Identifier
- St001528: Permutations ⟶ ℤ
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
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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..
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
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