Identifier
- St000873: Permutations ⟶ ℤ
Values
=>
[1,2]=>2
[2,1]=>0
[1,2,3]=>3
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>0
[3,1,2]=>1
[3,2,1]=>0
[1,2,3,4]=>4
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>1
[1,4,2,3]=>2
[1,4,3,2]=>1
[2,1,3,4]=>1
[2,1,4,3]=>1
[2,3,1,4]=>2
[2,3,4,1]=>0
[2,4,1,3]=>2
[2,4,3,1]=>0
[3,1,2,4]=>1
[3,1,4,2]=>1
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>2
[3,4,2,1]=>0
[4,1,2,3]=>1
[4,1,3,2]=>1
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,2,3,4,5]=>5
[1,2,3,5,4]=>3
[1,2,4,3,5]=>3
[1,2,4,5,3]=>2
[1,2,5,3,4]=>3
[1,2,5,4,3]=>2
[1,3,2,4,5]=>2
[1,3,2,5,4]=>2
[1,3,4,2,5]=>3
[1,3,4,5,2]=>1
[1,3,5,2,4]=>3
[1,3,5,4,2]=>1
[1,4,2,3,5]=>2
[1,4,2,5,3]=>2
[1,4,3,2,5]=>1
[1,4,3,5,2]=>1
[1,4,5,2,3]=>3
[1,4,5,3,2]=>1
[1,5,2,3,4]=>2
[1,5,2,4,3]=>2
[1,5,3,2,4]=>1
[1,5,3,4,2]=>1
[1,5,4,2,3]=>1
[1,5,4,3,2]=>1
[2,1,3,4,5]=>1
[2,1,3,5,4]=>1
[2,1,4,3,5]=>1
[2,1,4,5,3]=>1
[2,1,5,3,4]=>1
[2,1,5,4,3]=>1
[2,3,1,4,5]=>2
[2,3,1,5,4]=>2
[2,3,4,1,5]=>3
[2,3,4,5,1]=>0
[2,3,5,1,4]=>3
[2,3,5,4,1]=>0
[2,4,1,3,5]=>2
[2,4,1,5,3]=>2
[2,4,3,1,5]=>1
[2,4,3,5,1]=>0
[2,4,5,1,3]=>3
[2,4,5,3,1]=>0
[2,5,1,3,4]=>2
[2,5,1,4,3]=>2
[2,5,3,1,4]=>1
[2,5,3,4,1]=>0
[2,5,4,1,3]=>1
[2,5,4,3,1]=>0
[3,1,2,4,5]=>1
[3,1,2,5,4]=>1
[3,1,4,2,5]=>1
[3,1,4,5,2]=>1
[3,1,5,2,4]=>1
[3,1,5,4,2]=>1
[3,2,1,4,5]=>0
[3,2,1,5,4]=>0
[3,2,4,1,5]=>1
[3,2,4,5,1]=>0
[3,2,5,1,4]=>1
[3,2,5,4,1]=>0
[3,4,1,2,5]=>2
[3,4,1,5,2]=>2
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[3,4,5,1,2]=>3
[3,4,5,2,1]=>0
[3,5,1,2,4]=>2
[3,5,1,4,2]=>2
[3,5,2,1,4]=>0
[3,5,2,4,1]=>0
[3,5,4,1,2]=>1
[3,5,4,2,1]=>0
[4,1,2,3,5]=>1
[4,1,2,5,3]=>1
[4,1,3,2,5]=>1
[4,1,3,5,2]=>1
[4,1,5,2,3]=>1
[4,1,5,3,2]=>1
[4,2,1,3,5]=>0
[4,2,1,5,3]=>0
[4,2,3,1,5]=>1
[4,2,3,5,1]=>0
[4,2,5,1,3]=>1
[4,2,5,3,1]=>0
[4,3,1,2,5]=>0
[4,3,1,5,2]=>0
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>1
[4,3,5,2,1]=>0
[4,5,1,2,3]=>2
[4,5,1,3,2]=>2
[4,5,2,1,3]=>0
[4,5,2,3,1]=>0
[4,5,3,1,2]=>0
[4,5,3,2,1]=>0
[5,1,2,3,4]=>1
[5,1,2,4,3]=>1
[5,1,3,2,4]=>1
[5,1,3,4,2]=>1
[5,1,4,2,3]=>1
[5,1,4,3,2]=>1
[5,2,1,3,4]=>0
[5,2,1,4,3]=>0
[5,2,3,1,4]=>1
[5,2,3,4,1]=>0
[5,2,4,1,3]=>1
[5,2,4,3,1]=>0
[5,3,1,2,4]=>0
[5,3,1,4,2]=>0
[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]=>0
[5,4,1,3,2]=>0
[5,4,2,1,3]=>0
[5,4,2,3,1]=>0
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>6
[1,2,3,4,6,5]=>4
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>3
[1,2,3,6,4,5]=>4
[1,2,3,6,5,4]=>3
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>3
[1,2,4,5,3,6]=>4
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>4
[1,2,4,6,5,3]=>2
[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>2
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>2
[1,2,6,4,5,3]=>2
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>2
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>2
[1,3,2,6,4,5]=>2
[1,3,2,6,5,4]=>2
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>1
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>3
[1,3,5,4,2,6]=>2
[1,3,5,4,6,2]=>1
[1,3,5,6,2,4]=>4
[1,3,5,6,4,2]=>1
[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>3
[1,3,6,4,2,5]=>2
[1,3,6,4,5,2]=>1
[1,3,6,5,2,4]=>2
[1,3,6,5,4,2]=>1
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>2
[1,4,2,5,3,6]=>2
[1,4,2,5,6,3]=>2
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>2
[1,4,3,2,5,6]=>1
[1,4,3,2,6,5]=>1
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>1
[1,4,3,6,2,5]=>2
[1,4,3,6,5,2]=>1
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>1
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>4
[1,4,5,6,3,2]=>1
[1,4,6,2,3,5]=>3
[1,4,6,2,5,3]=>3
[1,4,6,3,2,5]=>1
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>2
[1,4,6,5,3,2]=>1
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>2
[1,5,2,6,3,4]=>2
[1,5,2,6,4,3]=>2
[1,5,3,2,4,6]=>1
[1,5,3,2,6,4]=>1
[1,5,3,4,2,6]=>2
[1,5,3,4,6,2]=>1
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>1
[1,5,4,2,3,6]=>1
[1,5,4,2,6,3]=>1
[1,5,4,3,2,6]=>1
[1,5,4,3,6,2]=>1
[1,5,4,6,2,3]=>2
[1,5,4,6,3,2]=>1
[1,5,6,2,3,4]=>3
[1,5,6,2,4,3]=>3
[1,5,6,3,2,4]=>1
[1,5,6,3,4,2]=>1
[1,5,6,4,2,3]=>1
[1,5,6,4,3,2]=>1
[1,6,2,3,4,5]=>2
[1,6,2,3,5,4]=>2
[1,6,2,4,3,5]=>2
[1,6,2,4,5,3]=>2
[1,6,2,5,3,4]=>2
[1,6,2,5,4,3]=>2
[1,6,3,2,4,5]=>1
[1,6,3,2,5,4]=>1
[1,6,3,4,2,5]=>2
[1,6,3,4,5,2]=>1
[1,6,3,5,2,4]=>2
[1,6,3,5,4,2]=>1
[1,6,4,2,3,5]=>1
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>1
[1,6,4,3,5,2]=>1
[1,6,4,5,2,3]=>2
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>1
[1,6,5,2,4,3]=>1
[1,6,5,3,2,4]=>1
[1,6,5,3,4,2]=>1
[1,6,5,4,2,3]=>1
[1,6,5,4,3,2]=>1
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>1
[2,1,3,5,4,6]=>1
[2,1,3,5,6,4]=>1
[2,1,3,6,4,5]=>1
[2,1,3,6,5,4]=>1
[2,1,4,3,5,6]=>1
[2,1,4,3,6,5]=>1
[2,1,4,5,3,6]=>1
[2,1,4,5,6,3]=>1
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>1
[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>1
[2,1,5,4,6,3]=>1
[2,1,5,6,3,4]=>1
[2,1,5,6,4,3]=>1
[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>1
[2,1,6,4,3,5]=>1
[2,1,6,4,5,3]=>1
[2,1,6,5,3,4]=>1
[2,1,6,5,4,3]=>1
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>2
[2,3,1,5,4,6]=>2
[2,3,1,5,6,4]=>2
[2,3,1,6,4,5]=>2
[2,3,1,6,5,4]=>2
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>3
[2,3,4,5,1,6]=>4
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>4
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>0
[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>3
[2,3,6,4,1,5]=>2
[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]=>2
[2,4,1,3,6,5]=>2
[2,4,1,5,3,6]=>2
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>2
[2,4,1,6,5,3]=>2
[2,4,3,1,5,6]=>1
[2,4,3,1,6,5]=>1
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>0
[2,4,3,6,1,5]=>2
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>3
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>0
[2,4,5,6,1,3]=>4
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>3
[2,4,6,3,1,5]=>1
[2,4,6,3,5,1]=>0
[2,4,6,5,1,3]=>2
[2,4,6,5,3,1]=>0
[2,5,1,3,4,6]=>2
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>2
[2,5,1,4,6,3]=>2
[2,5,1,6,3,4]=>2
[2,5,1,6,4,3]=>2
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>1
[2,5,3,4,1,6]=>2
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>2
[2,5,3,6,4,1]=>0
[2,5,4,1,3,6]=>1
[2,5,4,1,6,3]=>1
[2,5,4,3,1,6]=>1
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>2
[2,5,4,6,3,1]=>0
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>3
[2,5,6,3,1,4]=>1
[2,5,6,3,4,1]=>0
[2,5,6,4,1,3]=>1
[2,5,6,4,3,1]=>0
[2,6,1,3,4,5]=>2
[2,6,1,3,5,4]=>2
[2,6,1,4,3,5]=>2
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>2
[2,6,3,1,4,5]=>1
[2,6,3,1,5,4]=>1
[2,6,3,4,1,5]=>2
[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]=>1
[2,6,4,1,5,3]=>1
[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]=>1
[2,6,5,1,4,3]=>1
[2,6,5,3,1,4]=>1
[2,6,5,3,4,1]=>0
[2,6,5,4,1,3]=>1
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>1
[3,1,2,5,4,6]=>1
[3,1,2,5,6,4]=>1
[3,1,2,6,4,5]=>1
[3,1,2,6,5,4]=>1
[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]=>1
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>1
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>1
[3,1,5,6,4,2]=>1
[3,1,6,2,4,5]=>1
[3,1,6,2,5,4]=>1
[3,1,6,4,2,5]=>1
[3,1,6,4,5,2]=>1
[3,1,6,5,2,4]=>1
[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]=>1
[3,2,4,1,6,5]=>1
[3,2,4,5,1,6]=>1
[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]=>1
[3,2,5,4,1,6]=>1
[3,2,5,4,6,1]=>0
[3,2,5,6,1,4]=>1
[3,2,5,6,4,1]=>0
[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]=>1
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>2
[3,4,1,6,2,5]=>2
[3,4,1,6,5,2]=>2
[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>0
[3,4,2,5,1,6]=>2
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>0
[3,4,5,1,2,6]=>3
[3,4,5,1,6,2]=>3
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>4
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>3
[3,4,6,2,1,5]=>0
[3,4,6,2,5,1]=>0
[3,4,6,5,1,2]=>2
[3,4,6,5,2,1]=>0
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>2
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>2
[3,5,1,6,2,4]=>2
[3,5,1,6,4,2]=>2
[3,5,2,1,4,6]=>0
[3,5,2,1,6,4]=>0
[3,5,2,4,1,6]=>2
[3,5,2,4,6,1]=>0
[3,5,2,6,1,4]=>2
[3,5,2,6,4,1]=>0
[3,5,4,1,2,6]=>1
[3,5,4,1,6,2]=>1
[3,5,4,2,1,6]=>0
[3,5,4,2,6,1]=>0
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>0
[3,5,6,1,2,4]=>3
[3,5,6,1,4,2]=>3
[3,5,6,2,1,4]=>0
[3,5,6,2,4,1]=>0
[3,5,6,4,1,2]=>1
[3,5,6,4,2,1]=>0
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>2
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>2
[3,6,1,5,4,2]=>2
[3,6,2,1,4,5]=>0
[3,6,2,1,5,4]=>0
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>0
[3,6,2,5,1,4]=>2
[3,6,2,5,4,1]=>0
[3,6,4,1,2,5]=>1
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>0
[3,6,4,2,5,1]=>0
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>0
[3,6,5,1,2,4]=>1
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>0
[3,6,5,2,4,1]=>0
[3,6,5,4,1,2]=>1
[3,6,5,4,2,1]=>0
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>1
[4,1,2,5,3,6]=>1
[4,1,2,5,6,3]=>1
[4,1,2,6,3,5]=>1
[4,1,2,6,5,3]=>1
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>1
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>1
[4,1,3,6,2,5]=>1
[4,1,3,6,5,2]=>1
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>1
[4,1,5,6,2,3]=>1
[4,1,5,6,3,2]=>1
[4,1,6,2,3,5]=>1
[4,1,6,2,5,3]=>1
[4,1,6,3,2,5]=>1
[4,1,6,3,5,2]=>1
[4,1,6,5,2,3]=>1
[4,1,6,5,3,2]=>1
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>0
[4,2,1,5,3,6]=>0
[4,2,1,5,6,3]=>0
[4,2,1,6,3,5]=>0
[4,2,1,6,5,3]=>0
[4,2,3,1,5,6]=>1
[4,2,3,1,6,5]=>1
[4,2,3,5,1,6]=>1
[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]=>1
[4,2,5,1,6,3]=>1
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>0
[4,2,5,6,1,3]=>1
[4,2,5,6,3,1]=>0
[4,2,6,1,3,5]=>1
[4,2,6,1,5,3]=>1
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>0
[4,2,6,5,1,3]=>1
[4,2,6,5,3,1]=>0
[4,3,1,2,5,6]=>0
[4,3,1,2,6,5]=>0
[4,3,1,5,2,6]=>0
[4,3,1,5,6,2]=>0
[4,3,1,6,2,5]=>0
[4,3,1,6,5,2]=>0
[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]=>0
[4,3,2,6,5,1]=>0
[4,3,5,1,2,6]=>1
[4,3,5,1,6,2]=>1
[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>0
[4,3,5,6,1,2]=>1
[4,3,5,6,2,1]=>0
[4,3,6,1,2,5]=>1
[4,3,6,1,5,2]=>1
[4,3,6,2,1,5]=>0
[4,3,6,2,5,1]=>0
[4,3,6,5,1,2]=>1
[4,3,6,5,2,1]=>0
[4,5,1,2,3,6]=>2
[4,5,1,2,6,3]=>2
[4,5,1,3,2,6]=>2
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>2
[4,5,2,1,3,6]=>0
[4,5,2,1,6,3]=>0
[4,5,2,3,1,6]=>2
[4,5,2,3,6,1]=>0
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>0
[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>0
[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>3
[4,5,6,2,1,3]=>0
[4,5,6,2,3,1]=>0
[4,5,6,3,1,2]=>0
[4,5,6,3,2,1]=>0
[4,6,1,2,3,5]=>2
[4,6,1,2,5,3]=>2
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>2
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>2
[4,6,2,1,3,5]=>0
[4,6,2,1,5,3]=>0
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>0
[4,6,2,5,1,3]=>2
[4,6,2,5,3,1]=>0
[4,6,3,1,2,5]=>0
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>0
[4,6,3,2,5,1]=>0
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>0
[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>1
[4,6,5,2,1,3]=>0
[4,6,5,2,3,1]=>0
[4,6,5,3,1,2]=>0
[4,6,5,3,2,1]=>0
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>1
[5,1,2,4,3,6]=>1
[5,1,2,4,6,3]=>1
[5,1,2,6,3,4]=>1
[5,1,2,6,4,3]=>1
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>1
[5,1,3,4,6,2]=>1
[5,1,3,6,2,4]=>1
[5,1,3,6,4,2]=>1
[5,1,4,2,3,6]=>1
[5,1,4,2,6,3]=>1
[5,1,4,3,2,6]=>1
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>1
[5,1,4,6,3,2]=>1
[5,1,6,2,3,4]=>1
[5,1,6,2,4,3]=>1
[5,1,6,3,2,4]=>1
[5,1,6,3,4,2]=>1
[5,1,6,4,2,3]=>1
[5,1,6,4,3,2]=>1
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>0
[5,2,1,4,3,6]=>0
[5,2,1,4,6,3]=>0
[5,2,1,6,3,4]=>0
[5,2,1,6,4,3]=>0
[5,2,3,1,4,6]=>1
[5,2,3,1,6,4]=>1
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>0
[5,2,3,6,1,4]=>1
[5,2,3,6,4,1]=>0
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>1
[5,2,4,3,1,6]=>1
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>1
[5,2,4,6,3,1]=>0
[5,2,6,1,3,4]=>1
[5,2,6,1,4,3]=>1
[5,2,6,3,1,4]=>1
[5,2,6,3,4,1]=>0
[5,2,6,4,1,3]=>1
[5,2,6,4,3,1]=>0
[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>0
[5,3,1,4,2,6]=>0
[5,3,1,4,6,2]=>0
[5,3,1,6,2,4]=>0
[5,3,1,6,4,2]=>0
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>0
[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>0
[5,3,2,6,1,4]=>0
[5,3,2,6,4,1]=>0
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>1
[5,3,4,2,1,6]=>0
[5,3,4,2,6,1]=>0
[5,3,4,6,1,2]=>1
[5,3,4,6,2,1]=>0
[5,3,6,1,2,4]=>1
[5,3,6,1,4,2]=>1
[5,3,6,2,1,4]=>0
[5,3,6,2,4,1]=>0
[5,3,6,4,1,2]=>1
[5,3,6,4,2,1]=>0
[5,4,1,2,3,6]=>0
[5,4,1,2,6,3]=>0
[5,4,1,3,2,6]=>0
[5,4,1,3,6,2]=>0
[5,4,1,6,2,3]=>0
[5,4,1,6,3,2]=>0
[5,4,2,1,3,6]=>0
[5,4,2,1,6,3]=>0
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>0
[5,4,2,6,1,3]=>0
[5,4,2,6,3,1]=>0
[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>0
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>0
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>1
[5,4,6,2,1,3]=>0
[5,4,6,2,3,1]=>0
[5,4,6,3,1,2]=>0
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>2
[5,6,1,2,4,3]=>2
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>2
[5,6,1,4,3,2]=>2
[5,6,2,1,3,4]=>0
[5,6,2,1,4,3]=>0
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>0
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>0
[5,6,3,1,2,4]=>0
[5,6,3,1,4,2]=>0
[5,6,3,2,1,4]=>0
[5,6,3,2,4,1]=>0
[5,6,3,4,1,2]=>2
[5,6,3,4,2,1]=>0
[5,6,4,1,2,3]=>0
[5,6,4,1,3,2]=>0
[5,6,4,2,1,3]=>0
[5,6,4,2,3,1]=>0
[5,6,4,3,1,2]=>0
[5,6,4,3,2,1]=>0
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>1
[6,1,2,4,3,5]=>1
[6,1,2,4,5,3]=>1
[6,1,2,5,3,4]=>1
[6,1,2,5,4,3]=>1
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>1
[6,1,3,4,2,5]=>1
[6,1,3,4,5,2]=>1
[6,1,3,5,2,4]=>1
[6,1,3,5,4,2]=>1
[6,1,4,2,3,5]=>1
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>1
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>1
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>1
[6,1,5,2,4,3]=>1
[6,1,5,3,2,4]=>1
[6,1,5,3,4,2]=>1
[6,1,5,4,2,3]=>1
[6,1,5,4,3,2]=>1
[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]=>0
[6,2,1,5,4,3]=>0
[6,2,3,1,4,5]=>1
[6,2,3,1,5,4]=>1
[6,2,3,4,1,5]=>1
[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]=>1
[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]=>1
[6,2,5,1,4,3]=>1
[6,2,5,3,1,4]=>1
[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]=>0
[6,3,1,2,5,4]=>0
[6,3,1,4,2,5]=>0
[6,3,1,4,5,2]=>0
[6,3,1,5,2,4]=>0
[6,3,1,5,4,2]=>0
[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]=>0
[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]=>1
[6,3,5,1,4,2]=>1
[6,3,5,2,1,4]=>0
[6,3,5,2,4,1]=>0
[6,3,5,4,1,2]=>1
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>0
[6,4,1,3,5,2]=>0
[6,4,1,5,2,3]=>0
[6,4,1,5,3,2]=>0
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>0
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>0
[6,4,2,5,3,1]=>0
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>0
[6,4,3,5,2,1]=>0
[6,4,5,1,2,3]=>1
[6,4,5,1,3,2]=>1
[6,4,5,2,1,3]=>0
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>0
[6,4,5,3,2,1]=>0
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>0
[6,5,1,3,2,4]=>0
[6,5,1,3,4,2]=>0
[6,5,1,4,2,3]=>0
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>0
[6,5,2,1,4,3]=>0
[6,5,2,3,1,4]=>0
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>0
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>0
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>0
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>0
[6,5,4,2,1,3]=>0
[6,5,4,2,3,1]=>0
[6,5,4,3,1,2]=>0
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>7
[1,2,3,4,5,7,6]=>5
[1,2,3,4,6,5,7]=>5
[1,2,3,4,6,7,5]=>4
[1,2,3,4,7,5,6]=>5
[1,2,3,4,7,6,5]=>4
[1,2,3,5,4,6,7]=>4
[1,2,3,5,4,7,6]=>4
[1,2,3,5,6,4,7]=>5
[1,2,3,5,6,7,4]=>3
[1,2,3,5,7,4,6]=>5
[1,2,3,5,7,6,4]=>3
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>4
[1,2,3,6,5,4,7]=>3
[1,2,3,6,5,7,4]=>3
[1,2,3,6,7,4,5]=>5
[1,2,3,6,7,5,4]=>3
[1,2,3,7,4,5,6]=>4
[1,2,3,7,4,6,5]=>4
[1,2,3,7,5,4,6]=>3
[1,2,3,7,5,6,4]=>3
[1,2,3,7,6,4,5]=>3
[1,2,3,7,6,5,4]=>3
[1,2,4,3,5,6,7]=>3
[1,2,4,3,5,7,6]=>3
[1,2,4,3,6,5,7]=>3
[1,2,4,3,6,7,5]=>3
[1,2,4,3,7,5,6]=>3
[1,2,4,3,7,6,5]=>3
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>4
[1,2,4,5,6,3,7]=>5
[1,2,4,5,6,7,3]=>2
[1,2,4,5,7,3,6]=>5
[1,2,4,5,7,6,3]=>2
[1,2,4,6,3,5,7]=>4
[1,2,4,6,3,7,5]=>4
[1,2,4,6,5,3,7]=>3
[1,2,4,6,5,7,3]=>2
[1,2,4,6,7,3,5]=>5
[1,2,4,6,7,5,3]=>2
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>4
[1,2,4,7,5,3,6]=>3
[1,2,4,7,5,6,3]=>2
[1,2,4,7,6,3,5]=>3
[1,2,4,7,6,5,3]=>2
[1,2,5,3,4,6,7]=>3
[1,2,5,3,4,7,6]=>3
[1,2,5,3,6,4,7]=>3
[1,2,5,3,6,7,4]=>3
[1,2,5,3,7,4,6]=>3
[1,2,5,3,7,6,4]=>3
[1,2,5,4,3,6,7]=>2
[1,2,5,4,3,7,6]=>2
[1,2,5,4,6,3,7]=>3
[1,2,5,4,6,7,3]=>2
[1,2,5,4,7,3,6]=>3
[1,2,5,4,7,6,3]=>2
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>4
[1,2,5,6,4,3,7]=>2
[1,2,5,6,4,7,3]=>2
[1,2,5,6,7,3,4]=>5
[1,2,5,6,7,4,3]=>2
[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]=>2
[1,2,5,7,6,3,4]=>3
[1,2,5,7,6,4,3]=>2
[1,2,6,3,4,5,7]=>3
[1,2,6,3,4,7,5]=>3
[1,2,6,3,5,4,7]=>3
[1,2,6,3,5,7,4]=>3
[1,2,6,3,7,4,5]=>3
[1,2,6,3,7,5,4]=>3
[1,2,6,4,3,5,7]=>2
[1,2,6,4,3,7,5]=>2
[1,2,6,4,5,3,7]=>3
[1,2,6,4,5,7,3]=>2
[1,2,6,4,7,3,5]=>3
[1,2,6,4,7,5,3]=>2
[1,2,6,5,3,4,7]=>2
[1,2,6,5,3,7,4]=>2
[1,2,6,5,4,3,7]=>2
[1,2,6,5,4,7,3]=>2
[1,2,6,5,7,3,4]=>3
[1,2,6,5,7,4,3]=>2
[1,2,6,7,3,4,5]=>4
[1,2,6,7,3,5,4]=>4
[1,2,6,7,4,3,5]=>2
[1,2,6,7,4,5,3]=>2
[1,2,6,7,5,3,4]=>2
[1,2,6,7,5,4,3]=>2
[1,2,7,3,4,5,6]=>3
[1,2,7,3,4,6,5]=>3
[1,2,7,3,5,4,6]=>3
[1,2,7,3,5,6,4]=>3
[1,2,7,3,6,4,5]=>3
[1,2,7,3,6,5,4]=>3
[1,2,7,4,3,5,6]=>2
[1,2,7,4,3,6,5]=>2
[1,2,7,4,5,3,6]=>3
[1,2,7,4,5,6,3]=>2
[1,2,7,4,6,3,5]=>3
[1,2,7,4,6,5,3]=>2
[1,2,7,5,3,4,6]=>2
[1,2,7,5,3,6,4]=>2
[1,2,7,5,4,3,6]=>2
[1,2,7,5,4,6,3]=>2
[1,2,7,5,6,3,4]=>3
[1,2,7,5,6,4,3]=>2
[1,2,7,6,3,4,5]=>2
[1,2,7,6,3,5,4]=>2
[1,2,7,6,4,3,5]=>2
[1,2,7,6,4,5,3]=>2
[1,2,7,6,5,3,4]=>2
[1,2,7,6,5,4,3]=>2
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>2
[1,3,2,4,6,5,7]=>2
[1,3,2,4,6,7,5]=>2
[1,3,2,4,7,5,6]=>2
[1,3,2,4,7,6,5]=>2
[1,3,2,5,4,6,7]=>2
[1,3,2,5,4,7,6]=>2
[1,3,2,5,6,4,7]=>2
[1,3,2,5,6,7,4]=>2
[1,3,2,5,7,4,6]=>2
[1,3,2,5,7,6,4]=>2
[1,3,2,6,4,5,7]=>2
[1,3,2,6,4,7,5]=>2
[1,3,2,6,5,4,7]=>2
[1,3,2,6,5,7,4]=>2
[1,3,2,6,7,4,5]=>2
[1,3,2,6,7,5,4]=>2
[1,3,2,7,4,5,6]=>2
[1,3,2,7,4,6,5]=>2
[1,3,2,7,5,4,6]=>2
[1,3,2,7,5,6,4]=>2
[1,3,2,7,6,4,5]=>2
[1,3,2,7,6,5,4]=>2
[1,3,4,2,5,6,7]=>3
[1,3,4,2,5,7,6]=>3
[1,3,4,2,6,5,7]=>3
[1,3,4,2,6,7,5]=>3
[1,3,4,2,7,5,6]=>3
[1,3,4,2,7,6,5]=>3
[1,3,4,5,2,6,7]=>4
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>5
[1,3,4,5,6,7,2]=>1
[1,3,4,5,7,2,6]=>5
[1,3,4,5,7,6,2]=>1
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>4
[1,3,4,6,5,2,7]=>3
[1,3,4,6,5,7,2]=>1
[1,3,4,6,7,2,5]=>5
[1,3,4,6,7,5,2]=>1
[1,3,4,7,2,5,6]=>4
[1,3,4,7,2,6,5]=>4
[1,3,4,7,5,2,6]=>3
[1,3,4,7,5,6,2]=>1
[1,3,4,7,6,2,5]=>3
[1,3,4,7,6,5,2]=>1
[1,3,5,2,4,6,7]=>3
[1,3,5,2,4,7,6]=>3
[1,3,5,2,6,4,7]=>3
[1,3,5,2,6,7,4]=>3
[1,3,5,2,7,4,6]=>3
[1,3,5,2,7,6,4]=>3
[1,3,5,4,2,6,7]=>2
[1,3,5,4,2,7,6]=>2
[1,3,5,4,6,2,7]=>3
[1,3,5,4,6,7,2]=>1
[1,3,5,4,7,2,6]=>3
[1,3,5,4,7,6,2]=>1
[1,3,5,6,2,4,7]=>4
[1,3,5,6,2,7,4]=>4
[1,3,5,6,4,2,7]=>2
[1,3,5,6,4,7,2]=>1
[1,3,5,6,7,2,4]=>5
[1,3,5,6,7,4,2]=>1
[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]=>3
[1,3,5,7,6,4,2]=>1
[1,3,6,2,4,5,7]=>3
[1,3,6,2,4,7,5]=>3
[1,3,6,2,5,4,7]=>3
[1,3,6,2,5,7,4]=>3
[1,3,6,2,7,4,5]=>3
[1,3,6,2,7,5,4]=>3
[1,3,6,4,2,5,7]=>2
[1,3,6,4,2,7,5]=>2
[1,3,6,4,5,2,7]=>3
[1,3,6,4,5,7,2]=>1
[1,3,6,4,7,2,5]=>3
[1,3,6,4,7,5,2]=>1
[1,3,6,5,2,4,7]=>2
[1,3,6,5,2,7,4]=>2
[1,3,6,5,4,2,7]=>2
[1,3,6,5,4,7,2]=>1
[1,3,6,5,7,2,4]=>3
[1,3,6,5,7,4,2]=>1
[1,3,6,7,2,4,5]=>4
[1,3,6,7,2,5,4]=>4
[1,3,6,7,4,2,5]=>2
[1,3,6,7,4,5,2]=>1
[1,3,6,7,5,2,4]=>2
[1,3,6,7,5,4,2]=>1
[1,3,7,2,4,5,6]=>3
[1,3,7,2,4,6,5]=>3
[1,3,7,2,5,4,6]=>3
[1,3,7,2,5,6,4]=>3
[1,3,7,2,6,4,5]=>3
[1,3,7,2,6,5,4]=>3
[1,3,7,4,2,5,6]=>2
[1,3,7,4,2,6,5]=>2
[1,3,7,4,5,2,6]=>3
[1,3,7,4,5,6,2]=>1
[1,3,7,4,6,2,5]=>3
[1,3,7,4,6,5,2]=>1
[1,3,7,5,2,4,6]=>2
[1,3,7,5,2,6,4]=>2
[1,3,7,5,4,2,6]=>2
[1,3,7,5,4,6,2]=>1
[1,3,7,5,6,2,4]=>3
[1,3,7,5,6,4,2]=>1
[1,3,7,6,2,4,5]=>2
[1,3,7,6,2,5,4]=>2
[1,3,7,6,4,2,5]=>2
[1,3,7,6,4,5,2]=>1
[1,3,7,6,5,2,4]=>2
[1,3,7,6,5,4,2]=>1
[1,4,2,3,5,6,7]=>2
[1,4,2,3,5,7,6]=>2
[1,4,2,3,6,5,7]=>2
[1,4,2,3,6,7,5]=>2
[1,4,2,3,7,5,6]=>2
[1,4,2,3,7,6,5]=>2
[1,4,2,5,3,6,7]=>2
[1,4,2,5,3,7,6]=>2
[1,4,2,5,6,3,7]=>2
[1,4,2,5,6,7,3]=>2
[1,4,2,5,7,3,6]=>2
[1,4,2,5,7,6,3]=>2
[1,4,2,6,3,5,7]=>2
[1,4,2,6,3,7,5]=>2
[1,4,2,6,5,3,7]=>2
[1,4,2,6,5,7,3]=>2
[1,4,2,6,7,3,5]=>2
[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]=>2
[1,4,2,7,6,3,5]=>2
[1,4,2,7,6,5,3]=>2
[1,4,3,2,5,6,7]=>1
[1,4,3,2,5,7,6]=>1
[1,4,3,2,6,5,7]=>1
[1,4,3,2,6,7,5]=>1
[1,4,3,2,7,5,6]=>1
[1,4,3,2,7,6,5]=>1
[1,4,3,5,2,6,7]=>2
[1,4,3,5,2,7,6]=>2
[1,4,3,5,6,2,7]=>2
[1,4,3,5,6,7,2]=>1
[1,4,3,5,7,2,6]=>2
[1,4,3,5,7,6,2]=>1
[1,4,3,6,2,5,7]=>2
[1,4,3,6,2,7,5]=>2
[1,4,3,6,5,2,7]=>2
[1,4,3,6,5,7,2]=>1
[1,4,3,6,7,2,5]=>2
[1,4,3,6,7,5,2]=>1
[1,4,3,7,2,5,6]=>2
[1,4,3,7,2,6,5]=>2
[1,4,3,7,5,2,6]=>2
[1,4,3,7,5,6,2]=>1
[1,4,3,7,6,2,5]=>2
[1,4,3,7,6,5,2]=>1
[1,4,5,2,3,6,7]=>3
[1,4,5,2,3,7,6]=>3
[1,4,5,2,6,3,7]=>3
[1,4,5,2,6,7,3]=>3
[1,4,5,2,7,3,6]=>3
[1,4,5,2,7,6,3]=>3
[1,4,5,3,2,6,7]=>1
[1,4,5,3,2,7,6]=>1
[1,4,5,3,6,2,7]=>3
[1,4,5,3,6,7,2]=>1
[1,4,5,3,7,2,6]=>3
[1,4,5,3,7,6,2]=>1
[1,4,5,6,2,3,7]=>4
[1,4,5,6,2,7,3]=>4
[1,4,5,6,3,2,7]=>1
[1,4,5,6,3,7,2]=>1
[1,4,5,6,7,2,3]=>5
[1,4,5,6,7,3,2]=>1
[1,4,5,7,2,3,6]=>4
[1,4,5,7,2,6,3]=>4
[1,4,5,7,3,2,6]=>1
[1,4,5,7,3,6,2]=>1
[1,4,5,7,6,2,3]=>3
[1,4,5,7,6,3,2]=>1
[1,4,6,2,3,5,7]=>3
[1,4,6,2,3,7,5]=>3
[1,4,6,2,5,3,7]=>3
[1,4,6,2,5,7,3]=>3
[1,4,6,2,7,3,5]=>3
[1,4,6,2,7,5,3]=>3
[1,4,6,3,2,5,7]=>1
[1,4,6,3,2,7,5]=>1
[1,4,6,3,5,2,7]=>3
[1,4,6,3,5,7,2]=>1
[1,4,6,3,7,2,5]=>3
[1,4,6,3,7,5,2]=>1
[1,4,6,5,2,3,7]=>2
[1,4,6,5,2,7,3]=>2
[1,4,6,5,3,2,7]=>1
[1,4,6,5,3,7,2]=>1
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Description
The aix statistic of a permutation.
According to [1], this statistic on finite strings $\pi$ of integers is given as follows: let $m$ be the leftmost occurrence of the minimal entry and let $\pi = \alpha\ m\ \beta$. Then
$$ \operatorname{aix}\pi = \begin{cases} \operatorname{aix}\alpha & \text{ if } \alpha,\beta \neq \emptyset \\ 1 + \operatorname{aix}\beta & \text{ if } \alpha = \emptyset \\ 0 & \text{ if } \beta = \emptyset \end{cases}\ . $$
According to [1], this statistic on finite strings $\pi$ of integers is given as follows: let $m$ be the leftmost occurrence of the minimal entry and let $\pi = \alpha\ m\ \beta$. Then
$$ \operatorname{aix}\pi = \begin{cases} \operatorname{aix}\alpha & \text{ if } \alpha,\beta \neq \emptyset \\ 1 + \operatorname{aix}\beta & \text{ if } \alpha = \emptyset \\ 0 & \text{ if } \beta = \emptyset \end{cases}\ . $$
References
[1] Burstein, A. On the distribution of some Euler-Mahonian statistics MathSciNet:3357124
Code
def statistic(pi): pi = list(pi) if not pi: return 0 i = min(pi) j = pi.index(i) alpha = pi[:j] beta = pi[j+1:] if alpha and beta: return statistic(alpha) elif alpha == []: return 1 + statistic(beta) else: return 0
Created
Jun 27, 2017 at 11:42 by Christian Stump
Updated
Jun 27, 2017 at 11:42 by Christian Stump
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