Identifier
- St001559: 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]=>0
[2,4,3,1]=>0
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>1
[3,4,2,1]=>0
[4,1,2,3]=>0
[4,1,3,2]=>0
[4,2,1,3]=>0
[4,2,3,1]=>1
[4,3,1,2]=>0
[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]=>0
[1,3,5,4,2]=>0
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>1
[1,4,5,3,2]=>0
[1,5,2,3,4]=>0
[1,5,2,4,3]=>0
[1,5,3,2,4]=>0
[1,5,3,4,2]=>1
[1,5,4,2,3]=>0
[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]=>0
[2,3,5,4,1]=>0
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>1
[2,4,5,3,1]=>0
[2,5,1,3,4]=>0
[2,5,1,4,3]=>0
[2,5,3,1,4]=>0
[2,5,3,4,1]=>1
[2,5,4,1,3]=>0
[2,5,4,3,1]=>0
[3,1,2,4,5]=>0
[3,1,2,5,4]=>0
[3,1,4,2,5]=>0
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,4,2]=>0
[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]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>1
[3,4,1,5,2]=>1
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[3,4,5,1,2]=>1
[3,4,5,2,1]=>0
[3,5,1,2,4]=>1
[3,5,1,4,2]=>2
[3,5,2,1,4]=>0
[3,5,2,4,1]=>1
[3,5,4,1,2]=>1
[3,5,4,2,1]=>0
[4,1,2,3,5]=>0
[4,1,2,5,3]=>0
[4,1,3,2,5]=>0
[4,1,3,5,2]=>0
[4,1,5,2,3]=>1
[4,1,5,3,2]=>0
[4,2,1,3,5]=>0
[4,2,1,5,3]=>0
[4,2,3,1,5]=>1
[4,2,3,5,1]=>1
[4,2,5,1,3]=>2
[4,2,5,3,1]=>1
[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]=>1
[4,5,1,3,2]=>1
[4,5,2,1,3]=>1
[4,5,2,3,1]=>1
[4,5,3,1,2]=>1
[4,5,3,2,1]=>0
[5,1,2,3,4]=>0
[5,1,2,4,3]=>0
[5,1,3,2,4]=>0
[5,1,3,4,2]=>1
[5,1,4,2,3]=>0
[5,1,4,3,2]=>0
[5,2,1,3,4]=>0
[5,2,1,4,3]=>0
[5,2,3,1,4]=>1
[5,2,3,4,1]=>3
[5,2,4,1,3]=>1
[5,2,4,3,1]=>2
[5,3,1,2,4]=>0
[5,3,1,4,2]=>1
[5,3,2,1,4]=>0
[5,3,2,4,1]=>2
[5,3,4,1,2]=>1
[5,3,4,2,1]=>1
[5,4,1,2,3]=>0
[5,4,1,3,2]=>0
[5,4,2,1,3]=>0
[5,4,2,3,1]=>1
[5,4,3,1,2]=>0
[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]=>0
[1,2,4,6,5,3]=>0
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>0
[1,2,5,6,3,4]=>1
[1,2,5,6,4,3]=>0
[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]=>1
[1,2,6,5,3,4]=>0
[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]=>0
[1,3,4,6,5,2]=>0
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>0
[1,3,5,4,6,2]=>0
[1,3,5,6,2,4]=>1
[1,3,5,6,4,2]=>0
[1,3,6,2,4,5]=>0
[1,3,6,2,5,4]=>0
[1,3,6,4,2,5]=>0
[1,3,6,4,5,2]=>1
[1,3,6,5,2,4]=>0
[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]=>0
[1,4,2,5,6,3]=>0
[1,4,2,6,3,5]=>0
[1,4,2,6,5,3]=>0
[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]=>0
[1,4,3,6,5,2]=>0
[1,4,5,2,3,6]=>1
[1,4,5,2,6,3]=>1
[1,4,5,3,2,6]=>0
[1,4,5,3,6,2]=>0
[1,4,5,6,2,3]=>1
[1,4,5,6,3,2]=>0
[1,4,6,2,3,5]=>1
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>0
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>1
[1,4,6,5,3,2]=>0
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>0
[1,5,2,4,3,6]=>0
[1,5,2,4,6,3]=>0
[1,5,2,6,3,4]=>1
[1,5,2,6,4,3]=>0
[1,5,3,2,4,6]=>0
[1,5,3,2,6,4]=>0
[1,5,3,4,2,6]=>1
[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]=>0
[1,5,4,2,6,3]=>0
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>0
[1,5,4,6,2,3]=>1
[1,5,4,6,3,2]=>0
[1,5,6,2,3,4]=>1
[1,5,6,2,4,3]=>1
[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]=>0
[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]=>1
[1,6,2,5,3,4]=>0
[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]=>1
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>1
[1,6,3,5,4,2]=>2
[1,6,4,2,3,5]=>0
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>0
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>0
[1,6,5,2,4,3]=>0
[1,6,5,3,2,4]=>0
[1,6,5,3,4,2]=>1
[1,6,5,4,2,3]=>0
[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]=>0
[2,1,4,6,5,3]=>0
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>0
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>0
[2,1,5,6,3,4]=>1
[2,1,5,6,4,3]=>0
[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]=>1
[2,1,6,5,3,4]=>0
[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]=>0
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>0
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>1
[2,3,5,6,4,1]=>0
[2,3,6,1,4,5]=>0
[2,3,6,1,5,4]=>0
[2,3,6,4,1,5]=>0
[2,3,6,4,5,1]=>1
[2,3,6,5,1,4]=>0
[2,3,6,5,4,1]=>0
[2,4,1,3,5,6]=>0
[2,4,1,3,6,5]=>0
[2,4,1,5,3,6]=>0
[2,4,1,5,6,3]=>0
[2,4,1,6,3,5]=>0
[2,4,1,6,5,3]=>0
[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]=>0
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>1
[2,4,5,1,6,3]=>1
[2,4,5,3,1,6]=>0
[2,4,5,3,6,1]=>0
[2,4,5,6,1,3]=>1
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>1
[2,4,6,1,5,3]=>2
[2,4,6,3,1,5]=>0
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>1
[2,4,6,5,3,1]=>0
[2,5,1,3,4,6]=>0
[2,5,1,3,6,4]=>0
[2,5,1,4,3,6]=>0
[2,5,1,4,6,3]=>0
[2,5,1,6,3,4]=>1
[2,5,1,6,4,3]=>0
[2,5,3,1,4,6]=>0
[2,5,3,1,6,4]=>0
[2,5,3,4,1,6]=>1
[2,5,3,4,6,1]=>1
[2,5,3,6,1,4]=>2
[2,5,3,6,4,1]=>1
[2,5,4,1,3,6]=>0
[2,5,4,1,6,3]=>0
[2,5,4,3,1,6]=>0
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>1
[2,5,4,6,3,1]=>0
[2,5,6,1,3,4]=>1
[2,5,6,1,4,3]=>1
[2,5,6,3,1,4]=>1
[2,5,6,3,4,1]=>1
[2,5,6,4,1,3]=>1
[2,5,6,4,3,1]=>0
[2,6,1,3,4,5]=>0
[2,6,1,3,5,4]=>0
[2,6,1,4,3,5]=>0
[2,6,1,4,5,3]=>1
[2,6,1,5,3,4]=>0
[2,6,1,5,4,3]=>0
[2,6,3,1,4,5]=>0
[2,6,3,1,5,4]=>0
[2,6,3,4,1,5]=>1
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>1
[2,6,3,5,4,1]=>2
[2,6,4,1,3,5]=>0
[2,6,4,1,5,3]=>1
[2,6,4,3,1,5]=>0
[2,6,4,3,5,1]=>2
[2,6,4,5,1,3]=>1
[2,6,4,5,3,1]=>1
[2,6,5,1,3,4]=>0
[2,6,5,1,4,3]=>0
[2,6,5,3,1,4]=>0
[2,6,5,3,4,1]=>1
[2,6,5,4,1,3]=>0
[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]=>0
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>0
[3,1,4,5,6,2]=>0
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>0
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>0
[3,1,5,4,6,2]=>0
[3,1,5,6,2,4]=>1
[3,1,5,6,4,2]=>0
[3,1,6,2,4,5]=>0
[3,1,6,2,5,4]=>0
[3,1,6,4,2,5]=>0
[3,1,6,4,5,2]=>1
[3,1,6,5,2,4]=>0
[3,1,6,5,4,2]=>0
[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]=>0
[3,2,4,6,5,1]=>0
[3,2,5,1,4,6]=>0
[3,2,5,1,6,4]=>0
[3,2,5,4,1,6]=>0
[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]=>0
[3,2,6,1,5,4]=>0
[3,2,6,4,1,5]=>0
[3,2,6,4,5,1]=>1
[3,2,6,5,1,4]=>0
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>1
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>1
[3,4,1,6,2,5]=>1
[3,4,1,6,5,2]=>1
[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>0
[3,4,2,5,1,6]=>0
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>0
[3,4,2,6,5,1]=>0
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>1
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>1
[3,4,6,1,5,2]=>2
[3,4,6,2,1,5]=>0
[3,4,6,2,5,1]=>1
[3,4,6,5,1,2]=>1
[3,4,6,5,2,1]=>0
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>1
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>2
[3,5,1,6,2,4]=>3
[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]=>1
[3,5,2,4,6,1]=>1
[3,5,2,6,1,4]=>2
[3,5,2,6,4,1]=>1
[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]=>1
[3,5,4,6,2,1]=>0
[3,5,6,1,2,4]=>2
[3,5,6,1,4,2]=>2
[3,5,6,2,1,4]=>1
[3,5,6,2,4,1]=>1
[3,5,6,4,1,2]=>1
[3,5,6,4,2,1]=>0
[3,6,1,2,4,5]=>1
[3,6,1,2,5,4]=>1
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>2
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>0
[3,6,2,1,5,4]=>0
[3,6,2,4,1,5]=>1
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>1
[3,6,2,5,4,1]=>2
[3,6,4,1,2,5]=>1
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>0
[3,6,4,2,5,1]=>2
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>1
[3,6,5,1,2,4]=>1
[3,6,5,1,4,2]=>2
[3,6,5,2,1,4]=>0
[3,6,5,2,4,1]=>1
[3,6,5,4,1,2]=>1
[3,6,5,4,2,1]=>0
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>0
[4,1,2,5,3,6]=>0
[4,1,2,5,6,3]=>0
[4,1,2,6,3,5]=>0
[4,1,2,6,5,3]=>0
[4,1,3,2,5,6]=>0
[4,1,3,2,6,5]=>0
[4,1,3,5,2,6]=>0
[4,1,3,5,6,2]=>0
[4,1,3,6,2,5]=>0
[4,1,3,6,5,2]=>0
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>0
[4,1,5,3,6,2]=>0
[4,1,5,6,2,3]=>1
[4,1,5,6,3,2]=>0
[4,1,6,2,3,5]=>1
[4,1,6,2,5,3]=>2
[4,1,6,3,2,5]=>0
[4,1,6,3,5,2]=>1
[4,1,6,5,2,3]=>1
[4,1,6,5,3,2]=>0
[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]=>1
[4,2,3,6,1,5]=>1
[4,2,3,6,5,1]=>1
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>2
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>1
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>3
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>2
[4,2,6,5,1,3]=>2
[4,2,6,5,3,1]=>1
[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]=>2
[4,3,6,2,1,5]=>0
[4,3,6,2,5,1]=>1
[4,3,6,5,1,2]=>1
[4,3,6,5,2,1]=>0
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>1
[4,5,1,3,2,6]=>1
[4,5,1,3,6,2]=>1
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>1
[4,5,2,1,3,6]=>1
[4,5,2,1,6,3]=>1
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>1
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>1
[4,5,3,1,2,6]=>1
[4,5,3,1,6,2]=>1
[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>2
[4,5,6,2,3,1]=>1
[4,5,6,3,1,2]=>1
[4,5,6,3,2,1]=>0
[4,6,1,2,3,5]=>1
[4,6,1,2,5,3]=>2
[4,6,1,3,2,5]=>1
[4,6,1,3,5,2]=>3
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>2
[4,6,2,1,3,5]=>1
[4,6,2,1,5,3]=>2
[4,6,2,3,1,5]=>1
[4,6,2,3,5,1]=>3
[4,6,2,5,1,3]=>2
[4,6,2,5,3,1]=>2
[4,6,3,1,2,5]=>1
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>0
[4,6,3,2,5,1]=>2
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>1
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>2
[4,6,5,2,1,3]=>1
[4,6,5,2,3,1]=>1
[4,6,5,3,1,2]=>1
[4,6,5,3,2,1]=>0
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>0
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>0
[5,1,2,6,3,4]=>1
[5,1,2,6,4,3]=>0
[5,1,3,2,4,6]=>0
[5,1,3,2,6,4]=>0
[5,1,3,4,2,6]=>1
[5,1,3,4,6,2]=>1
[5,1,3,6,2,4]=>2
[5,1,3,6,4,2]=>1
[5,1,4,2,3,6]=>0
[5,1,4,2,6,3]=>0
[5,1,4,3,2,6]=>0
[5,1,4,3,6,2]=>0
[5,1,4,6,2,3]=>1
[5,1,4,6,3,2]=>0
[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]=>0
[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]=>1
[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]=>3
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>4
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>1
[5,2,4,3,1,6]=>2
[5,2,4,3,6,1]=>2
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>2
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>2
[5,2,6,3,1,4]=>3
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>2
[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>0
[5,3,1,4,2,6]=>1
[5,3,1,4,6,2]=>1
[5,3,1,6,2,4]=>2
[5,3,1,6,4,2]=>1
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>0
[5,3,2,4,1,6]=>2
[5,3,2,4,6,1]=>2
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>2
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>1
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>2
[5,3,4,6,2,1]=>1
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>2
[5,3,6,2,1,4]=>2
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>2
[5,3,6,4,2,1]=>1
[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]=>1
[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]=>1
[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>2
[5,4,2,6,3,1]=>1
[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]=>1
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>2
[5,4,6,1,3,2]=>1
[5,4,6,2,1,3]=>2
[5,4,6,2,3,1]=>1
[5,4,6,3,1,2]=>1
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>1
[5,6,1,3,2,4]=>1
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>1
[5,6,1,4,3,2]=>1
[5,6,2,1,3,4]=>1
[5,6,2,1,4,3]=>1
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>2
[5,6,3,1,2,4]=>1
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>1
[5,6,3,2,4,1]=>2
[5,6,3,4,1,2]=>2
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>1
[5,6,4,1,3,2]=>1
[5,6,4,2,1,3]=>1
[5,6,4,2,3,1]=>1
[5,6,4,3,1,2]=>1
[5,6,4,3,2,1]=>0
[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]=>1
[6,1,2,5,3,4]=>0
[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]=>1
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>1
[6,1,3,5,4,2]=>2
[6,1,4,2,3,5]=>0
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>2
[6,1,4,5,2,3]=>1
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>0
[6,1,5,2,4,3]=>0
[6,1,5,3,2,4]=>0
[6,1,5,3,4,2]=>1
[6,1,5,4,2,3]=>0
[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]=>1
[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]=>3
[6,2,3,4,5,1]=>6
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>5
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>2
[6,2,4,3,1,5]=>2
[6,2,4,3,5,1]=>5
[6,2,4,5,1,3]=>3
[6,2,4,5,3,1]=>4
[6,2,5,1,3,4]=>1
[6,2,5,1,4,3]=>1
[6,2,5,3,1,4]=>2
[6,2,5,3,4,1]=>4
[6,2,5,4,1,3]=>2
[6,2,5,4,3,1]=>3
[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>0
[6,3,1,4,2,5]=>1
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>1
[6,3,1,5,4,2]=>2
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>0
[6,3,2,4,1,5]=>2
[6,3,2,4,5,1]=>5
[6,3,2,5,1,4]=>2
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>1
[6,3,4,1,5,2]=>3
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>4
[6,3,4,5,1,2]=>3
[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>1
[6,3,5,1,4,2]=>2
[6,3,5,2,1,4]=>1
[6,3,5,2,4,1]=>3
[6,3,5,4,1,2]=>2
[6,3,5,4,2,1]=>2
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>1
[6,4,1,3,2,5]=>0
[6,4,1,3,5,2]=>2
[6,4,1,5,2,3]=>1
[6,4,1,5,3,2]=>1
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>1
[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>4
[6,4,2,5,1,3]=>2
[6,4,2,5,3,1]=>3
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>2
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>3
[6,4,3,5,1,2]=>2
[6,4,3,5,2,1]=>2
[6,4,5,1,2,3]=>1
[6,4,5,1,3,2]=>1
[6,4,5,2,1,3]=>1
[6,4,5,2,3,1]=>2
[6,4,5,3,1,2]=>1
[6,4,5,3,2,1]=>1
[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]=>1
[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]=>1
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>1
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>1
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>2
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>1
[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]=>1
[6,5,4,3,1,2]=>0
[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]=>0
[1,2,3,5,7,6,4]=>0
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,3,6,5,4,7]=>0
[1,2,3,6,5,7,4]=>0
[1,2,3,6,7,4,5]=>1
[1,2,3,6,7,5,4]=>0
[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]=>1
[1,2,3,7,6,4,5]=>0
[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]=>0
[1,2,4,5,7,6,3]=>0
[1,2,4,6,3,5,7]=>0
[1,2,4,6,3,7,5]=>0
[1,2,4,6,5,3,7]=>0
[1,2,4,6,5,7,3]=>0
[1,2,4,6,7,3,5]=>1
[1,2,4,6,7,5,3]=>0
[1,2,4,7,3,5,6]=>0
[1,2,4,7,3,6,5]=>0
[1,2,4,7,5,3,6]=>0
[1,2,4,7,5,6,3]=>1
[1,2,4,7,6,3,5]=>0
[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]=>0
[1,2,5,3,6,7,4]=>0
[1,2,5,3,7,4,6]=>0
[1,2,5,3,7,6,4]=>0
[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]=>0
[1,2,5,4,7,6,3]=>0
[1,2,5,6,3,4,7]=>1
[1,2,5,6,3,7,4]=>1
[1,2,5,6,4,3,7]=>0
[1,2,5,6,4,7,3]=>0
[1,2,5,6,7,3,4]=>1
[1,2,5,6,7,4,3]=>0
[1,2,5,7,3,4,6]=>1
[1,2,5,7,3,6,4]=>2
[1,2,5,7,4,3,6]=>0
[1,2,5,7,4,6,3]=>1
[1,2,5,7,6,3,4]=>1
[1,2,5,7,6,4,3]=>0
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>0
[1,2,6,3,5,4,7]=>0
[1,2,6,3,5,7,4]=>0
[1,2,6,3,7,4,5]=>1
[1,2,6,3,7,5,4]=>0
[1,2,6,4,3,5,7]=>0
[1,2,6,4,3,7,5]=>0
[1,2,6,4,5,3,7]=>1
[1,2,6,4,5,7,3]=>1
[1,2,6,4,7,3,5]=>2
[1,2,6,4,7,5,3]=>1
[1,2,6,5,3,4,7]=>0
[1,2,6,5,3,7,4]=>0
[1,2,6,5,4,3,7]=>0
[1,2,6,5,4,7,3]=>0
[1,2,6,5,7,3,4]=>1
[1,2,6,5,7,4,3]=>0
[1,2,6,7,3,4,5]=>1
[1,2,6,7,3,5,4]=>1
[1,2,6,7,4,3,5]=>1
[1,2,6,7,4,5,3]=>1
[1,2,6,7,5,3,4]=>1
[1,2,6,7,5,4,3]=>0
[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]=>1
[1,2,7,3,6,4,5]=>0
[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]=>1
[1,2,7,4,5,6,3]=>3
[1,2,7,4,6,3,5]=>1
[1,2,7,4,6,5,3]=>2
[1,2,7,5,3,4,6]=>0
[1,2,7,5,3,6,4]=>1
[1,2,7,5,4,3,6]=>0
[1,2,7,5,4,6,3]=>2
[1,2,7,5,6,3,4]=>1
[1,2,7,5,6,4,3]=>1
[1,2,7,6,3,4,5]=>0
[1,2,7,6,3,5,4]=>0
[1,2,7,6,4,3,5]=>0
[1,2,7,6,4,5,3]=>1
[1,2,7,6,5,3,4]=>0
[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]=>0
[1,3,2,5,7,6,4]=>0
[1,3,2,6,4,5,7]=>0
[1,3,2,6,4,7,5]=>0
[1,3,2,6,5,4,7]=>0
[1,3,2,6,5,7,4]=>0
[1,3,2,6,7,4,5]=>1
[1,3,2,6,7,5,4]=>0
[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]=>1
[1,3,2,7,6,4,5]=>0
[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]=>0
[1,3,4,5,7,6,2]=>0
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>0
[1,3,4,6,5,2,7]=>0
[1,3,4,6,5,7,2]=>0
[1,3,4,6,7,2,5]=>1
[1,3,4,6,7,5,2]=>0
[1,3,4,7,2,5,6]=>0
[1,3,4,7,2,6,5]=>0
[1,3,4,7,5,2,6]=>0
[1,3,4,7,5,6,2]=>1
[1,3,4,7,6,2,5]=>0
[1,3,4,7,6,5,2]=>0
[1,3,5,2,4,6,7]=>0
[1,3,5,2,4,7,6]=>0
[1,3,5,2,6,4,7]=>0
[1,3,5,2,6,7,4]=>0
[1,3,5,2,7,4,6]=>0
[1,3,5,2,7,6,4]=>0
[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]=>0
[1,3,5,4,7,6,2]=>0
[1,3,5,6,2,4,7]=>1
[1,3,5,6,2,7,4]=>1
[1,3,5,6,4,2,7]=>0
[1,3,5,6,4,7,2]=>0
[1,3,5,6,7,2,4]=>1
[1,3,5,6,7,4,2]=>0
[1,3,5,7,2,4,6]=>1
[1,3,5,7,2,6,4]=>2
[1,3,5,7,4,2,6]=>0
[1,3,5,7,4,6,2]=>1
[1,3,5,7,6,2,4]=>1
[1,3,5,7,6,4,2]=>0
[1,3,6,2,4,5,7]=>0
[1,3,6,2,4,7,5]=>0
[1,3,6,2,5,4,7]=>0
[1,3,6,2,5,7,4]=>0
[1,3,6,2,7,4,5]=>1
[1,3,6,2,7,5,4]=>0
[1,3,6,4,2,5,7]=>0
[1,3,6,4,2,7,5]=>0
[1,3,6,4,5,2,7]=>1
[1,3,6,4,5,7,2]=>1
[1,3,6,4,7,2,5]=>2
[1,3,6,4,7,5,2]=>1
[1,3,6,5,2,4,7]=>0
[1,3,6,5,2,7,4]=>0
[1,3,6,5,4,2,7]=>0
[1,3,6,5,4,7,2]=>0
[1,3,6,5,7,2,4]=>1
[1,3,6,5,7,4,2]=>0
[1,3,6,7,2,4,5]=>1
[1,3,6,7,2,5,4]=>1
[1,3,6,7,4,2,5]=>1
[1,3,6,7,4,5,2]=>1
[1,3,6,7,5,2,4]=>1
[1,3,6,7,5,4,2]=>0
[1,3,7,2,4,5,6]=>0
[1,3,7,2,4,6,5]=>0
[1,3,7,2,5,4,6]=>0
[1,3,7,2,5,6,4]=>1
[1,3,7,2,6,4,5]=>0
[1,3,7,2,6,5,4]=>0
[1,3,7,4,2,5,6]=>0
[1,3,7,4,2,6,5]=>0
[1,3,7,4,5,2,6]=>1
[1,3,7,4,5,6,2]=>3
[1,3,7,4,6,2,5]=>1
[1,3,7,4,6,5,2]=>2
[1,3,7,5,2,4,6]=>0
[1,3,7,5,2,6,4]=>1
[1,3,7,5,4,2,6]=>0
[1,3,7,5,4,6,2]=>2
[1,3,7,5,6,2,4]=>1
[1,3,7,5,6,4,2]=>1
[1,3,7,6,2,4,5]=>0
[1,3,7,6,2,5,4]=>0
[1,3,7,6,4,2,5]=>0
[1,3,7,6,4,5,2]=>1
[1,3,7,6,5,2,4]=>0
[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]=>0
[1,4,2,5,3,7,6]=>0
[1,4,2,5,6,3,7]=>0
[1,4,2,5,6,7,3]=>0
[1,4,2,5,7,3,6]=>0
[1,4,2,5,7,6,3]=>0
[1,4,2,6,3,5,7]=>0
[1,4,2,6,3,7,5]=>0
[1,4,2,6,5,3,7]=>0
[1,4,2,6,5,7,3]=>0
[1,4,2,6,7,3,5]=>1
[1,4,2,6,7,5,3]=>0
[1,4,2,7,3,5,6]=>0
[1,4,2,7,3,6,5]=>0
[1,4,2,7,5,3,6]=>0
[1,4,2,7,5,6,3]=>1
[1,4,2,7,6,3,5]=>0
[1,4,2,7,6,5,3]=>0
[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]=>0
[1,4,3,5,7,6,2]=>0
[1,4,3,6,2,5,7]=>0
[1,4,3,6,2,7,5]=>0
[1,4,3,6,5,2,7]=>0
[1,4,3,6,5,7,2]=>0
[1,4,3,6,7,2,5]=>1
[1,4,3,6,7,5,2]=>0
[1,4,3,7,2,5,6]=>0
[1,4,3,7,2,6,5]=>0
[1,4,3,7,5,2,6]=>0
[1,4,3,7,5,6,2]=>1
[1,4,3,7,6,2,5]=>0
[1,4,3,7,6,5,2]=>0
[1,4,5,2,3,6,7]=>1
[1,4,5,2,3,7,6]=>1
[1,4,5,2,6,3,7]=>1
[1,4,5,2,6,7,3]=>1
[1,4,5,2,7,3,6]=>1
[1,4,5,2,7,6,3]=>1
[1,4,5,3,2,6,7]=>0
[1,4,5,3,2,7,6]=>0
[1,4,5,3,6,2,7]=>0
[1,4,5,3,6,7,2]=>0
[1,4,5,3,7,2,6]=>0
[1,4,5,3,7,6,2]=>0
[1,4,5,6,2,3,7]=>1
[1,4,5,6,2,7,3]=>1
[1,4,5,6,3,2,7]=>0
[1,4,5,6,3,7,2]=>0
[1,4,5,6,7,2,3]=>1
[1,4,5,6,7,3,2]=>0
[1,4,5,7,2,3,6]=>1
[1,4,5,7,2,6,3]=>2
[1,4,5,7,3,2,6]=>0
[1,4,5,7,3,6,2]=>1
[1,4,5,7,6,2,3]=>1
[1,4,5,7,6,3,2]=>0
[1,4,6,2,3,5,7]=>1
[1,4,6,2,3,7,5]=>1
[1,4,6,2,5,3,7]=>2
[1,4,6,2,5,7,3]=>2
[1,4,6,2,7,3,5]=>3
[1,4,6,2,7,5,3]=>2
[1,4,6,3,2,5,7]=>0
[1,4,6,3,2,7,5]=>0
[1,4,6,3,5,2,7]=>1
[1,4,6,3,5,7,2]=>1
[1,4,6,3,7,2,5]=>2
[1,4,6,3,7,5,2]=>1
[1,4,6,5,2,3,7]=>1
[1,4,6,5,2,7,3]=>1
[1,4,6,5,3,2,7]=>0
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Description
The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions.
This statistic is the difference between St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. and St000018The number of inversions of a permutation..
A permutation is smooth if and only if this number is zero. Equivalently, this number is zero if and only if the permutation avoids the two patterns $4231$ and $3412$.
This statistic is the difference between St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. and St000018The number of inversions of a permutation..
A permutation is smooth if and only if this number is zero. Equivalently, this number is zero if and only if the permutation avoids the two patterns $4231$ and $3412$.
Code
def statistic(pi):
n = len(pi)
B = Permutations(n).bruhat_poset(facade=True)
return sum(1 for tau in B.principal_order_ideal(pi) if tau.number_of_fixed_points() == n-2) - pi.number_of_inversions()
Created
Jul 07, 2020 at 09:59 by Christian Stump
Updated
Oct 07, 2020 at 22:05 by Martin Rubey
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