Identifier
- St001537: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>0
[1,2,4,3]=>0
[1,3,2,4]=>0
[1,3,4,2]=>0
[1,4,2,3]=>0
[1,4,3,2]=>0
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>1
[2,4,3,1]=>0
[3,1,2,4]=>0
[3,1,4,2]=>1
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>4
[3,4,2,1]=>1
[4,1,2,3]=>0
[4,1,3,2]=>0
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>1
[4,3,2,1]=>0
[1,2,3,4,5]=>0
[1,2,3,5,4]=>0
[1,2,4,3,5]=>0
[1,2,4,5,3]=>0
[1,2,5,3,4]=>0
[1,2,5,4,3]=>0
[1,3,2,4,5]=>0
[1,3,2,5,4]=>0
[1,3,4,2,5]=>0
[1,3,4,5,2]=>0
[1,3,5,2,4]=>1
[1,3,5,4,2]=>0
[1,4,2,3,5]=>0
[1,4,2,5,3]=>1
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>4
[1,4,5,3,2]=>1
[1,5,2,3,4]=>0
[1,5,2,4,3]=>0
[1,5,3,2,4]=>0
[1,5,3,4,2]=>0
[1,5,4,2,3]=>1
[1,5,4,3,2]=>0
[2,1,3,4,5]=>0
[2,1,3,5,4]=>0
[2,1,4,3,5]=>0
[2,1,4,5,3]=>0
[2,1,5,3,4]=>0
[2,1,5,4,3]=>0
[2,3,1,4,5]=>0
[2,3,1,5,4]=>0
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>1
[2,3,5,4,1]=>0
[2,4,1,3,5]=>1
[2,4,1,5,3]=>2
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>4
[2,4,5,3,1]=>1
[2,5,1,3,4]=>1
[2,5,1,4,3]=>1
[2,5,3,1,4]=>1
[2,5,3,4,1]=>0
[2,5,4,1,3]=>2
[2,5,4,3,1]=>0
[3,1,2,4,5]=>0
[3,1,2,5,4]=>0
[3,1,4,2,5]=>1
[3,1,4,5,2]=>1
[3,1,5,2,4]=>2
[3,1,5,4,2]=>1
[3,2,1,4,5]=>0
[3,2,1,5,4]=>0
[3,2,4,1,5]=>0
[3,2,4,5,1]=>0
[3,2,5,1,4]=>1
[3,2,5,4,1]=>0
[3,4,1,2,5]=>4
[3,4,1,5,2]=>4
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>5
[3,4,5,2,1]=>4
[3,5,1,2,4]=>4
[3,5,1,4,2]=>4
[3,5,2,1,4]=>2
[3,5,2,4,1]=>1
[3,5,4,1,2]=>4
[3,5,4,2,1]=>2
[4,1,2,3,5]=>0
[4,1,2,5,3]=>1
[4,1,3,2,5]=>0
[4,1,3,5,2]=>1
[4,1,5,2,3]=>4
[4,1,5,3,2]=>2
[4,2,1,3,5]=>0
[4,2,1,5,3]=>1
[4,2,3,1,5]=>0
[4,2,3,5,1]=>0
[4,2,5,1,3]=>4
[4,2,5,3,1]=>1
[4,3,1,2,5]=>1
[4,3,1,5,2]=>2
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>4
[4,3,5,2,1]=>2
[4,5,1,2,3]=>5
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>1
[4,5,3,1,2]=>4
[4,5,3,2,1]=>1
[5,1,2,3,4]=>0
[5,1,2,4,3]=>0
[5,1,3,2,4]=>0
[5,1,3,4,2]=>0
[5,1,4,2,3]=>1
[5,1,4,3,2]=>0
[5,2,1,3,4]=>0
[5,2,1,4,3]=>0
[5,2,3,1,4]=>0
[5,2,3,4,1]=>0
[5,2,4,1,3]=>1
[5,2,4,3,1]=>0
[5,3,1,2,4]=>1
[5,3,1,4,2]=>1
[5,3,2,1,4]=>0
[5,3,2,4,1]=>0
[5,3,4,1,2]=>1
[5,3,4,2,1]=>0
[5,4,1,2,3]=>4
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>0
[5,4,3,1,2]=>1
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>0
[1,2,3,5,4,6]=>0
[1,2,3,5,6,4]=>0
[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>0
[1,2,4,3,5,6]=>0
[1,2,4,3,6,5]=>0
[1,2,4,5,3,6]=>0
[1,2,4,5,6,3]=>0
[1,2,4,6,3,5]=>1
[1,2,4,6,5,3]=>0
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>1
[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>0
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>1
[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>0
[1,2,6,4,3,5]=>0
[1,2,6,4,5,3]=>0
[1,2,6,5,3,4]=>1
[1,2,6,5,4,3]=>0
[1,3,2,4,5,6]=>0
[1,3,2,4,6,5]=>0
[1,3,2,5,4,6]=>0
[1,3,2,5,6,4]=>0
[1,3,2,6,4,5]=>0
[1,3,2,6,5,4]=>0
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>0
[1,3,4,5,2,6]=>0
[1,3,4,5,6,2]=>0
[1,3,4,6,2,5]=>1
[1,3,4,6,5,2]=>0
[1,3,5,2,4,6]=>1
[1,3,5,2,6,4]=>2
[1,3,5,4,2,6]=>0
[1,3,5,4,6,2]=>0
[1,3,5,6,2,4]=>4
[1,3,5,6,4,2]=>1
[1,3,6,2,4,5]=>1
[1,3,6,2,5,4]=>1
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>0
[1,3,6,5,2,4]=>2
[1,3,6,5,4,2]=>0
[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>0
[1,4,2,5,3,6]=>1
[1,4,2,5,6,3]=>1
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>1
[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>0
[1,4,3,5,2,6]=>0
[1,4,3,5,6,2]=>0
[1,4,3,6,2,5]=>1
[1,4,3,6,5,2]=>0
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>4
[1,4,5,3,2,6]=>1
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>5
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>2
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>2
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>1
[1,5,2,4,3,6]=>0
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>4
[1,5,2,6,4,3]=>2
[1,5,3,2,4,6]=>0
[1,5,3,2,6,4]=>1
[1,5,3,4,2,6]=>0
[1,5,3,4,6,2]=>0
[1,5,3,6,2,4]=>4
[1,5,3,6,4,2]=>1
[1,5,4,2,3,6]=>1
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>0
[1,5,4,6,2,3]=>4
[1,5,4,6,3,2]=>2
[1,5,6,2,3,4]=>5
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>4
[1,5,6,3,4,2]=>1
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>1
[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>0
[1,6,2,4,3,5]=>0
[1,6,2,4,5,3]=>0
[1,6,2,5,3,4]=>1
[1,6,2,5,4,3]=>0
[1,6,3,2,4,5]=>0
[1,6,3,2,5,4]=>0
[1,6,3,4,2,5]=>0
[1,6,3,4,5,2]=>0
[1,6,3,5,2,4]=>1
[1,6,3,5,4,2]=>0
[1,6,4,2,3,5]=>1
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>0
[1,6,4,3,5,2]=>0
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>0
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>2
[1,6,5,3,4,2]=>0
[1,6,5,4,2,3]=>1
[1,6,5,4,3,2]=>0
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>0
[2,1,3,5,4,6]=>0
[2,1,3,5,6,4]=>0
[2,1,3,6,4,5]=>0
[2,1,3,6,5,4]=>0
[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>0
[2,1,4,5,6,3]=>0
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>0
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>0
[2,1,5,6,3,4]=>4
[2,1,5,6,4,3]=>1
[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>0
[2,1,6,4,3,5]=>0
[2,1,6,4,5,3]=>0
[2,1,6,5,3,4]=>1
[2,1,6,5,4,3]=>0
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>0
[2,3,1,5,4,6]=>0
[2,3,1,5,6,4]=>0
[2,3,1,6,4,5]=>0
[2,3,1,6,5,4]=>0
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>0
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>1
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>1
[2,3,5,1,6,4]=>2
[2,3,5,4,1,6]=>0
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>1
[2,3,6,1,4,5]=>1
[2,3,6,1,5,4]=>1
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>0
[2,3,6,5,1,4]=>2
[2,3,6,5,4,1]=>0
[2,4,1,3,5,6]=>1
[2,4,1,3,6,5]=>1
[2,4,1,5,3,6]=>2
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>3
[2,4,1,6,5,3]=>2
[2,4,3,1,5,6]=>0
[2,4,3,1,6,5]=>0
[2,4,3,5,1,6]=>0
[2,4,3,5,6,1]=>0
[2,4,3,6,1,5]=>1
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>4
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>1
[2,4,5,6,1,3]=>5
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>4
[2,4,6,1,5,3]=>4
[2,4,6,3,1,5]=>2
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>2
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>2
[2,5,1,6,3,4]=>5
[2,5,1,6,4,3]=>3
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>2
[2,5,3,4,1,6]=>0
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>4
[2,5,3,6,4,1]=>1
[2,5,4,1,3,6]=>2
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>0
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>2
[2,5,6,1,3,4]=>6
[2,5,6,1,4,3]=>5
[2,5,6,3,1,4]=>4
[2,5,6,3,4,1]=>1
[2,5,6,4,1,3]=>4
[2,5,6,4,3,1]=>1
[2,6,1,3,4,5]=>1
[2,6,1,3,5,4]=>1
[2,6,1,4,3,5]=>1
[2,6,1,4,5,3]=>1
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>1
[2,6,3,1,4,5]=>1
[2,6,3,1,5,4]=>1
[2,6,3,4,1,5]=>1
[2,6,3,4,5,1]=>0
[2,6,3,5,1,4]=>2
[2,6,3,5,4,1]=>0
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>2
[2,6,4,3,1,5]=>1
[2,6,4,3,5,1]=>0
[2,6,4,5,1,3]=>2
[2,6,4,5,3,1]=>0
[2,6,5,1,3,4]=>5
[2,6,5,1,4,3]=>3
[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>0
[2,6,5,4,1,3]=>2
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>0
[3,1,2,5,4,6]=>0
[3,1,2,5,6,4]=>0
[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>0
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>1
[3,1,4,5,2,6]=>1
[3,1,4,5,6,2]=>1
[3,1,4,6,2,5]=>2
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>2
[3,1,5,2,6,4]=>3
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>5
[3,1,5,6,4,2]=>2
[3,1,6,2,4,5]=>2
[3,1,6,2,5,4]=>2
[3,1,6,4,2,5]=>2
[3,1,6,4,5,2]=>1
[3,1,6,5,2,4]=>3
[3,1,6,5,4,2]=>1
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>0
[3,2,1,5,4,6]=>0
[3,2,1,5,6,4]=>0
[3,2,1,6,4,5]=>0
[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>0
[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>1
[3,2,4,6,5,1]=>0
[3,2,5,1,4,6]=>1
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>0
[3,2,5,4,6,1]=>0
[3,2,5,6,1,4]=>4
[3,2,5,6,4,1]=>1
[3,2,6,1,4,5]=>1
[3,2,6,1,5,4]=>1
[3,2,6,4,1,5]=>1
[3,2,6,4,5,1]=>0
[3,2,6,5,1,4]=>2
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>4
[3,4,1,5,2,6]=>4
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>5
[3,4,1,6,5,2]=>4
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>1
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>1
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>1
[3,4,5,1,2,6]=>5
[3,4,5,1,6,2]=>5
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>6
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>6
[3,4,6,1,5,2]=>5
[3,4,6,2,1,5]=>5
[3,4,6,2,5,1]=>4
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>4
[3,5,1,2,4,6]=>4
[3,5,1,2,6,4]=>5
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>4
[3,5,1,6,2,4]=>8
[3,5,1,6,4,2]=>5
[3,5,2,1,4,6]=>2
[3,5,2,1,6,4]=>3
[3,5,2,4,1,6]=>1
[3,5,2,4,6,1]=>1
[3,5,2,6,1,4]=>5
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>4
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>5
[3,5,4,6,2,1]=>4
[3,5,6,1,2,4]=>9
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>7
[3,5,6,2,4,1]=>4
[3,5,6,4,1,2]=>5
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>4
[3,6,1,4,2,5]=>4
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>5
[3,6,1,5,4,2]=>4
[3,6,2,1,4,5]=>2
[3,6,2,1,5,4]=>2
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>1
[3,6,2,5,1,4]=>3
[3,6,2,5,4,1]=>1
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>4
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>2
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>2
[3,6,5,1,2,4]=>7
[3,6,5,1,4,2]=>5
[3,6,5,2,1,4]=>6
[3,6,5,2,4,1]=>3
[3,6,5,4,1,2]=>4
[3,6,5,4,2,1]=>2
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>0
[4,1,2,5,3,6]=>1
[4,1,2,5,6,3]=>1
[4,1,2,6,3,5]=>2
[4,1,2,6,5,3]=>1
[4,1,3,2,5,6]=>0
[4,1,3,2,6,5]=>0
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>1
[4,1,3,6,2,5]=>2
[4,1,3,6,5,2]=>1
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>4
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>2
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>5
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>4
[4,1,6,3,2,5]=>3
[4,1,6,3,5,2]=>2
[4,1,6,5,2,3]=>5
[4,1,6,5,3,2]=>3
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>0
[4,2,1,5,3,6]=>1
[4,2,1,5,6,3]=>1
[4,2,1,6,3,5]=>2
[4,2,1,6,5,3]=>1
[4,2,3,1,5,6]=>0
[4,2,3,1,6,5]=>0
[4,2,3,5,1,6]=>0
[4,2,3,5,6,1]=>0
[4,2,3,6,1,5]=>1
[4,2,3,6,5,1]=>0
[4,2,5,1,3,6]=>4
[4,2,5,1,6,3]=>4
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>5
[4,2,5,6,3,1]=>4
[4,2,6,1,3,5]=>4
[4,2,6,1,5,3]=>4
[4,2,6,3,1,5]=>2
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>4
[4,2,6,5,3,1]=>2
[4,3,1,2,5,6]=>1
[4,3,1,2,6,5]=>1
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>2
[4,3,1,6,2,5]=>3
[4,3,1,6,5,2]=>2
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>0
[4,3,2,5,1,6]=>0
[4,3,2,5,6,1]=>0
[4,3,2,6,1,5]=>1
[4,3,2,6,5,1]=>0
[4,3,5,1,2,6]=>4
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>2
[4,3,5,2,6,1]=>2
[4,3,5,6,1,2]=>5
[4,3,5,6,2,1]=>4
[4,3,6,1,2,5]=>5
[4,3,6,1,5,2]=>4
[4,3,6,2,1,5]=>3
[4,3,6,2,5,1]=>2
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>3
[4,5,1,2,3,6]=>5
[4,5,1,2,6,3]=>6
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>9
[4,5,1,6,3,2]=>7
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>5
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>1
[4,5,2,6,1,3]=>6
[4,5,2,6,3,1]=>4
[4,5,3,1,2,6]=>4
[4,5,3,1,6,2]=>4
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>4
[4,5,6,1,2,3]=>12
[4,5,6,1,3,2]=>9
[4,5,6,2,1,3]=>9
[4,5,6,2,3,1]=>6
[4,5,6,3,1,2]=>6
[4,5,6,3,2,1]=>5
[4,6,1,2,3,5]=>5
[4,6,1,2,5,3]=>5
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>6
[4,6,1,5,3,2]=>5
[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>4
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>1
[4,6,2,5,1,3]=>4
[4,6,2,5,3,1]=>2
[4,6,3,1,2,5]=>4
[4,6,3,1,5,2]=>4
[4,6,3,2,1,5]=>2
[4,6,3,2,5,1]=>1
[4,6,3,5,1,2]=>4
[4,6,3,5,2,1]=>2
[4,6,5,1,2,3]=>9
[4,6,5,1,3,2]=>8
[4,6,5,2,1,3]=>7
[4,6,5,2,3,1]=>5
[4,6,5,3,1,2]=>5
[4,6,5,3,2,1]=>3
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>1
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>1
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>2
[5,1,3,2,4,6]=>0
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>0
[5,1,3,4,6,2]=>1
[5,1,3,6,2,4]=>4
[5,1,3,6,4,2]=>2
[5,1,4,2,3,6]=>1
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>0
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>3
[5,1,6,2,3,4]=>5
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>2
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>2
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>1
[5,2,1,4,3,6]=>0
[5,2,1,4,6,3]=>1
[5,2,1,6,3,4]=>4
[5,2,1,6,4,3]=>2
[5,2,3,1,4,6]=>0
[5,2,3,1,6,4]=>1
[5,2,3,4,1,6]=>0
[5,2,3,4,6,1]=>0
[5,2,3,6,1,4]=>4
[5,2,3,6,4,1]=>1
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>2
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>4
[5,2,4,6,3,1]=>2
[5,2,6,1,3,4]=>5
[5,2,6,1,4,3]=>4
[5,2,6,3,1,4]=>4
[5,2,6,3,4,1]=>1
[5,2,6,4,1,3]=>4
[5,2,6,4,3,1]=>1
[5,3,1,2,4,6]=>1
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>1
[5,3,1,4,6,2]=>2
[5,3,1,6,2,4]=>5
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>1
[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>0
[5,3,2,6,1,4]=>4
[5,3,2,6,4,1]=>1
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>2
[5,3,4,2,1,6]=>0
[5,3,4,2,6,1]=>0
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>2
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>4
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>4
[5,3,6,4,2,1]=>2
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>5
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>3
[5,4,1,6,2,3]=>7
[5,4,1,6,3,2]=>6
[5,4,2,1,3,6]=>2
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>0
[5,4,2,6,1,3]=>5
[5,4,2,6,3,1]=>3
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>2
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>4
[5,4,3,6,2,1]=>2
[5,4,6,1,2,3]=>9
[5,4,6,1,3,2]=>7
[5,4,6,2,1,3]=>8
[5,4,6,2,3,1]=>5
[5,4,6,3,1,2]=>5
[5,4,6,3,2,1]=>3
[5,6,1,2,3,4]=>6
[5,6,1,2,4,3]=>5
[5,6,1,3,2,4]=>5
[5,6,1,3,4,2]=>4
[5,6,1,4,2,3]=>5
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>5
[5,6,2,1,4,3]=>4
[5,6,2,3,1,4]=>4
[5,6,2,3,4,1]=>1
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>1
[5,6,3,1,2,4]=>5
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>4
[5,6,3,2,4,1]=>1
[5,6,3,4,1,2]=>4
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>6
[5,6,4,1,3,2]=>5
[5,6,4,2,1,3]=>5
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>4
[5,6,4,3,2,1]=>1
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>0
[6,1,2,4,3,5]=>0
[6,1,2,4,5,3]=>0
[6,1,2,5,3,4]=>1
[6,1,2,5,4,3]=>0
[6,1,3,2,4,5]=>0
[6,1,3,2,5,4]=>0
[6,1,3,4,2,5]=>0
[6,1,3,4,5,2]=>0
[6,1,3,5,2,4]=>1
[6,1,3,5,4,2]=>0
[6,1,4,2,3,5]=>1
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>0
[6,1,4,5,2,3]=>1
[6,1,4,5,3,2]=>0
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>2
[6,1,5,3,2,4]=>2
[6,1,5,3,4,2]=>0
[6,1,5,4,2,3]=>1
[6,1,5,4,3,2]=>0
[6,2,1,3,4,5]=>0
[6,2,1,3,5,4]=>0
[6,2,1,4,3,5]=>0
[6,2,1,4,5,3]=>0
[6,2,1,5,3,4]=>1
[6,2,1,5,4,3]=>0
[6,2,3,1,4,5]=>0
[6,2,3,1,5,4]=>0
[6,2,3,4,1,5]=>0
[6,2,3,4,5,1]=>0
[6,2,3,5,1,4]=>1
[6,2,3,5,4,1]=>0
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>1
[6,2,4,3,1,5]=>0
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>1
[6,2,4,5,3,1]=>0
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>2
[6,2,5,3,1,4]=>2
[6,2,5,3,4,1]=>0
[6,2,5,4,1,3]=>1
[6,2,5,4,3,1]=>0
[6,3,1,2,4,5]=>1
[6,3,1,2,5,4]=>1
[6,3,1,4,2,5]=>1
[6,3,1,4,5,2]=>1
[6,3,1,5,2,4]=>2
[6,3,1,5,4,2]=>1
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>0
[6,3,2,4,1,5]=>0
[6,3,2,4,5,1]=>0
[6,3,2,5,1,4]=>1
[6,3,2,5,4,1]=>0
[6,3,4,1,2,5]=>1
[6,3,4,1,5,2]=>1
[6,3,4,2,1,5]=>0
[6,3,4,2,5,1]=>0
[6,3,4,5,1,2]=>1
[6,3,4,5,2,1]=>0
[6,3,5,1,2,4]=>4
[6,3,5,1,4,2]=>2
[6,3,5,2,1,4]=>3
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>1
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>2
[6,4,1,3,5,2]=>2
[6,4,1,5,2,3]=>4
[6,4,1,5,3,2]=>3
[6,4,2,1,3,5]=>2
[6,4,2,1,5,3]=>2
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>2
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>1
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>0
[6,4,5,1,2,3]=>6
[6,4,5,1,3,2]=>5
[6,4,5,2,1,3]=>5
[6,4,5,2,3,1]=>4
[6,4,5,3,1,2]=>2
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>5
[6,5,1,2,4,3]=>4
[6,5,1,3,2,4]=>4
[6,5,1,3,4,2]=>2
[6,5,1,4,2,3]=>4
[6,5,1,4,3,2]=>2
[6,5,2,1,3,4]=>4
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>2
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>2
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>4
[6,5,3,1,4,2]=>2
[6,5,3,2,1,4]=>2
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>5
[6,5,4,1,3,2]=>3
[6,5,4,2,1,3]=>3
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>0
[1,2,3,4,6,5,7]=>0
[1,2,3,4,6,7,5]=>0
[1,2,3,4,7,5,6]=>0
[1,2,3,4,7,6,5]=>0
[1,2,3,5,4,6,7]=>0
[1,2,3,5,4,7,6]=>0
[1,2,3,5,6,4,7]=>0
[1,2,3,5,6,7,4]=>0
[1,2,3,5,7,4,6]=>1
[1,2,3,5,7,6,4]=>0
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>1
[1,2,3,6,5,4,7]=>0
[1,2,3,6,5,7,4]=>0
[1,2,3,6,7,4,5]=>4
[1,2,3,6,7,5,4]=>1
[1,2,3,7,4,5,6]=>0
[1,2,3,7,4,6,5]=>0
[1,2,3,7,5,4,6]=>0
[1,2,3,7,5,6,4]=>0
[1,2,3,7,6,4,5]=>1
[1,2,3,7,6,5,4]=>0
[1,2,4,3,5,6,7]=>0
[1,2,4,3,5,7,6]=>0
[1,2,4,3,6,5,7]=>0
[1,2,4,3,6,7,5]=>0
[1,2,4,3,7,5,6]=>0
[1,2,4,3,7,6,5]=>0
[1,2,4,5,3,6,7]=>0
[1,2,4,5,3,7,6]=>0
[1,2,4,5,6,3,7]=>0
[1,2,4,5,6,7,3]=>0
[1,2,4,5,7,3,6]=>1
[1,2,4,5,7,6,3]=>0
[1,2,4,6,3,5,7]=>1
[1,2,4,6,3,7,5]=>2
[1,2,4,6,5,3,7]=>0
[1,2,4,6,5,7,3]=>0
[1,2,4,6,7,3,5]=>4
[1,2,4,6,7,5,3]=>1
[1,2,4,7,3,5,6]=>1
[1,2,4,7,3,6,5]=>1
[1,2,4,7,5,3,6]=>1
[1,2,4,7,5,6,3]=>0
[1,2,4,7,6,3,5]=>2
[1,2,4,7,6,5,3]=>0
[1,2,5,3,4,6,7]=>0
[1,2,5,3,4,7,6]=>0
[1,2,5,3,6,4,7]=>1
[1,2,5,3,6,7,4]=>1
[1,2,5,3,7,4,6]=>2
[1,2,5,3,7,6,4]=>1
[1,2,5,4,3,6,7]=>0
[1,2,5,4,3,7,6]=>0
[1,2,5,4,6,3,7]=>0
[1,2,5,4,6,7,3]=>0
[1,2,5,4,7,3,6]=>1
[1,2,5,4,7,6,3]=>0
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>4
[1,2,5,6,4,3,7]=>1
[1,2,5,6,4,7,3]=>1
[1,2,5,6,7,3,4]=>5
[1,2,5,6,7,4,3]=>4
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>4
[1,2,5,7,4,3,6]=>2
[1,2,5,7,4,6,3]=>1
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>2
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>1
[1,2,6,3,5,4,7]=>0
[1,2,6,3,5,7,4]=>1
[1,2,6,3,7,4,5]=>4
[1,2,6,3,7,5,4]=>2
[1,2,6,4,3,5,7]=>0
[1,2,6,4,3,7,5]=>1
[1,2,6,4,5,3,7]=>0
[1,2,6,4,5,7,3]=>0
[1,2,6,4,7,3,5]=>4
[1,2,6,4,7,5,3]=>1
[1,2,6,5,3,4,7]=>1
[1,2,6,5,3,7,4]=>2
[1,2,6,5,4,3,7]=>0
[1,2,6,5,4,7,3]=>0
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>2
[1,2,6,7,3,4,5]=>5
[1,2,6,7,3,5,4]=>4
[1,2,6,7,4,3,5]=>4
[1,2,6,7,4,5,3]=>1
[1,2,6,7,5,3,4]=>4
[1,2,6,7,5,4,3]=>1
[1,2,7,3,4,5,6]=>0
[1,2,7,3,4,6,5]=>0
[1,2,7,3,5,4,6]=>0
[1,2,7,3,5,6,4]=>0
[1,2,7,3,6,4,5]=>1
[1,2,7,3,6,5,4]=>0
[1,2,7,4,3,5,6]=>0
[1,2,7,4,3,6,5]=>0
[1,2,7,4,5,3,6]=>0
[1,2,7,4,5,6,3]=>0
[1,2,7,4,6,3,5]=>1
[1,2,7,4,6,5,3]=>0
[1,2,7,5,3,4,6]=>1
[1,2,7,5,3,6,4]=>1
[1,2,7,5,4,3,6]=>0
[1,2,7,5,4,6,3]=>0
[1,2,7,5,6,3,4]=>1
[1,2,7,5,6,4,3]=>0
[1,2,7,6,3,4,5]=>4
[1,2,7,6,3,5,4]=>2
[1,2,7,6,4,3,5]=>2
[1,2,7,6,4,5,3]=>0
[1,2,7,6,5,3,4]=>1
[1,2,7,6,5,4,3]=>0
[1,3,2,4,5,6,7]=>0
[1,3,2,4,5,7,6]=>0
[1,3,2,4,6,5,7]=>0
[1,3,2,4,6,7,5]=>0
[1,3,2,4,7,5,6]=>0
[1,3,2,4,7,6,5]=>0
[1,3,2,5,4,6,7]=>0
[1,3,2,5,4,7,6]=>0
[1,3,2,5,6,4,7]=>0
[1,3,2,5,6,7,4]=>0
[1,3,2,5,7,4,6]=>1
[1,3,2,5,7,6,4]=>0
[1,3,2,6,4,5,7]=>0
[1,3,2,6,4,7,5]=>1
[1,3,2,6,5,4,7]=>0
[1,3,2,6,5,7,4]=>0
[1,3,2,6,7,4,5]=>4
[1,3,2,6,7,5,4]=>1
[1,3,2,7,4,5,6]=>0
[1,3,2,7,4,6,5]=>0
[1,3,2,7,5,4,6]=>0
[1,3,2,7,5,6,4]=>0
[1,3,2,7,6,4,5]=>1
[1,3,2,7,6,5,4]=>0
[1,3,4,2,5,6,7]=>0
[1,3,4,2,5,7,6]=>0
[1,3,4,2,6,5,7]=>0
[1,3,4,2,6,7,5]=>0
[1,3,4,2,7,5,6]=>0
[1,3,4,2,7,6,5]=>0
[1,3,4,5,2,6,7]=>0
[1,3,4,5,2,7,6]=>0
[1,3,4,5,6,2,7]=>0
[1,3,4,5,6,7,2]=>0
[1,3,4,5,7,2,6]=>1
[1,3,4,5,7,6,2]=>0
[1,3,4,6,2,5,7]=>1
[1,3,4,6,2,7,5]=>2
[1,3,4,6,5,2,7]=>0
[1,3,4,6,5,7,2]=>0
[1,3,4,6,7,2,5]=>4
[1,3,4,6,7,5,2]=>1
[1,3,4,7,2,5,6]=>1
[1,3,4,7,2,6,5]=>1
[1,3,4,7,5,2,6]=>1
[1,3,4,7,5,6,2]=>0
[1,3,4,7,6,2,5]=>2
[1,3,4,7,6,5,2]=>0
[1,3,5,2,4,6,7]=>1
[1,3,5,2,4,7,6]=>1
[1,3,5,2,6,4,7]=>2
[1,3,5,2,6,7,4]=>2
[1,3,5,2,7,4,6]=>3
[1,3,5,2,7,6,4]=>2
[1,3,5,4,2,6,7]=>0
[1,3,5,4,2,7,6]=>0
[1,3,5,4,6,2,7]=>0
[1,3,5,4,6,7,2]=>0
[1,3,5,4,7,2,6]=>1
[1,3,5,4,7,6,2]=>0
[1,3,5,6,2,4,7]=>4
[1,3,5,6,2,7,4]=>4
[1,3,5,6,4,2,7]=>1
[1,3,5,6,4,7,2]=>1
[1,3,5,6,7,2,4]=>5
[1,3,5,6,7,4,2]=>4
[1,3,5,7,2,4,6]=>4
[1,3,5,7,2,6,4]=>4
[1,3,5,7,4,2,6]=>2
[1,3,5,7,4,6,2]=>1
[1,3,5,7,6,2,4]=>4
[1,3,5,7,6,4,2]=>2
[1,3,6,2,4,5,7]=>1
[1,3,6,2,4,7,5]=>2
[1,3,6,2,5,4,7]=>1
[1,3,6,2,5,7,4]=>2
[1,3,6,2,7,4,5]=>5
[1,3,6,2,7,5,4]=>3
[1,3,6,4,2,5,7]=>1
[1,3,6,4,2,7,5]=>2
[1,3,6,4,5,2,7]=>0
[1,3,6,4,5,7,2]=>0
[1,3,6,4,7,2,5]=>4
[1,3,6,4,7,5,2]=>1
[1,3,6,5,2,4,7]=>2
[1,3,6,5,2,7,4]=>3
[1,3,6,5,4,2,7]=>0
[1,3,6,5,4,7,2]=>0
[1,3,6,5,7,2,4]=>4
[1,3,6,5,7,4,2]=>2
[1,3,6,7,2,4,5]=>6
[1,3,6,7,2,5,4]=>5
[1,3,6,7,4,2,5]=>4
[1,3,6,7,4,5,2]=>1
[1,3,6,7,5,2,4]=>4
[1,3,6,7,5,4,2]=>1
[1,3,7,2,4,5,6]=>1
[1,3,7,2,4,6,5]=>1
[1,3,7,2,5,4,6]=>1
[1,3,7,2,5,6,4]=>1
[1,3,7,2,6,4,5]=>2
[1,3,7,2,6,5,4]=>1
[1,3,7,4,2,5,6]=>1
[1,3,7,4,2,6,5]=>1
[1,3,7,4,5,2,6]=>1
[1,3,7,4,5,6,2]=>0
[1,3,7,4,6,2,5]=>2
[1,3,7,4,6,5,2]=>0
[1,3,7,5,2,4,6]=>2
[1,3,7,5,2,6,4]=>2
[1,3,7,5,4,2,6]=>1
[1,3,7,5,4,6,2]=>0
[1,3,7,5,6,2,4]=>2
[1,3,7,5,6,4,2]=>0
[1,3,7,6,2,4,5]=>5
[1,3,7,6,2,5,4]=>3
[1,3,7,6,4,2,5]=>3
[1,3,7,6,4,5,2]=>0
[1,3,7,6,5,2,4]=>2
[1,3,7,6,5,4,2]=>0
[1,4,2,3,5,6,7]=>0
[1,4,2,3,5,7,6]=>0
[1,4,2,3,6,5,7]=>0
[1,4,2,3,6,7,5]=>0
[1,4,2,3,7,5,6]=>0
[1,4,2,3,7,6,5]=>0
[1,4,2,5,3,6,7]=>1
[1,4,2,5,3,7,6]=>1
[1,4,2,5,6,3,7]=>1
[1,4,2,5,6,7,3]=>1
[1,4,2,5,7,3,6]=>2
[1,4,2,5,7,6,3]=>1
[1,4,2,6,3,5,7]=>2
[1,4,2,6,3,7,5]=>3
[1,4,2,6,5,3,7]=>1
[1,4,2,6,5,7,3]=>1
[1,4,2,6,7,3,5]=>5
[1,4,2,6,7,5,3]=>2
[1,4,2,7,3,5,6]=>2
[1,4,2,7,3,6,5]=>2
[1,4,2,7,5,3,6]=>2
[1,4,2,7,5,6,3]=>1
[1,4,2,7,6,3,5]=>3
[1,4,2,7,6,5,3]=>1
[1,4,3,2,5,6,7]=>0
[1,4,3,2,5,7,6]=>0
[1,4,3,2,6,5,7]=>0
[1,4,3,2,6,7,5]=>0
[1,4,3,2,7,5,6]=>0
[1,4,3,2,7,6,5]=>0
[1,4,3,5,2,6,7]=>0
[1,4,3,5,2,7,6]=>0
[1,4,3,5,6,2,7]=>0
[1,4,3,5,6,7,2]=>0
[1,4,3,5,7,2,6]=>1
[1,4,3,5,7,6,2]=>0
[1,4,3,6,2,5,7]=>1
[1,4,3,6,2,7,5]=>2
[1,4,3,6,5,2,7]=>0
[1,4,3,6,5,7,2]=>0
[1,4,3,6,7,2,5]=>4
[1,4,3,6,7,5,2]=>1
[1,4,3,7,2,5,6]=>1
[1,4,3,7,2,6,5]=>1
[1,4,3,7,5,2,6]=>1
[1,4,3,7,5,6,2]=>0
[1,4,3,7,6,2,5]=>2
[1,4,3,7,6,5,2]=>0
[1,4,5,2,3,6,7]=>4
[1,4,5,2,3,7,6]=>4
[1,4,5,2,6,3,7]=>4
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>5
[1,4,5,2,7,6,3]=>4
[1,4,5,3,2,6,7]=>1
[1,4,5,3,2,7,6]=>1
[1,4,5,3,6,2,7]=>1
[1,4,5,3,6,7,2]=>1
[1,4,5,3,7,2,6]=>2
[1,4,5,3,7,6,2]=>1
[1,4,5,6,2,3,7]=>5
[1,4,5,6,2,7,3]=>5
[1,4,5,6,3,2,7]=>4
[1,4,5,6,3,7,2]=>4
[1,4,5,6,7,2,3]=>6
[1,4,5,6,7,3,2]=>5
[1,4,5,7,2,3,6]=>6
[1,4,5,7,2,6,3]=>5
[1,4,5,7,3,2,6]=>5
[1,4,5,7,3,6,2]=>4
[1,4,5,7,6,2,3]=>5
[1,4,5,7,6,3,2]=>4
[1,4,6,2,3,5,7]=>4
[1,4,6,2,3,7,5]=>5
[1,4,6,2,5,3,7]=>4
[1,4,6,2,5,7,3]=>4
[1,4,6,2,7,3,5]=>8
[1,4,6,2,7,5,3]=>5
[1,4,6,3,2,5,7]=>2
[1,4,6,3,2,7,5]=>3
[1,4,6,3,5,2,7]=>1
[1,4,6,3,5,7,2]=>1
[1,4,6,3,7,2,5]=>5
[1,4,6,3,7,5,2]=>2
[1,4,6,5,2,3,7]=>4
[1,4,6,5,2,7,3]=>4
[1,4,6,5,3,2,7]=>2
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Description
The number of cyclic crossings of a permutation.
The pair $(i,j)$ is a cyclic crossing of a permutation $\pi$ if $i, \pi(j), \pi(i), j$ are cyclically ordered and all distinct, see Section 5 of [1].
The pair $(i,j)$ is a cyclic crossing of a permutation $\pi$ if $i, \pi(j), \pi(i), j$ are cyclically ordered and all distinct, see Section 5 of [1].
References
[1] Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
Code
def in_cyclic_order(i, j, k, l):
return (i < j < k < l or
j < k < l < i or
k < l < i < j or
l < i < j < k)
def statistic(pi):
n = len(pi)
a = 0
for i, pi_i in enumerate(pi, 1):
for j, pi_j in enumerate(pi, 1):
if in_cyclic_order(i, pi_j, pi_i, j):
a += 1
return a
Created
May 09, 2020 at 22:20 by Martin Rubey
Updated
May 09, 2020 at 22:20 by Martin Rubey
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