Identifier
Values
=>
[1]=>0
[-1]=>1
[1,2]=>0
[1,-2]=>3
[-1,2]=>1
[-1,-2]=>4
[2,1]=>1
[2,-1]=>2
[-2,1]=>2
[-2,-1]=>3
[1,2,3]=>0
[1,2,-3]=>5
[1,-2,3]=>3
[1,-2,-3]=>8
[-1,2,3]=>1
[-1,2,-3]=>6
[-1,-2,3]=>4
[-1,-2,-3]=>9
[1,3,2]=>1
[1,3,-2]=>4
[1,-3,2]=>4
[1,-3,-2]=>7
[-1,3,2]=>2
[-1,3,-2]=>5
[-1,-3,2]=>5
[-1,-3,-2]=>8
[2,1,3]=>1
[2,1,-3]=>6
[2,-1,3]=>2
[2,-1,-3]=>7
[-2,1,3]=>2
[-2,1,-3]=>7
[-2,-1,3]=>3
[-2,-1,-3]=>8
[2,3,1]=>2
[2,3,-1]=>3
[2,-3,1]=>5
[2,-3,-1]=>6
[-2,3,1]=>3
[-2,3,-1]=>4
[-2,-3,1]=>6
[-2,-3,-1]=>7
[3,1,2]=>2
[3,1,-2]=>5
[3,-1,2]=>3
[3,-1,-2]=>6
[-3,1,2]=>3
[-3,1,-2]=>6
[-3,-1,2]=>4
[-3,-1,-2]=>7
[3,2,1]=>3
[3,2,-1]=>4
[3,-2,1]=>4
[3,-2,-1]=>5
[-3,2,1]=>4
[-3,2,-1]=>5
[-3,-2,1]=>5
[-3,-2,-1]=>6
[1,2,3,4]=>0
[1,2,3,-4]=>7
[1,2,-3,4]=>5
[1,2,-3,-4]=>12
[1,-2,3,4]=>3
[1,-2,3,-4]=>10
[1,-2,-3,4]=>8
[1,-2,-3,-4]=>15
[-1,2,3,4]=>1
[-1,2,3,-4]=>8
[-1,2,-3,4]=>6
[-1,2,-3,-4]=>13
[-1,-2,3,4]=>4
[-1,-2,3,-4]=>11
[-1,-2,-3,4]=>9
[-1,-2,-3,-4]=>16
[1,2,4,3]=>1
[1,2,4,-3]=>6
[1,2,-4,3]=>6
[1,2,-4,-3]=>11
[1,-2,4,3]=>4
[1,-2,4,-3]=>9
[1,-2,-4,3]=>9
[1,-2,-4,-3]=>14
[-1,2,4,3]=>2
[-1,2,4,-3]=>7
[-1,2,-4,3]=>7
[-1,2,-4,-3]=>12
[-1,-2,4,3]=>5
[-1,-2,4,-3]=>10
[-1,-2,-4,3]=>10
[-1,-2,-4,-3]=>15
[1,3,2,4]=>1
[1,3,2,-4]=>8
[1,3,-2,4]=>4
[1,3,-2,-4]=>11
[1,-3,2,4]=>4
[1,-3,2,-4]=>11
[1,-3,-2,4]=>7
[1,-3,-2,-4]=>14
[-1,3,2,4]=>2
[-1,3,2,-4]=>9
[-1,3,-2,4]=>5
[-1,3,-2,-4]=>12
[-1,-3,2,4]=>5
[-1,-3,2,-4]=>12
[-1,-3,-2,4]=>8
[-1,-3,-2,-4]=>15
[1,3,4,2]=>2
[1,3,4,-2]=>5
[1,3,-4,2]=>7
[1,3,-4,-2]=>10
[1,-3,4,2]=>5
[1,-3,4,-2]=>8
[1,-3,-4,2]=>10
[1,-3,-4,-2]=>13
[-1,3,4,2]=>3
[-1,3,4,-2]=>6
[-1,3,-4,2]=>8
[-1,3,-4,-2]=>11
[-1,-3,4,2]=>6
[-1,-3,4,-2]=>9
[-1,-3,-4,2]=>11
[-1,-3,-4,-2]=>14
[1,4,2,3]=>2
[1,4,2,-3]=>7
[1,4,-2,3]=>5
[1,4,-2,-3]=>10
[1,-4,2,3]=>5
[1,-4,2,-3]=>10
[1,-4,-2,3]=>8
[1,-4,-2,-3]=>13
[-1,4,2,3]=>3
[-1,4,2,-3]=>8
[-1,4,-2,3]=>6
[-1,4,-2,-3]=>11
[-1,-4,2,3]=>6
[-1,-4,2,-3]=>11
[-1,-4,-2,3]=>9
[-1,-4,-2,-3]=>14
[1,4,3,2]=>3
[1,4,3,-2]=>6
[1,4,-3,2]=>6
[1,4,-3,-2]=>9
[1,-4,3,2]=>6
[1,-4,3,-2]=>9
[1,-4,-3,2]=>9
[1,-4,-3,-2]=>12
[-1,4,3,2]=>4
[-1,4,3,-2]=>7
[-1,4,-3,2]=>7
[-1,4,-3,-2]=>10
[-1,-4,3,2]=>7
[-1,-4,3,-2]=>10
[-1,-4,-3,2]=>10
[-1,-4,-3,-2]=>13
[2,1,3,4]=>1
[2,1,3,-4]=>8
[2,1,-3,4]=>6
[2,1,-3,-4]=>13
[2,-1,3,4]=>2
[2,-1,3,-4]=>9
[2,-1,-3,4]=>7
[2,-1,-3,-4]=>14
[-2,1,3,4]=>2
[-2,1,3,-4]=>9
[-2,1,-3,4]=>7
[-2,1,-3,-4]=>14
[-2,-1,3,4]=>3
[-2,-1,3,-4]=>10
[-2,-1,-3,4]=>8
[-2,-1,-3,-4]=>15
[2,1,4,3]=>2
[2,1,4,-3]=>7
[2,1,-4,3]=>7
[2,1,-4,-3]=>12
[2,-1,4,3]=>3
[2,-1,4,-3]=>8
[2,-1,-4,3]=>8
[2,-1,-4,-3]=>13
[-2,1,4,3]=>3
[-2,1,4,-3]=>8
[-2,1,-4,3]=>8
[-2,1,-4,-3]=>13
[-2,-1,4,3]=>4
[-2,-1,4,-3]=>9
[-2,-1,-4,3]=>9
[-2,-1,-4,-3]=>14
[2,3,1,4]=>2
[2,3,1,-4]=>9
[2,3,-1,4]=>3
[2,3,-1,-4]=>10
[2,-3,1,4]=>5
[2,-3,1,-4]=>12
[2,-3,-1,4]=>6
[2,-3,-1,-4]=>13
[-2,3,1,4]=>3
[-2,3,1,-4]=>10
[-2,3,-1,4]=>4
[-2,3,-1,-4]=>11
[-2,-3,1,4]=>6
[-2,-3,1,-4]=>13
[-2,-3,-1,4]=>7
[-2,-3,-1,-4]=>14
[2,3,4,1]=>3
[2,3,4,-1]=>4
[2,3,-4,1]=>8
[2,3,-4,-1]=>9
[2,-3,4,1]=>6
[2,-3,4,-1]=>7
[2,-3,-4,1]=>11
[2,-3,-4,-1]=>12
[-2,3,4,1]=>4
[-2,3,4,-1]=>5
[-2,3,-4,1]=>9
[-2,3,-4,-1]=>10
[-2,-3,4,1]=>7
[-2,-3,4,-1]=>8
[-2,-3,-4,1]=>12
[-2,-3,-4,-1]=>13
[2,4,1,3]=>3
[2,4,1,-3]=>8
[2,4,-1,3]=>4
[2,4,-1,-3]=>9
[2,-4,1,3]=>6
[2,-4,1,-3]=>11
[2,-4,-1,3]=>7
[2,-4,-1,-3]=>12
[-2,4,1,3]=>4
[-2,4,1,-3]=>9
[-2,4,-1,3]=>5
[-2,4,-1,-3]=>10
[-2,-4,1,3]=>7
[-2,-4,1,-3]=>12
[-2,-4,-1,3]=>8
[-2,-4,-1,-3]=>13
[2,4,3,1]=>4
[2,4,3,-1]=>5
[2,4,-3,1]=>7
[2,4,-3,-1]=>8
[2,-4,3,1]=>7
[2,-4,3,-1]=>8
[2,-4,-3,1]=>10
[2,-4,-3,-1]=>11
[-2,4,3,1]=>5
[-2,4,3,-1]=>6
[-2,4,-3,1]=>8
[-2,4,-3,-1]=>9
[-2,-4,3,1]=>8
[-2,-4,3,-1]=>9
[-2,-4,-3,1]=>11
[-2,-4,-3,-1]=>12
[3,1,2,4]=>2
[3,1,2,-4]=>9
[3,1,-2,4]=>5
[3,1,-2,-4]=>12
[3,-1,2,4]=>3
[3,-1,2,-4]=>10
[3,-1,-2,4]=>6
[3,-1,-2,-4]=>13
[-3,1,2,4]=>3
[-3,1,2,-4]=>10
[-3,1,-2,4]=>6
[-3,1,-2,-4]=>13
[-3,-1,2,4]=>4
[-3,-1,2,-4]=>11
[-3,-1,-2,4]=>7
[-3,-1,-2,-4]=>14
[3,1,4,2]=>3
[3,1,4,-2]=>6
[3,1,-4,2]=>8
[3,1,-4,-2]=>11
[3,-1,4,2]=>4
[3,-1,4,-2]=>7
[3,-1,-4,2]=>9
[3,-1,-4,-2]=>12
[-3,1,4,2]=>4
[-3,1,4,-2]=>7
[-3,1,-4,2]=>9
[-3,1,-4,-2]=>12
[-3,-1,4,2]=>5
[-3,-1,4,-2]=>8
[-3,-1,-4,2]=>10
[-3,-1,-4,-2]=>13
[3,2,1,4]=>3
[3,2,1,-4]=>10
[3,2,-1,4]=>4
[3,2,-1,-4]=>11
[3,-2,1,4]=>4
[3,-2,1,-4]=>11
[3,-2,-1,4]=>5
[3,-2,-1,-4]=>12
[-3,2,1,4]=>4
[-3,2,1,-4]=>11
[-3,2,-1,4]=>5
[-3,2,-1,-4]=>12
[-3,-2,1,4]=>5
[-3,-2,1,-4]=>12
[-3,-2,-1,4]=>6
[-3,-2,-1,-4]=>13
[3,2,4,1]=>4
[3,2,4,-1]=>5
[3,2,-4,1]=>9
[3,2,-4,-1]=>10
[3,-2,4,1]=>5
[3,-2,4,-1]=>6
[3,-2,-4,1]=>10
[3,-2,-4,-1]=>11
[-3,2,4,1]=>5
[-3,2,4,-1]=>6
[-3,2,-4,1]=>10
[-3,2,-4,-1]=>11
[-3,-2,4,1]=>6
[-3,-2,4,-1]=>7
[-3,-2,-4,1]=>11
[-3,-2,-4,-1]=>12
[3,4,1,2]=>4
[3,4,1,-2]=>7
[3,4,-1,2]=>5
[3,4,-1,-2]=>8
[3,-4,1,2]=>7
[3,-4,1,-2]=>10
[3,-4,-1,2]=>8
[3,-4,-1,-2]=>11
[-3,4,1,2]=>5
[-3,4,1,-2]=>8
[-3,4,-1,2]=>6
[-3,4,-1,-2]=>9
[-3,-4,1,2]=>8
[-3,-4,1,-2]=>11
[-3,-4,-1,2]=>9
[-3,-4,-1,-2]=>12
[3,4,2,1]=>5
[3,4,2,-1]=>6
[3,4,-2,1]=>6
[3,4,-2,-1]=>7
[3,-4,2,1]=>8
[3,-4,2,-1]=>9
[3,-4,-2,1]=>9
[3,-4,-2,-1]=>10
[-3,4,2,1]=>6
[-3,4,2,-1]=>7
[-3,4,-2,1]=>7
[-3,4,-2,-1]=>8
[-3,-4,2,1]=>9
[-3,-4,2,-1]=>10
[-3,-4,-2,1]=>10
[-3,-4,-2,-1]=>11
[4,1,2,3]=>3
[4,1,2,-3]=>8
[4,1,-2,3]=>6
[4,1,-2,-3]=>11
[4,-1,2,3]=>4
[4,-1,2,-3]=>9
[4,-1,-2,3]=>7
[4,-1,-2,-3]=>12
[-4,1,2,3]=>4
[-4,1,2,-3]=>9
[-4,1,-2,3]=>7
[-4,1,-2,-3]=>12
[-4,-1,2,3]=>5
[-4,-1,2,-3]=>10
[-4,-1,-2,3]=>8
[-4,-1,-2,-3]=>13
[4,1,3,2]=>4
[4,1,3,-2]=>7
[4,1,-3,2]=>7
[4,1,-3,-2]=>10
[4,-1,3,2]=>5
[4,-1,3,-2]=>8
[4,-1,-3,2]=>8
[4,-1,-3,-2]=>11
[-4,1,3,2]=>5
[-4,1,3,-2]=>8
[-4,1,-3,2]=>8
[-4,1,-3,-2]=>11
[-4,-1,3,2]=>6
[-4,-1,3,-2]=>9
[-4,-1,-3,2]=>9
[-4,-1,-3,-2]=>12
[4,2,1,3]=>4
[4,2,1,-3]=>9
[4,2,-1,3]=>5
[4,2,-1,-3]=>10
[4,-2,1,3]=>5
[4,-2,1,-3]=>10
[4,-2,-1,3]=>6
[4,-2,-1,-3]=>11
[-4,2,1,3]=>5
[-4,2,1,-3]=>10
[-4,2,-1,3]=>6
[-4,2,-1,-3]=>11
[-4,-2,1,3]=>6
[-4,-2,1,-3]=>11
[-4,-2,-1,3]=>7
[-4,-2,-1,-3]=>12
[4,2,3,1]=>5
[4,2,3,-1]=>6
[4,2,-3,1]=>8
[4,2,-3,-1]=>9
[4,-2,3,1]=>6
[4,-2,3,-1]=>7
[4,-2,-3,1]=>9
[4,-2,-3,-1]=>10
[-4,2,3,1]=>6
[-4,2,3,-1]=>7
[-4,2,-3,1]=>9
[-4,2,-3,-1]=>10
[-4,-2,3,1]=>7
[-4,-2,3,-1]=>8
[-4,-2,-3,1]=>10
[-4,-2,-3,-1]=>11
[4,3,1,2]=>5
[4,3,1,-2]=>8
[4,3,-1,2]=>6
[4,3,-1,-2]=>9
[4,-3,1,2]=>6
[4,-3,1,-2]=>9
[4,-3,-1,2]=>7
[4,-3,-1,-2]=>10
[-4,3,1,2]=>6
[-4,3,1,-2]=>9
[-4,3,-1,2]=>7
[-4,3,-1,-2]=>10
[-4,-3,1,2]=>7
[-4,-3,1,-2]=>10
[-4,-3,-1,2]=>8
[-4,-3,-1,-2]=>11
[4,3,2,1]=>6
[4,3,2,-1]=>7
[4,3,-2,1]=>7
[4,3,-2,-1]=>8
[4,-3,2,1]=>7
[4,-3,2,-1]=>8
[4,-3,-2,1]=>8
[4,-3,-2,-1]=>9
[-4,3,2,1]=>7
[-4,3,2,-1]=>8
[-4,3,-2,1]=>8
[-4,3,-2,-1]=>9
[-4,-3,2,1]=>8
[-4,-3,2,-1]=>9
[-4,-3,-2,1]=>9
[-4,-3,-2,-1]=>10
[1,2,3,4,5]=>0
[1,2,3,4,-5]=>9
[-1,2,3,4,5]=>1
[1,2,3,5,4]=>1
[1,2,3,5,-4]=>8
[-1,2,3,5,4]=>2
[1,2,4,3,5]=>1
[1,2,4,3,-5]=>10
[-1,2,4,3,5]=>2
[1,2,4,5,3]=>2
[1,2,4,5,-3]=>7
[-1,2,4,5,3]=>3
[1,2,5,3,4]=>2
[1,2,5,3,-4]=>9
[-1,2,5,3,4]=>3
[1,2,5,4,3]=>3
[1,2,5,4,-3]=>8
[-1,2,5,4,3]=>4
[1,3,2,4,5]=>1
[1,3,2,4,-5]=>10
[-1,3,2,4,5]=>2
[1,3,2,5,4]=>2
[1,3,2,5,-4]=>9
[-1,3,2,5,4]=>3
[1,3,4,2,5]=>2
[1,3,4,2,-5]=>11
[-1,3,4,2,5]=>3
[1,3,4,5,2]=>3
[1,3,4,5,-2]=>6
[-1,3,4,5,2]=>4
[1,3,5,2,4]=>3
[1,3,5,2,-4]=>10
[-1,3,5,2,4]=>4
[1,3,5,4,2]=>4
[1,3,5,4,-2]=>7
[-1,3,5,4,2]=>5
[1,4,2,3,5]=>2
[1,4,2,3,-5]=>11
[-1,4,2,3,5]=>3
[1,4,2,5,3]=>3
[1,4,2,5,-3]=>8
[-1,4,2,5,3]=>4
[1,4,3,2,5]=>3
[1,4,3,2,-5]=>12
[-1,4,3,2,5]=>4
[1,4,3,5,2]=>4
[1,4,3,5,-2]=>7
[-1,4,3,5,2]=>5
[1,4,5,2,3]=>4
[1,4,5,2,-3]=>9
[-1,4,5,2,3]=>5
[1,4,5,3,2]=>5
[1,4,5,3,-2]=>8
[-1,4,5,3,2]=>6
[1,5,2,3,4]=>3
[1,5,2,3,-4]=>10
[-1,5,2,3,4]=>4
[1,5,2,4,3]=>4
[1,5,2,4,-3]=>9
[-1,5,2,4,3]=>5
[1,5,3,2,4]=>4
[1,5,3,2,-4]=>11
[-1,5,3,2,4]=>5
[1,5,3,4,2]=>5
[1,5,3,4,-2]=>8
[-1,5,3,4,2]=>6
[1,5,4,2,3]=>5
[1,5,4,2,-3]=>10
[-1,5,4,2,3]=>6
[1,5,4,3,2]=>6
[1,5,4,3,-2]=>9
[-1,5,4,3,2]=>7
[2,1,3,4,5]=>1
[2,1,3,4,-5]=>10
[2,-1,3,4,5]=>2
[2,1,3,5,4]=>2
[2,1,3,5,-4]=>9
[2,-1,3,5,4]=>3
[2,1,4,3,5]=>2
[2,1,4,3,-5]=>11
[2,-1,4,3,5]=>3
[2,1,4,5,3]=>3
[2,1,4,5,-3]=>8
[2,-1,4,5,3]=>4
[2,1,5,3,4]=>3
[2,1,5,3,-4]=>10
[2,-1,5,3,4]=>4
[2,1,5,4,3]=>4
[2,1,5,4,-3]=>9
[2,-1,5,4,3]=>5
[2,3,1,4,5]=>2
[2,3,1,4,-5]=>11
[2,3,-1,4,5]=>3
[2,3,1,5,4]=>3
[2,3,1,5,-4]=>10
[2,3,-1,5,4]=>4
[2,3,4,1,5]=>3
[2,3,4,1,-5]=>12
[2,3,4,-1,5]=>4
[2,3,4,5,1]=>4
[2,3,4,5,-1]=>5
[2,3,5,1,4]=>4
[2,3,5,1,-4]=>11
[2,3,5,-1,4]=>5
[2,3,5,4,1]=>5
[2,3,5,4,-1]=>6
[2,4,1,3,5]=>3
[2,4,1,3,-5]=>12
[2,4,-1,3,5]=>4
[2,4,1,5,3]=>4
[2,4,1,5,-3]=>9
[2,4,-1,5,3]=>5
[2,4,3,1,5]=>4
[2,4,3,1,-5]=>13
[2,4,3,-1,5]=>5
[2,4,3,5,1]=>5
[2,4,3,5,-1]=>6
[2,4,5,1,3]=>5
[2,4,5,1,-3]=>10
[2,4,5,-1,3]=>6
[2,4,5,3,1]=>6
[2,4,5,3,-1]=>7
[2,5,1,3,4]=>4
[2,5,1,3,-4]=>11
[2,5,-1,3,4]=>5
[2,5,1,4,3]=>5
[2,5,1,4,-3]=>10
[2,5,-1,4,3]=>6
[2,5,3,1,4]=>5
[2,5,3,1,-4]=>12
[2,5,3,-1,4]=>6
[2,5,3,4,1]=>6
[2,5,3,4,-1]=>7
[2,5,4,1,3]=>6
[2,5,4,1,-3]=>11
[2,5,4,-1,3]=>7
[2,5,4,3,1]=>7
[2,5,4,3,-1]=>8
[3,1,2,4,5]=>2
[3,1,2,4,-5]=>11
[3,-1,2,4,5]=>3
[3,1,2,5,4]=>3
[3,1,2,5,-4]=>10
[3,-1,2,5,4]=>4
[3,1,4,2,5]=>3
[3,1,4,2,-5]=>12
[3,-1,4,2,5]=>4
[3,1,4,5,2]=>4
[3,1,4,5,-2]=>7
[3,-1,4,5,2]=>5
[3,1,5,2,4]=>4
[3,1,5,2,-4]=>11
[3,-1,5,2,4]=>5
[3,1,5,4,2]=>5
[3,1,5,4,-2]=>8
[3,-1,5,4,2]=>6
[3,2,1,4,5]=>3
[3,2,1,4,-5]=>12
[3,2,-1,4,5]=>4
[3,2,1,5,4]=>4
[3,2,1,5,-4]=>11
[3,2,-1,5,4]=>5
[3,2,4,1,5]=>4
[3,2,4,1,-5]=>13
[3,2,4,-1,5]=>5
[3,2,4,5,1]=>5
[3,2,4,5,-1]=>6
[3,2,5,1,4]=>5
[3,2,5,1,-4]=>12
[3,2,5,-1,4]=>6
[3,2,5,4,1]=>6
[3,2,5,4,-1]=>7
[3,4,1,2,5]=>4
[3,4,1,2,-5]=>13
[3,4,-1,2,5]=>5
[3,4,1,5,2]=>5
[3,4,1,5,-2]=>8
[3,4,-1,5,2]=>6
[3,4,2,1,5]=>5
[3,4,2,1,-5]=>14
[3,4,2,-1,5]=>6
[3,4,2,5,1]=>6
[3,4,2,5,-1]=>7
[3,4,5,1,2]=>6
[3,4,5,1,-2]=>9
[3,4,5,-1,2]=>7
[3,4,5,2,1]=>7
[3,4,5,2,-1]=>8
[3,5,1,2,4]=>5
[3,5,1,2,-4]=>12
[3,5,-1,2,4]=>6
[3,5,1,4,2]=>6
[3,5,1,4,-2]=>9
[3,5,-1,4,2]=>7
[3,5,2,1,4]=>6
[3,5,2,1,-4]=>13
[3,5,2,-1,4]=>7
[3,5,2,4,1]=>7
[3,5,2,4,-1]=>8
[3,5,4,1,2]=>7
[3,5,4,1,-2]=>10
[3,5,4,-1,2]=>8
[3,5,4,2,1]=>8
[3,5,4,2,-1]=>9
[4,1,2,3,5]=>3
[4,1,2,3,-5]=>12
[4,-1,2,3,5]=>4
[4,1,2,5,3]=>4
[4,1,2,5,-3]=>9
[4,-1,2,5,3]=>5
[4,1,3,2,5]=>4
[4,1,3,2,-5]=>13
[4,-1,3,2,5]=>5
[4,1,3,5,2]=>5
[4,1,3,5,-2]=>8
[4,-1,3,5,2]=>6
[4,1,5,2,3]=>5
[4,1,5,2,-3]=>10
[4,-1,5,2,3]=>6
[4,1,5,3,2]=>6
[4,1,5,3,-2]=>9
[4,-1,5,3,2]=>7
[4,2,1,3,5]=>4
[4,2,1,3,-5]=>13
[4,2,-1,3,5]=>5
[4,2,1,5,3]=>5
[4,2,1,5,-3]=>10
[4,2,-1,5,3]=>6
[4,2,3,1,5]=>5
[4,2,3,1,-5]=>14
[4,2,3,-1,5]=>6
[4,2,3,5,1]=>6
[4,2,3,5,-1]=>7
[4,2,5,1,3]=>6
[4,2,5,1,-3]=>11
[4,2,5,-1,3]=>7
[4,2,5,3,1]=>7
[4,2,5,3,-1]=>8
[4,3,1,2,5]=>5
[4,3,1,2,-5]=>14
[4,3,-1,2,5]=>6
[4,3,1,5,2]=>6
[4,3,1,5,-2]=>9
[4,3,-1,5,2]=>7
[4,3,2,1,5]=>6
[4,3,2,1,-5]=>15
[4,3,2,-1,5]=>7
[4,3,2,5,1]=>7
[4,3,2,5,-1]=>8
[4,3,5,1,2]=>7
[4,3,5,1,-2]=>10
[4,3,5,-1,2]=>8
[4,3,5,2,1]=>8
[4,3,5,2,-1]=>9
[4,5,1,2,3]=>6
[4,5,1,2,-3]=>11
[4,5,-1,2,3]=>7
[4,5,1,3,2]=>7
[4,5,1,3,-2]=>10
[4,5,-1,3,2]=>8
[4,5,2,1,3]=>7
[4,5,2,1,-3]=>12
[4,5,2,-1,3]=>8
[4,5,2,3,1]=>8
[4,5,2,3,-1]=>9
[4,5,3,1,2]=>8
[4,5,3,1,-2]=>11
[4,5,3,-1,2]=>9
[4,5,3,2,1]=>9
[4,5,3,2,-1]=>10
[5,1,2,3,4]=>4
[5,1,2,3,-4]=>11
[5,-1,2,3,4]=>5
[5,1,2,4,3]=>5
[5,1,2,4,-3]=>10
[5,-1,2,4,3]=>6
[5,1,3,2,4]=>5
[5,1,3,2,-4]=>12
[5,-1,3,2,4]=>6
[5,1,3,4,2]=>6
[5,1,3,4,-2]=>9
[5,-1,3,4,2]=>7
[5,1,4,2,3]=>6
[5,1,4,2,-3]=>11
[5,-1,4,2,3]=>7
[5,1,4,3,2]=>7
[5,1,4,3,-2]=>10
[5,-1,4,3,2]=>8
[5,2,1,3,4]=>5
[5,2,1,3,-4]=>12
[5,2,-1,3,4]=>6
[5,2,1,4,3]=>6
[5,2,1,4,-3]=>11
[5,2,-1,4,3]=>7
[5,2,3,1,4]=>6
[5,2,3,1,-4]=>13
[5,2,3,-1,4]=>7
[5,2,3,4,1]=>7
[5,2,3,4,-1]=>8
[5,2,4,1,3]=>7
[5,2,4,1,-3]=>12
[5,2,4,-1,3]=>8
[5,2,4,3,1]=>8
[5,2,4,3,-1]=>9
[5,3,1,2,4]=>6
[5,3,1,2,-4]=>13
[5,3,-1,2,4]=>7
[5,3,1,4,2]=>7
[5,3,1,4,-2]=>10
[5,3,-1,4,2]=>8
[5,3,2,1,4]=>7
[5,3,2,1,-4]=>14
[5,3,2,-1,4]=>8
[5,3,2,4,1]=>8
[5,3,2,4,-1]=>9
[5,3,4,1,2]=>8
[5,3,4,1,-2]=>11
[5,3,4,-1,2]=>9
[5,3,4,2,1]=>9
[5,3,4,2,-1]=>10
[5,4,1,2,3]=>7
[5,4,1,2,-3]=>12
[5,4,-1,2,3]=>8
[5,4,1,3,2]=>8
[5,4,1,3,-2]=>11
[5,4,-1,3,2]=>9
[5,4,2,1,3]=>8
[5,4,2,1,-3]=>13
[5,4,2,-1,3]=>9
[5,4,2,3,1]=>9
[5,4,2,3,-1]=>10
[5,4,3,1,2]=>9
[5,4,3,1,-2]=>12
[5,4,3,-1,2]=>10
[5,4,3,2,1]=>10
[5,4,3,2,-1]=>11
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>3
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>2
[1,2,4,5,6,3]=>3
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>4
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>3
[1,2,6,4,5,3]=>5
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>4
[1,3,4,2,5,6]=>2
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>6
[1,3,6,2,4,5]=>4
[1,3,6,4,5,2]=>6
[1,3,6,5,4,2]=>7
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>3
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>4
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>5
[1,4,3,6,5,2]=>6
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>7
[1,4,6,2,3,5]=>5
[1,4,6,5,3,2]=>8
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>4
[1,5,2,6,3,4]=>5
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>6
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>7
[1,5,4,6,3,2]=>8
[1,5,6,2,3,4]=>6
[1,5,6,4,3,2]=>9
[1,6,2,3,4,5]=>4
[1,6,3,4,5,2]=>7
[1,6,3,5,4,2]=>8
[1,6,4,3,5,2]=>8
[1,6,4,5,3,2]=>9
[1,6,5,4,3,2]=>10
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>3
[2,1,3,6,5,4]=>4
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>5
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>5
[2,1,5,6,3,4]=>5
[2,1,5,6,4,3]=>6
[2,1,6,3,4,5]=>4
[2,1,6,4,5,3]=>6
[2,1,6,5,4,3]=>7
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>5
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>4
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>5
[2,3,4,6,5,1]=>6
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>5
[2,3,5,4,6,1]=>6
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>7
[2,3,6,1,4,5]=>5
[2,3,6,4,5,1]=>7
[2,3,6,5,4,1]=>8
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>4
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>5
[2,4,3,1,5,6]=>4
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>6
[2,4,3,6,5,1]=>7
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>6
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>7
[2,4,5,6,1,3]=>7
[2,4,5,6,3,1]=>8
[2,4,6,1,3,5]=>6
[2,4,6,5,3,1]=>9
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>5
[2,5,1,6,3,4]=>6
[2,5,3,4,1,6]=>6
[2,5,3,4,6,1]=>7
[2,5,4,3,1,6]=>7
[2,5,4,3,6,1]=>8
[2,5,4,6,3,1]=>9
[2,5,6,1,3,4]=>7
[2,5,6,4,3,1]=>10
[2,6,1,3,4,5]=>5
[2,6,3,4,5,1]=>8
[2,6,3,5,4,1]=>9
[2,6,4,3,5,1]=>9
[2,6,4,5,3,1]=>10
[2,6,5,4,3,1]=>11
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>4
[3,1,4,2,5,6]=>3
[3,1,4,2,6,5]=>4
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>5
[3,1,4,6,2,5]=>5
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>5
[3,1,5,6,2,4]=>6
[3,1,6,2,4,5]=>5
[3,2,1,4,5,6]=>3
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>5
[3,2,1,6,5,4]=>6
[3,2,4,1,5,6]=>4
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>5
[3,2,4,5,6,1]=>6
[3,2,4,6,5,1]=>7
[3,2,5,1,4,6]=>5
[3,2,5,4,1,6]=>6
[3,2,5,4,6,1]=>7
[3,2,5,6,4,1]=>8
[3,2,6,1,4,5]=>6
[3,2,6,4,5,1]=>8
[3,2,6,5,4,1]=>9
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>6
[3,4,1,6,2,5]=>6
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>6
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>7
[3,4,2,6,5,1]=>8
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>7
[3,4,5,2,1,6]=>7
[3,4,5,2,6,1]=>8
[3,4,5,6,1,2]=>8
[3,4,5,6,2,1]=>9
[3,4,6,1,2,5]=>7
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>5
[3,5,1,2,6,4]=>6
[3,5,1,6,2,4]=>7
[3,5,4,2,1,6]=>8
[3,5,4,2,6,1]=>9
[3,5,4,6,2,1]=>10
[3,5,6,1,2,4]=>8
[3,5,6,4,2,1]=>11
[3,6,1,2,4,5]=>6
[3,6,1,5,4,2]=>9
[3,6,2,5,1,4]=>9
[3,6,5,4,2,1]=>12
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>4
[4,1,2,5,6,3]=>5
[4,1,2,6,3,5]=>5
[4,1,5,2,3,6]=>5
[4,1,5,2,6,3]=>6
[4,1,5,6,2,3]=>7
[4,1,6,2,3,5]=>6
[4,2,1,3,5,6]=>4
[4,2,3,1,5,6]=>5
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>6
[4,2,3,5,6,1]=>7
[4,2,3,6,5,1]=>8
[4,2,5,1,3,6]=>6
[4,2,6,1,3,5]=>7
[4,3,1,2,5,6]=>5
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>7
[4,3,2,5,1,6]=>7
[4,3,2,5,6,1]=>8
[4,3,2,6,1,5]=>8
[4,3,2,6,5,1]=>9
[4,3,5,1,2,6]=>7
[4,3,5,2,1,6]=>8
[4,3,5,2,6,1]=>9
[4,3,5,6,1,2]=>9
[4,3,5,6,2,1]=>10
[4,3,6,1,2,5]=>8
[4,3,6,5,2,1]=>11
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>7
[4,5,1,6,2,3]=>8
[4,5,2,1,3,6]=>7
[4,5,2,3,1,6]=>8
[4,5,2,3,6,1]=>9
[4,5,3,1,2,6]=>8
[4,5,3,2,1,6]=>9
[4,5,3,2,6,1]=>10
[4,5,3,6,1,2]=>10
[4,5,3,6,2,1]=>11
[4,5,6,1,2,3]=>9
[4,5,6,2,1,3]=>10
[4,5,6,2,3,1]=>11
[4,5,6,3,1,2]=>11
[4,5,6,3,2,1]=>12
[4,6,1,2,3,5]=>7
[4,6,2,5,1,3]=>10
[4,6,3,5,1,2]=>11
[4,6,5,1,3,2]=>11
[4,6,5,3,2,1]=>13
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>5
[5,1,2,6,3,4]=>6
[5,1,6,2,3,4]=>7
[5,2,1,3,4,6]=>5
[5,2,3,1,4,6]=>6
[5,2,3,4,1,6]=>7
[5,2,3,4,6,1]=>8
[5,2,4,1,3,6]=>7
[5,2,4,3,1,6]=>8
[5,2,4,3,6,1]=>9
[5,2,6,1,3,4]=>8
[5,3,1,2,4,6]=>6
[5,3,2,1,4,6]=>7
[5,3,2,4,1,6]=>8
[5,3,2,4,6,1]=>9
[5,3,2,6,1,4]=>9
[5,3,4,1,2,6]=>8
[5,3,4,2,1,6]=>9
[5,3,4,2,6,1]=>10
[5,3,4,6,1,2]=>10
[5,3,4,6,2,1]=>11
[5,3,6,1,2,4]=>9
[5,4,1,2,3,6]=>7
[5,4,2,1,3,6]=>8
[5,4,2,3,1,6]=>9
[5,4,2,3,6,1]=>10
[5,4,2,6,1,3]=>10
[5,4,3,1,2,6]=>9
[5,4,3,2,1,6]=>10
[5,4,3,2,6,1]=>11
[5,4,3,6,1,2]=>11
[5,4,3,6,2,1]=>12
[5,4,6,1,2,3]=>10
[5,4,6,2,1,3]=>11
[5,4,6,2,3,1]=>12
[5,4,6,3,1,2]=>12
[5,4,6,3,2,1]=>13
[5,6,1,2,3,4]=>8
[5,6,2,1,3,4]=>9
[5,6,2,3,1,4]=>10
[5,6,2,3,4,1]=>11
[5,6,2,4,1,3]=>11
[5,6,3,1,2,4]=>10
[5,6,3,2,1,4]=>11
[5,6,3,2,4,1]=>12
[5,6,3,4,1,2]=>12
[5,6,3,4,2,1]=>13
[5,6,4,1,2,3]=>11
[5,6,4,2,1,3]=>12
[5,6,4,2,3,1]=>13
[5,6,4,3,1,2]=>13
[5,6,4,3,2,1]=>14
[6,1,2,3,4,5]=>5
[6,2,1,3,4,5]=>6
[6,2,3,1,4,5]=>7
[6,2,3,4,1,5]=>8
[6,2,3,4,5,1]=>9
[6,2,3,5,4,1]=>10
[6,2,4,1,3,5]=>8
[6,2,4,3,5,1]=>10
[6,2,4,5,3,1]=>11
[6,2,5,1,3,4]=>9
[6,2,5,4,3,1]=>12
[6,3,1,2,4,5]=>7
[6,3,2,1,4,5]=>8
[6,3,2,4,1,5]=>9
[6,3,2,4,5,1]=>10
[6,3,2,5,1,4]=>10
[6,3,2,5,4,1]=>11
[6,3,4,1,2,5]=>9
[6,3,4,2,1,5]=>10
[6,3,4,2,5,1]=>11
[6,3,4,5,1,2]=>11
[6,3,4,5,2,1]=>12
[6,3,5,1,2,4]=>10
[6,3,5,4,2,1]=>13
[6,4,1,2,3,5]=>8
[6,4,2,1,3,5]=>9
[6,4,2,3,1,5]=>10
[6,4,2,3,5,1]=>11
[6,4,2,5,1,3]=>11
[6,4,3,1,2,5]=>10
[6,4,3,2,1,5]=>11
[6,4,3,2,5,1]=>12
[6,4,3,5,1,2]=>12
[6,4,3,5,2,1]=>13
[6,4,5,1,2,3]=>11
[6,4,5,2,1,3]=>12
[6,4,5,2,3,1]=>13
[6,4,5,3,1,2]=>13
[6,4,5,3,2,1]=>14
[6,5,1,2,3,4]=>9
[6,5,2,1,3,4]=>10
[6,5,2,3,1,4]=>11
[6,5,2,3,4,1]=>12
[6,5,2,4,1,3]=>12
[6,5,3,1,2,4]=>11
[6,5,3,2,1,4]=>12
[6,5,3,2,4,1]=>13
[6,5,3,4,1,2]=>13
[6,5,3,4,2,1]=>14
[6,5,4,1,2,3]=>12
[6,5,4,2,1,3]=>13
[6,5,4,2,3,1]=>14
[6,5,4,3,1,2]=>14
[6,5,4,3,2,1]=>15
[2,1,4,3,6,5,8,7]=>4
[3,4,1,2,6,5,8,7]=>6
[4,5,6,1,2,3,8,7]=>10
[3,5,1,6,2,4,8,7]=>8
[2,1,5,6,3,4,8,7]=>6
[5,6,7,8,1,2,3,4]=>16
[4,6,7,1,8,2,3,5]=>14
[3,6,1,7,8,2,4,5]=>12
[2,1,6,7,8,3,4,5]=>10
[2,1,5,7,3,8,4,6]=>8
[3,5,1,7,2,8,4,6]=>10
[4,5,7,1,2,8,3,6]=>12
[3,4,1,2,7,8,5,6]=>8
[2,1,4,3,7,8,5,6]=>6
[4,3,2,1,6,5,8,7]=>8
[5,3,2,6,1,4,8,7]=>10
[6,3,2,5,4,1,8,7]=>12
[7,3,2,5,4,8,1,6]=>14
[8,3,2,5,4,7,6,1]=>16
[8,4,5,2,3,7,6,1]=>18
[7,4,5,2,3,8,1,6]=>16
[6,4,5,2,3,1,8,7]=>14
[5,4,6,2,1,3,8,7]=>12
[2,1,6,5,4,3,8,7]=>8
[3,6,1,5,4,2,8,7]=>10
[4,6,5,1,3,2,8,7]=>12
[5,6,4,3,1,2,8,7]=>14
[6,5,4,3,2,1,8,7]=>16
[7,5,4,3,2,8,1,6]=>18
[8,5,4,3,2,7,6,1]=>20
[8,6,4,3,7,2,5,1]=>22
[7,6,4,3,8,2,1,5]=>20
[6,7,4,3,8,1,2,5]=>18
[5,7,4,3,1,8,2,6]=>16
[4,7,5,1,3,8,2,6]=>14
[3,7,1,5,4,8,2,6]=>12
[2,1,7,5,4,8,3,6]=>10
[2,1,8,5,4,7,6,3]=>12
[3,8,1,5,4,7,6,2]=>14
[4,8,5,1,3,7,6,2]=>16
[5,8,4,3,1,7,6,2]=>18
[6,8,4,3,7,1,5,2]=>20
[7,8,4,3,6,5,1,2]=>22
[8,7,4,3,6,5,2,1]=>24
[8,7,5,6,3,4,2,1]=>26
[7,8,5,6,3,4,1,2]=>24
[6,8,5,7,3,1,4,2]=>22
[5,8,6,7,1,3,4,2]=>20
[4,8,6,1,7,3,5,2]=>18
[3,8,1,6,7,4,5,2]=>16
[2,1,8,6,7,4,5,3]=>14
[2,1,7,6,8,4,3,5]=>12
[3,7,1,6,8,4,2,5]=>14
[4,7,6,1,8,3,2,5]=>16
[5,7,6,8,1,3,2,4]=>18
[6,7,5,8,3,1,2,4]=>20
[7,6,5,8,3,2,1,4]=>22
[8,6,5,7,3,2,4,1]=>24
[8,5,6,7,2,3,4,1]=>22
[7,5,6,8,2,3,1,4]=>20
[6,5,7,8,2,1,3,4]=>18
[5,4,7,2,1,8,3,6]=>14
[6,4,7,2,8,1,3,5]=>16
[7,4,6,2,8,3,1,5]=>18
[8,4,6,2,7,3,5,1]=>20
[8,3,2,6,7,4,5,1]=>18
[7,3,2,6,8,4,1,5]=>16
[6,3,2,7,8,1,4,5]=>14
[5,3,2,7,1,8,4,6]=>12
[4,3,2,1,7,8,5,6]=>10
[2,1,4,3,8,7,6,5]=>8
[3,4,1,2,8,7,6,5]=>10
[4,3,2,1,8,7,6,5]=>12
[5,3,2,8,1,7,6,4]=>14
[6,3,2,8,7,1,5,4]=>16
[7,3,2,8,6,5,1,4]=>18
[8,3,2,7,6,5,4,1]=>20
[8,4,7,2,6,5,3,1]=>22
[7,4,8,2,6,5,1,3]=>20
[6,4,8,2,7,1,5,3]=>18
[5,4,8,2,1,7,6,3]=>16
[4,5,8,1,2,7,6,3]=>14
[3,5,1,8,2,7,6,4]=>12
[2,1,5,8,3,7,6,4]=>10
[2,1,6,8,7,3,5,4]=>12
[3,6,1,8,7,2,5,4]=>14
[4,6,8,1,7,2,5,3]=>16
[5,6,8,7,1,2,4,3]=>18
[6,5,8,7,2,1,4,3]=>20
[7,5,8,6,2,4,1,3]=>22
[8,5,7,6,2,4,3,1]=>24
[8,6,7,5,4,2,3,1]=>26
[7,6,8,5,4,2,1,3]=>24
[6,7,8,5,4,1,2,3]=>22
[5,7,8,6,1,4,2,3]=>20
[4,7,8,1,6,5,2,3]=>18
[3,7,1,8,6,5,2,4]=>16
[2,1,7,8,6,5,3,4]=>14
[2,1,8,7,6,5,4,3]=>16
[3,8,1,7,6,5,4,2]=>18
[4,8,7,1,6,5,3,2]=>20
[5,8,7,6,1,4,3,2]=>22
[6,8,7,5,4,1,3,2]=>24
[7,8,6,5,4,3,1,2]=>26
[8,7,6,5,4,3,2,1]=>28
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Description
The number of B-inversions of a signed permutation.
The number of B-inversions of a signed permutation $\sigma$ of length $n$ is
$$ \operatorname{inv}_B(\sigma) = \big|\{ 1 \leq i < j \leq n \mid \sigma(i) > \sigma(j) \}\big| + \big|\{ 1 \leq i \leq j \leq n \mid \sigma(-i) > \sigma(j) \}\big|, $$
see [1, Eq. (8.2)]. According to [1, Eq. (8.4)], this is the Coxeter length of $\sigma$.
The number of B-inversions of a signed permutation $\sigma$ of length $n$ is
$$ \operatorname{inv}_B(\sigma) = \big|\{ 1 \leq i < j \leq n \mid \sigma(i) > \sigma(j) \}\big| + \big|\{ 1 \leq i \leq j \leq n \mid \sigma(-i) > \sigma(j) \}\big|, $$
see [1, Eq. (8.2)]. According to [1, Eq. (8.4)], this is the Coxeter length of $\sigma$.
References
[1] Björner, A., Brenti, F. Combinatorics of Coxeter groups MathSciNet:2133266
Code
def statistic(pi):
pi = list(pi)
n = len(pi)
return (sum(1 for i in range(n) for j in range(i+1,n) if pi[i] > pi[j]) +
sum(1 for i in range(n) for j in range(i ,n) if -pi[i] > pi[j]))
Created
Jun 21, 2019 at 14:03 by Christian Stump
Updated
Jan 08, 2023 at 10:53 by Martin Rubey
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