,3] => 265
[6,4,2,5,3,1] => 265
[6,4,3,1,2,5] => 264
[6,4,3,1,5,2] => 135
[6,4,3,2,1,5] => 264
[6,4,3,2,5,1] => 135
[6,4,3,5,1,2] => 264
[6,4,3,5,2,1] => 264
[6,4,5,1,2,3] => 265
[6,4,5,1,3,2] => 265
[6,4,5,2,1,3] => 265
[6,4,5,2,3,1] => 265
[6,4,5,3,1,2] => 265
[6,4,5,3,2,1] => 265
[6,5,1,2,3,4] => 265
[6,5,1,2,4,3] => 265
[6,5,1,3,2,4] => 265
[6,5,1,3,4,2] => 265
[6,5,1,4,2,3] => 264
[6,5,1,4,3,2] => 264
[6,5,2,1,3,4] => 265
[6,5,2,1,4,3] => 265
[6,5,2,3,1,4] => 265
[6,5,2,3,4,1] => 265
[6,5,2,4,1,3] => 264
[6,5,2,4,3,1] => 264
[6,5,3,1,2,4] => 264
[6,5,3,1,4,2] => 264
[6,5,3,2,1,4] => 264
[6,5,3,2,4,1] => 264
[6,5,3,4,1,2] => 135
[6,5,3,4,2,1] => 135
[6,5,4,1,2,3] => 265
[6,5,4,1,3,2] => 265
[6,5,4,2,1,3] => 265
[6,5,4,2,3,1] => 265
[6,5,4,3,1,2] => 265
[6,5,4,3,2,1] => 265
[1,2,3,4,5,6,7] => 1
[1,2,3,4,5,7,6] => 21
[1,2,3,4,6,5,7] => 21
[1,2,3,4,6,7,5] => 70
[1,2,3,4,7,5,6] => 70
[1,2,3,4,7,6,5] => 21
[1,2,3,5,4,6,7] => 21
[1,2,3,5,4,7,6] => 315
[1,2,3,5,6,4,7] => 70
[1,2,3,5,6,7,4] => 315
[1,2,3,5,7,4,6] => 315
[1,2,3,5,7,6,4] => 70
[1,2,3,6,4,5,7] => 70
[1,2,3,6,4,7,5] => 315
[1,2,3,6,5,4,7] => 21
[1,2,3,6,5,7,4] => 70
[1,2,3,6,7,4,5] => 315
[1,2,3,6,7,5,4] => 315
[1,2,3,7,4,5,6] => 315
[1,2,3,7,4,6,5] => 70
[1,2,3,7,5,4,6] => 70
[1,2,3,7,5,6,4] => 21
[1,2,3,7,6,4,5] => 315
[1,2,3,7,6,5,4] => 315
[1,2,4,3,5,6,7] => 21
[1,2,4,3,5,7,6] => 315
[1,2,4,3,6,5,7] => 315
[1,2,4,3,6,7,5] => 924
[1,2,4,3,7,5,6] => 924
[1,2,4,3,7,6,5] => 315
[1,2,4,5,3,6,7] => 70
[1,2,4,5,3,7,6] => 924
[1,2,4,5,6,3,7] => 315
[1,2,4,5,6,7,3] => 924
[1,2,4,5,7,3,6] => 924
[1,2,4,5,7,6,3] => 315
[1,2,4,6,3,5,7] => 315
[1,2,4,6,3,7,5] => 924
[1,2,4,6,5,3,7] => 70
[1,2,4,6,5,7,3] => 315
[1,2,4,6,7,3,5] => 924
[1,2,4,6,7,5,3] => 924
[1,2,4,7,3,5,6] => 924
[1,2,4,7,3,6,5] => 315
[1,2,4,7,5,3,6] => 315
[1,2,4,7,5,6,3] => 70
[1,2,4,7,6,3,5] => 924
[1,2,4,7,6,5,3] => 924
[1,2,5,3,4,6,7] => 70
[1,2,5,3,4,7,6] => 924
[1,2,5,3,6,4,7] => 315
[1,2,5,3,6,7,4] => 924
[1,2,5,3,7,4,6] => 924
[1,2,5,3,7,6,4] => 315
[1,2,5,4,3,6,7] => 21
[1,2,5,4,3,7,6] => 315
[1,2,5,4,6,3,7] => 70
[1,2,5,4,6,7,3] => 315
[1,2,5,4,7,3,6] => 315
[1,2,5,4,7,6,3] => 70
[1,2,5,6,3,4,7] => 315
[1,2,5,6,3,7,4] => 924
[1,2,5,6,4,3,7] => 315
[1,2,5,6,4,7,3] => 924
[1,2,5,6,7,3,4] => 924
[1,2,5,6,7,4,3] => 924
[1,2,5,7,3,4,6] => 924
[1,2,5,7,3,6,4] => 315
[1,2,5,7,4,3,6] => 924
[1,2,5,7,4,6,3] => 315
[1,2,5,7,6,3,4] => 924
[1,2,5,7,6,4,3] => 924
[1,2,6,3,4,5,7] => 315
[1,2,6,3,4,7,5] => 924
[1,2,6,3,5,4,7] => 70
[1,2,6,3,5,7,4] => 315
[1,2,6,3,7,4,5] => 924
[1,2,6,3,7,5,4] => 924
[1,2,6,4,3,5,7] => 70
[1,2,6,4,3,7,5] => 315
[1,2,6,4,5,3,7] => 21
[1,2,6,4,5,7,3] => 70
[1,2,6,4,7,3,5] => 315
[1,2,6,4,7,5,3] => 315
[1,2,6,5,3,4,7] => 315
[1,2,6,5,3,7,4] => 924
[1,2,6,5,4,3,7] => 315
[1,2,6,5,4,7,3] => 924
[1,2,6,5,7,3,4] => 924
[1,2,6,5,7,4,3] => 924
[1,2,6,7,3,4,5] => 924
[1,2,6,7,3,5,4] => 924
[1,2,6,7,4,3,5] => 924
[1,2,6,7,4,5,3] => 924
[1,2,6,7,5,3,4] => 315
[1,2,6,7,5,4,3] => 315
[1,2,7,3,4,5,6] => 924
[1,2,7,3,4,6,5] => 315
[1,2,7,3,5,4,6] => 315
[1,2,7,3,5,6,4] => 70
[1,2,7,3,6,4,5] => 924
[1,2,7,3,6,5,4] => 924
[1,2,7,4,3,5,6] => 315
[1,2,7,4,3,6,5] => 70
[1,2,7,4,5,3,6] => 70
[1,2,7,4,5,6,3] => 21
[1,2,7,4,6,3,5] => 315
[1,2,7,4,6,5,3] => 315
[1,2,7,5,3,4,6] => 924
[1,2,7,5,3,6,4] => 315
[1,2,7,5,4,3,6] => 924
[1,2,7,5,4,6,3] => 315
[1,2,7,5,6,3,4] => 924
[1,2,7,5,6,4,3] => 924
[1,2,7,6,3,4,5] => 924
[1,2,7,6,3,5,4] => 924
[1,2,7,6,4,3,5] => 924
[1,2,7,6,4,5,3] => 924
[1,2,7,6,5,3,4] => 315
[1,2,7,6,5,4,3] => 315
[1,3,2,4,5,6,7] => 21
[1,3,2,4,5,7,6] => 315
[1,3,2,4,6,5,7] => 315
[1,3,2,4,6,7,5] => 924
[1,3,2,4,7,5,6] => 924
[1,3,2,4,7,6,5] => 315
[1,3,2,5,4,6,7] => 315
[1,3,2,5,4,7,6] => 1855
[1,3,2,5,6,4,7] => 924
[1,3,2,5,6,7,4] => 1855
[1,3,2,5,7,4,6] => 1855
[1,3,2,5,7,6,4] => 924
[1,3,2,6,4,5,7] => 924
[1,3,2,6,4,7,5] => 1855
[1,3,2,6,5,4,7] => 315
[1,3,2,6,5,7,4] => 924
[1,3,2,6,7,4,5] => 1855
[1,3,2,6,7,5,4] => 1855
[1,3,2,7,4,5,6] => 1855
[1,3,2,7,4,6,5] => 924
[1,3,2,7,5,4,6] => 924
[1,3,2,7,5,6,4] => 315
[1,3,2,7,6,4,5] => 1855
[1,3,2,7,6,5,4] => 1855
[1,3,4,2,5,6,7] => 70
[1,3,4,2,5,7,6] => 924
[1,3,4,2,6,5,7] => 924
[1,3,4,2,6,7,5] => 1855
[1,3,4,2,7,5,6] => 1855
[1,3,4,2,7,6,5] => 924
[1,3,4,5,2,6,7] => 315
[1,3,4,5,2,7,6] => 1855
[1,3,4,5,6,2,7] => 924
[1,3,4,5,6,7,2] => 1855
[1,3,4,5,7,2,6] => 1855
[1,3,4,5,7,6,2] => 924
[1,3,4,6,2,5,7] => 924
[1,3,4,6,2,7,5] => 1855
[1,3,4,6,5,2,7] => 315
[1,3,4,6,5,7,2] => 924
[1,3,4,6,7,2,5] => 1855
[1,3,4,6,7,5,2] => 1855
[1,3,4,7,2,5,6] => 1855
[1,3,4,7,2,6,5] => 924
[1,3,4,7,5,2,6] => 924
[1,3,4,7,5,6,2] => 315
[1,3,4,7,6,2,5] => 1855
[1,3,4,7,6,5,2] => 1855
[1,3,5,2,4,6,7] => 315
[1,3,5,2,4,7,6] => 1855
[1,3,5,2,6,4,7] => 924
[1,3,5,2,6,7,4] => 1855
[1,3,5,2,7,4,6] => 1855
[1,3,5,2,7,6,4] => 924
[1,3,5,4,2,6,7] => 70
[1,3,5,4,2,7,6] => 924
[1,3,5,4,6,2,7] => 315
[1,3,5,4,6,7,2] => 924
[1,3,5,4,7,2,6] => 924
[1,3,5,4,7,6,2] => 315
[1,3,5,6,2,4,7] => 924
[1,3,5,6,2,7,4] => 1855
[1,3,5,6,4,2,7] => 924
[1,3,5,6,4,7,2] => 1855
[1,3,5,6,7,2,4] => 1855
[1,3,5,6,7,4,2] => 1855
[1,3,5,7,2,4,6] => 1855
[1,3,5,7,2,6,4] => 924
[1,3,5,7,4,2,6] => 1855
[1,3,5,7,4,6,2] => 924
[1,3,5,7,6,2,4] => 1855
[1,3,5,7,6,4,2] => 1855
[1,3,6,2,4,5,7] => 924
[1,3,6,2,4,7,5] => 1855
[1,3,6,2,5,4,7] => 315
[1,3,6,2,5,7,4] => 924
[1,3,6,2,7,4,5] => 1855
[1,3,6,2,7,5,4] => 1855
[1,3,6,4,2,5,7] => 315
[1,3,6,4,2,7,5] => 924
[1,3,6,4,5,2,7] => 70
[1,3,6,4,5,7,2] => 315
[1,3,6,4,7,2,5] => 924
[1,3,6,4,7,5,2] => 924
[1,3,6,5,2,4,7] => 924
[1,3,6,5,2,7,4] => 1855
[1,3,6,5,4,2,7] => 924
[1,3,6,5,4,7,2] => 1855
[1,3,6,5,7,2,4] => 1855
[1,3,6,5,7,4,2] => 1855
[1,3,6,7,2,4,5] => 1855
[1,3,6,7,2,5,4] => 1855
[1,3,6,7,4,2,5] => 1855
[1,3,6,7,4,5,2] => 1855
[1,3,6,7,5,2,4] => 924
[1,3,6,7,5,4,2] => 924
[1,3,7,2,4,5,6] => 1855
[1,3,7,2,4,6,5] => 924
[1,3,7,2,5,4,6] => 924
[1,3,7,2,5,6,4] => 315
[1,3,7,2,6,4,5] => 1855
[1,3,7,2,6,5,4] => 1855
[1,3,7,4,2,5,6] => 924
[1,3,7,4,2,6,5] => 315
[1,3,7,4,5,2,6] => 315
[1,3,7,4,5,6,2] => 70
[1,3,7,4,6,2,5] => 924
[1,3,7,4,6,5,2] => 924
[1,3,7,5,2,4,6] => 1855
[1,3,7,5,2,6,4] => 924
[1,3,7,5,4,2,6] => 1855
[1,3,7,5,4,6,2] => 924
[1,3,7,5,6,2,4] => 1855
[1,3,7,5,6,4,2] => 1855
[1,3,7,6,2,4,5] => 1855
[1,3,7,6,2,5,4] => 1855
[1,3,7,6,4,2,5] => 1855
[1,3,7,6,4,5,2] => 1855
[1,3,7,6,5,2,4] => 924
[1,3,7,6,5,4,2] => 924
[1,4,2,3,5,6,7] => 70
[1,4,2,3,5,7,6] => 924
[1,4,2,3,6,5,7] => 924
[1,4,2,3,6,7,5] => 1855
[1,4,2,3,7,5,6] => 1855
[1,4,2,3,7,6,5] => 924
[1,4,2,5,3,6,7] => 315
[1,4,2,5,3,7,6] => 1855
[1,4,2,5,6,3,7] => 924
[1,4,2,5,6,7,3] => 1855
[1,4,2,5,7,3,6] => 1855
[1,4,2,5,7,6,3] => 924
[1,4,2,6,3,5,7] => 924
[1,4,2,6,3,7,5] => 1855
[1,4,2,6,5,3,7] => 315
[1,4,2,6,5,7,3] => 924
[1,4,2,6,7,3,5] => 1855
[1,4,2,6,7,5,3] => 1855
[1,4,2,7,3,5,6] => 1855
[1,4,2,7,3,6,5] => 924
[1,4,2,7,5,3,6] => 924
[1,4,2,7,5,6,3] => 315
[1,4,2,7,6,3,5] => 1855
[1,4,2,7,6,5,3] => 1855
[1,4,3,2,5,6,7] => 21
[1,4,3,2,5,7,6] => 315
[1,4,3,2,6,5,7] => 315
[1,4,3,2,6,7,5] => 924
[1,4,3,2,7,5,6] => 924
[1,4,3,2,7,6,5] => 315
[1,4,3,5,2,6,7] => 70
[1,4,3,5,2,7,6] => 924
[1,4,3,5,6,2,7] => 315
[1,4,3,5,6,7,2] => 924
[1,4,3,5,7,2,6] => 924
[1,4,3,5,7,6,2] => 315
[1,4,3,6,2,5,7] => 315
[1,4,3,6,2,7,5] => 924
[1,4,3,6,5,2,7] => 70
[1,4,3,6,5,7,2] => 315
[1,4,3,6,7,2,5] => 924
[1,4,3,6,7,5,2] => 924
[1,4,3,7,2,5,6] => 924
[1,4,3,7,2,6,5] => 315
[1,4,3,7,5,2,6] => 315
[1,4,3,7,5,6,2] => 70
[1,4,3,7,6,2,5] => 924
[1,4,3,7,6,5,2] => 924
[1,4,5,2,3,6,7] => 315
[1,4,5,2,3,7,6] => 1855
[1,4,5,2,6,3,7] => 924
[1,4,5,2,6,7,3] => 1855
[1,4,5,2,7,3,6] => 1855
[1,4,5,2,7,6,3] => 924
[1,4,5,3,2,6,7] => 315
[1,4,5,3,2,7,6] => 1855
[1,4,5,3,6,2,7] => 924
[1,4,5,3,6,7,2] => 1855
[1,4,5,3,7,2,6] => 1855
[1,4,5,3,7,6,2] => 924
[1,4,5,6,2,3,7] => 924
[1,4,5,6,2,7,3] => 1855
[1,4,5,6,3,2,7] => 924
[1,4,5,6,3,7,2] => 1855
[1,4,5,6,7,2,3] => 1855
[1,4,5,6,7,3,2] => 1855
[1,4,5,7,2,3,6] => 1855
[1,4,5,7,2,6,3] => 924
[1,4,5,7,3,2,6] => 1855
[1,4,5,7,3,6,2] => 924
[1,4,5,7,6,2,3] => 1855
[1,4,5,7,6,3,2] => 1855
[1,4,6,2,3,5,7] => 924
[1,4,6,2,3,7,5] => 1855
[1,4,6,2,5,3,7] => 315
[1,4,6,2,5,7,3] => 924
[1,4,6,2,7,3,5] => 1855
[1,4,6,2,7,5,3] => 1855
[1,4,6,3,2,5,7] => 924
[1,4,6,3,2,7,5] => 1855
[1,4,6,3,5,2,7] => 315
[1,4,6,3,5,7,2] => 924
[1,4,6,3,7,2,5] => 1855
[1,4,6,3,7,5,2] => 1855
[1,4,6,5,2,3,7] => 924
[1,4,6,5,2,7,3] => 1855
[1,4,6,5,3,2,7] => 924
Description
The number of permutations such that the product with the permutation has the same number of fixed points.
More formally, given a permutation $\pi$, this is the number of permutations $\sigma$ such that $\pi$ and $\pi\sigma$ have the same number of fixed points.
Note that the number of permutations $\sigma$ such that $\pi$ and $\pi\sigma$ have the same cycle type is the size of the conjugacy class of $\pi$, St000690The size of the conjugacy class of a permutation..
References
[1] balli Number of Permutations? MathOverflow:144899
Code
def statistic(pi):
    m = pi.number_of_fixed_points()
    return sum(1 for tau in Permutations(pi.size()) if (pi*tau).number_of_fixed_points() == m)

Created
Apr 09, 2020 at 18:37 by Martin Rubey
Updated
Apr 09, 2020 at 18:37 by Martin Rubey
Identifier
St000000: Dyck paths ⟶ ℤ
Values
[1,0] generating graphics... => 0
[1,0,1,0] generating graphics... => 0
[1,1,0,0] generating graphics... => 1
[1,0,1,0,1,0] generating graphics... => 0
[1,0,1,1,0,0] generating graphics... => 1
[1,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,1,0,0] generating graphics... => 1
[1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,0] generating graphics... => 1
[1,0,1,1,1,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 1
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 1
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 1
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 1
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 3
Description
For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules).
The statistic gives half of the rank of the matrix C^t-C.
Code


DeclareOperation("radicalmathelp",[IsList]);

InstallMethod(radicalmathelp, "for a representation of a quiver", [IsList],0,function(LIST)

local A,projA,U,W,i,WW,injA,j,g,l,RegA,R,GG;

A:=LIST[1];
M:=LIST[2];
projA:=IndecProjectiveModules(A);
GG:=[];for i in projA do Append(GG,[RadicalOfModule(i)]);od;
W:=[];for i in GG do Append(W,[Size(HomOverAlgebra(i,M))]);od;
return(W);

end);





DeclareOperation("radicalmat",[IsList]);

InstallMethod(radicalmat, "for a representation of a quiver", [IsList],0,function(LIST)

local A,projA,U,W,i,WW,injA,j,g,l,RegA,R,GG;

A:=LIST[1];
g:=GlobalDimensionOfAlgebra(A,33);
projA:=IndecProjectiveModules(A);
GG:=[];for i in projA do Append(GG,[RadicalOfModule(i)]);od;
W:=[];for i in GG do Append(W,[radicalmathelp([A,i])]);od;
return(TransposedMat(W)-W);

end);
Created
Jan 05, 2020 at 16:56 by Rene Marczinzik
Updated
Jan 05, 2020 at 16:56 by Rene Marczinzik
Identifier
St000000: Dyck paths ⟶ ℤ
Values
[1,0] generating graphics... => 1
[1,0,1,0] generating graphics... => 3
[1,1,0,0] generating graphics... => 1
[1,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 6
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 7
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 7
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 7
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 7
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 7
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 7
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 7
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 6
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 7
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 7
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 7
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 7
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 7
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 6
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 7
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 6
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 7
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 7
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 7
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 7
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 7
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 5
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 6
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 6
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 7
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
Description
The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra.
Code

DeclareOperation("numberevenprojdiminj", [IsList]);

InstallMethod(numberevenprojdiminj, "for a representation of a quiver", [IsList],0,function(L)


local U,A,injA,W;

A:=L[1];
injA:=IndecInjectiveModules(A);
W:=Filtered(injA,x->IsEvenInt(ProjDimensionOfModule(x,33))=true);
return(Size(W));
end
);
Created
Dec 16, 2019 at 14:09 by Rene Marczinzik
Updated
Dec 16, 2019 at 14:09 by Rene Marczinzik