Identifier
- St000216: Permutations ⟶ ℤ
Values
=>
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>1
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>2
[2,3,4,1]=>3
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>2
[3,1,4,2]=>3
[3,2,1,4]=>1
[3,2,4,1]=>2
[3,4,1,2]=>2
[3,4,2,1]=>3
[4,1,2,3]=>3
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>1
[4,3,1,2]=>3
[4,3,2,1]=>2
[1,2,3,4,5]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>1
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>2
[1,3,4,5,2]=>3
[1,3,5,2,4]=>3
[1,3,5,4,2]=>2
[1,4,2,3,5]=>2
[1,4,2,5,3]=>3
[1,4,3,2,5]=>1
[1,4,3,5,2]=>2
[1,4,5,2,3]=>2
[1,4,5,3,2]=>3
[1,5,2,3,4]=>3
[1,5,2,4,3]=>2
[1,5,3,2,4]=>2
[1,5,3,4,2]=>1
[1,5,4,2,3]=>3
[1,5,4,3,2]=>2
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>3
[2,1,5,3,4]=>3
[2,1,5,4,3]=>2
[2,3,1,4,5]=>2
[2,3,1,5,4]=>3
[2,3,4,1,5]=>3
[2,3,4,5,1]=>4
[2,3,5,1,4]=>4
[2,3,5,4,1]=>3
[2,4,1,3,5]=>3
[2,4,1,5,3]=>4
[2,4,3,1,5]=>2
[2,4,3,5,1]=>3
[2,4,5,1,3]=>3
[2,4,5,3,1]=>4
[2,5,1,3,4]=>4
[2,5,1,4,3]=>3
[2,5,3,1,4]=>3
[2,5,3,4,1]=>2
[2,5,4,1,3]=>4
[2,5,4,3,1]=>3
[3,1,2,4,5]=>2
[3,1,2,5,4]=>3
[3,1,4,2,5]=>3
[3,1,4,5,2]=>4
[3,1,5,2,4]=>4
[3,1,5,4,2]=>3
[3,2,1,4,5]=>1
[3,2,1,5,4]=>2
[3,2,4,1,5]=>2
[3,2,4,5,1]=>3
[3,2,5,1,4]=>3
[3,2,5,4,1]=>2
[3,4,1,2,5]=>2
[3,4,1,5,2]=>3
[3,4,2,1,5]=>3
[3,4,2,5,1]=>4
[3,4,5,1,2]=>4
[3,4,5,2,1]=>3
[3,5,1,2,4]=>3
[3,5,1,4,2]=>2
[3,5,2,1,4]=>4
[3,5,2,4,1]=>3
[3,5,4,1,2]=>3
[3,5,4,2,1]=>4
[4,1,2,3,5]=>3
[4,1,2,5,3]=>4
[4,1,3,2,5]=>2
[4,1,3,5,2]=>3
[4,1,5,2,3]=>3
[4,1,5,3,2]=>4
[4,2,1,3,5]=>2
[4,2,1,5,3]=>3
[4,2,3,1,5]=>1
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>3
[4,3,1,5,2]=>4
[4,3,2,1,5]=>2
[4,3,2,5,1]=>3
[4,3,5,1,2]=>3
[4,3,5,2,1]=>4
[4,5,1,2,3]=>4
[4,5,1,3,2]=>3
[4,5,2,1,3]=>3
[4,5,2,3,1]=>4
[4,5,3,1,2]=>2
[4,5,3,2,1]=>3
[5,1,2,3,4]=>4
[5,1,2,4,3]=>3
[5,1,3,2,4]=>3
[5,1,3,4,2]=>2
[5,1,4,2,3]=>4
[5,1,4,3,2]=>3
[5,2,1,3,4]=>3
[5,2,1,4,3]=>2
[5,2,3,1,4]=>2
[5,2,3,4,1]=>1
[5,2,4,1,3]=>3
[5,2,4,3,1]=>2
[5,3,1,2,4]=>4
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>2
[5,3,4,1,2]=>4
[5,3,4,2,1]=>3
[5,4,1,2,3]=>3
[5,4,1,3,2]=>4
[5,4,2,1,3]=>4
[5,4,2,3,1]=>3
[5,4,3,1,2]=>3
[5,4,3,2,1]=>2
[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]=>1
[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]=>2
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>1
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>3
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>2
[1,2,6,4,3,5]=>2
[1,2,6,4,5,3]=>1
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>2
[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]=>2
[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]=>3
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>2
[1,3,5,4,6,2]=>3
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>4
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>3
[1,3,6,4,2,5]=>3
[1,3,6,4,5,2]=>2
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>3
[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
[1,4,2,6,5,3]=>3
[1,4,3,2,5,6]=>1
[1,4,3,2,6,5]=>2
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>3
[1,4,3,6,2,5]=>3
[1,4,3,6,5,2]=>2
[1,4,5,2,3,6]=>2
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>4
[1,4,5,6,2,3]=>4
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>3
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>3
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>3
[1,5,2,6,3,4]=>3
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>2
[1,5,3,2,6,4]=>3
[1,5,3,4,2,6]=>1
[1,5,3,4,6,2]=>2
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>3
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>2
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>3
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>4
[1,5,6,2,4,3]=>3
[1,5,6,3,2,4]=>3
[1,5,6,3,4,2]=>4
[1,5,6,4,2,3]=>2
[1,5,6,4,3,2]=>3
[1,6,2,3,4,5]=>4
[1,6,2,3,5,4]=>3
[1,6,2,4,3,5]=>3
[1,6,2,4,5,3]=>2
[1,6,2,5,3,4]=>4
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>2
[1,6,3,4,2,5]=>2
[1,6,3,4,5,2]=>1
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>2
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>3
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>3
[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>2
[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]=>2
[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]=>3
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>3
[2,1,5,6,3,4]=>3
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>3
[2,1,6,4,3,5]=>3
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>4
[2,1,6,5,4,3]=>3
[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]=>3
[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]=>4
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>4
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>5
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>4
[2,3,6,4,1,5]=>4
[2,3,6,4,5,1]=>3
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>4
[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
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>3
[2,4,3,5,1,6]=>3
[2,4,3,5,6,1]=>4
[2,4,3,6,1,5]=>4
[2,4,3,6,5,1]=>3
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>4
[2,4,5,3,6,1]=>5
[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]=>3
[2,4,6,3,1,5]=>5
[2,4,6,3,5,1]=>4
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>5
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>3
[2,5,1,4,6,3]=>4
[2,5,1,6,3,4]=>4
[2,5,1,6,4,3]=>5
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>4
[2,5,3,4,1,6]=>2
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>3
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>5
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>4
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>5
[2,5,6,1,3,4]=>5
[2,5,6,1,4,3]=>4
[2,5,6,3,1,4]=>4
[2,5,6,3,4,1]=>5
[2,5,6,4,1,3]=>3
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>5
[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>4
[2,6,1,4,5,3]=>3
[2,6,1,5,3,4]=>5
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>4
[2,6,3,1,5,4]=>3
[2,6,3,4,1,5]=>3
[2,6,3,4,5,1]=>2
[2,6,3,5,1,4]=>4
[2,6,3,5,4,1]=>3
[2,6,4,1,3,5]=>5
[2,6,4,1,5,3]=>4
[2,6,4,3,1,5]=>4
[2,6,4,3,5,1]=>3
[2,6,4,5,1,3]=>5
[2,6,4,5,3,1]=>4
[2,6,5,1,3,4]=>4
[2,6,5,1,4,3]=>5
[2,6,5,3,1,4]=>5
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>4
[2,6,5,4,3,1]=>3
[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
[3,1,2,6,5,4]=>3
[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
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>5
[3,1,5,4,2,6]=>3
[3,1,5,4,6,2]=>4
[3,1,5,6,2,4]=>4
[3,1,5,6,4,2]=>5
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>4
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>3
[3,1,6,5,2,4]=>5
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>2
[3,2,1,5,4,6]=>2
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>3
[3,2,1,6,5,4]=>2
[3,2,4,1,5,6]=>2
[3,2,4,1,6,5]=>3
[3,2,4,5,1,6]=>3
[3,2,4,5,6,1]=>4
[3,2,4,6,1,5]=>4
[3,2,4,6,5,1]=>3
[3,2,5,1,4,6]=>3
[3,2,5,1,6,4]=>4
[3,2,5,4,1,6]=>2
[3,2,5,4,6,1]=>3
[3,2,5,6,1,4]=>3
[3,2,5,6,4,1]=>4
[3,2,6,1,4,5]=>4
[3,2,6,1,5,4]=>3
[3,2,6,4,1,5]=>3
[3,2,6,4,5,1]=>2
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>3
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>3
[3,4,1,5,2,6]=>3
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>4
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>4
[3,4,2,5,6,1]=>5
[3,4,2,6,1,5]=>5
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>4
[3,4,5,1,6,2]=>5
[3,4,5,2,1,6]=>3
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>4
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>5
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>4
[3,5,1,2,4,6]=>3
[3,5,1,2,6,4]=>4
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>3
[3,5,1,6,2,4]=>3
[3,5,1,6,4,2]=>4
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>5
[3,5,2,4,1,6]=>3
[3,5,2,4,6,1]=>4
[3,5,2,6,1,4]=>4
[3,5,2,6,4,1]=>5
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>4
[3,5,4,2,6,1]=>5
[3,5,4,6,1,2]=>5
[3,5,4,6,2,1]=>4
[3,5,6,1,2,4]=>4
[3,5,6,1,4,2]=>5
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>4
[3,5,6,4,1,2]=>4
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>3
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>4
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>5
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>4
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>5
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>5
[3,6,4,2,5,1]=>4
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>5
[3,6,5,1,2,4]=>5
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>4
[3,6,5,2,4,1]=>5
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>4
[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
[4,1,2,6,5,3]=>4
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>3
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>4
[4,1,3,6,5,2]=>3
[4,1,5,2,3,6]=>3
[4,1,5,2,6,3]=>4
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>5
[4,1,5,6,3,2]=>4
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>3
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>4
[4,1,6,5,2,3]=>4
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>3
[4,2,1,5,3,6]=>3
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>4
[4,2,1,6,5,3]=>3
[4,2,3,1,5,6]=>1
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>2
[4,2,3,5,6,1]=>3
[4,2,3,6,1,5]=>3
[4,2,3,6,5,1]=>2
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>3
[4,2,5,3,1,6]=>3
[4,2,5,3,6,1]=>4
[4,2,5,6,1,3]=>4
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>3
[4,2,6,1,5,3]=>2
[4,2,6,3,1,5]=>4
[4,2,6,3,5,1]=>3
[4,2,6,5,1,3]=>3
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>3
[4,3,1,2,6,5]=>4
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>5
[4,3,1,6,2,5]=>5
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>2
[4,3,2,1,6,5]=>3
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>4
[4,3,2,6,1,5]=>4
[4,3,2,6,5,1]=>3
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>4
[4,3,5,2,6,1]=>5
[4,3,5,6,1,2]=>5
[4,3,5,6,2,1]=>4
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>5
[4,5,1,2,3,6]=>4
[4,5,1,2,6,3]=>5
[4,5,1,3,2,6]=>3
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>4
[4,5,1,6,3,2]=>5
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>4
[4,5,2,3,1,6]=>4
[4,5,2,3,6,1]=>5
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>4
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>4
[4,5,3,6,1,2]=>4
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>4
[4,5,6,2,1,3]=>4
[4,5,6,2,3,1]=>5
[4,5,6,3,1,2]=>5
[4,5,6,3,2,1]=>4
[4,6,1,2,3,5]=>5
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>3
[4,6,1,5,2,3]=>5
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>3
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>4
[4,6,2,5,1,3]=>4
[4,6,2,5,3,1]=>5
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>2
[4,6,3,2,1,5]=>4
[4,6,3,2,5,1]=>3
[4,6,3,5,1,2]=>3
[4,6,3,5,2,1]=>4
[4,6,5,1,2,3]=>4
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>5
[4,6,5,2,3,1]=>4
[4,6,5,3,1,2]=>4
[4,6,5,3,2,1]=>5
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>5
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>5
[5,1,3,2,4,6]=>3
[5,1,3,2,6,4]=>4
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>3
[5,1,3,6,2,4]=>3
[5,1,3,6,4,2]=>4
[5,1,4,2,3,6]=>4
[5,1,4,2,6,3]=>5
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>4
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>5
[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]=>5
[5,1,6,4,2,3]=>3
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>3
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>2
[5,2,1,4,6,3]=>3
[5,2,1,6,3,4]=>3
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>2
[5,2,3,1,6,4]=>3
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>2
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>4
[5,2,4,3,1,6]=>2
[5,2,4,3,6,1]=>3
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>4
[5,2,6,1,4,3]=>3
[5,2,6,3,1,4]=>3
[5,2,6,3,4,1]=>4
[5,2,6,4,1,3]=>2
[5,2,6,4,3,1]=>3
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>5
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>4
[5,3,1,6,2,4]=>4
[5,3,1,6,4,2]=>5
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>2
[5,3,2,4,6,1]=>3
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>5
[5,3,4,2,1,6]=>3
[5,3,4,2,6,1]=>4
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>5
[5,3,6,1,2,4]=>5
[5,3,6,1,4,2]=>4
[5,3,6,2,1,4]=>4
[5,3,6,2,4,1]=>5
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>3
[5,4,1,2,6,3]=>4
[5,4,1,3,2,6]=>4
[5,4,1,3,6,2]=>5
[5,4,1,6,2,3]=>5
[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>4
[5,4,2,1,6,3]=>5
[5,4,2,3,1,6]=>3
[5,4,2,3,6,1]=>4
[5,4,2,6,1,3]=>4
[5,4,2,6,3,1]=>5
[5,4,3,1,2,6]=>3
[5,4,3,1,6,2]=>4
[5,4,3,2,1,6]=>2
[5,4,3,2,6,1]=>3
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>4
[5,4,6,1,3,2]=>5
[5,4,6,2,1,3]=>3
[5,4,6,2,3,1]=>4
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>5
[5,6,1,2,3,4]=>4
[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]=>4
[5,6,1,4,3,2]=>3
[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]=>5
[5,6,2,4,1,3]=>3
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>4
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>2
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>4
[5,6,4,2,3,1]=>5
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>4
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>5
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>4
[6,1,3,2,5,4]=>3
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>2
[6,1,3,5,2,4]=>4
[6,1,3,5,4,2]=>3
[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>4
[6,1,4,3,2,5]=>4
[6,1,4,3,5,2]=>3
[6,1,4,5,2,3]=>5
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>5
[6,1,5,3,2,4]=>5
[6,1,5,3,4,2]=>4
[6,1,5,4,2,3]=>4
[6,1,5,4,3,2]=>3
[6,2,1,3,4,5]=>4
[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>3
[6,2,1,4,5,3]=>2
[6,2,1,5,3,4]=>4
[6,2,1,5,4,3]=>3
[6,2,3,1,4,5]=>3
[6,2,3,1,5,4]=>2
[6,2,3,4,1,5]=>2
[6,2,3,4,5,1]=>1
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>4
[6,2,4,1,5,3]=>3
[6,2,4,3,1,5]=>3
[6,2,4,3,5,1]=>2
[6,2,4,5,1,3]=>4
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>3
[6,2,5,1,4,3]=>4
[6,2,5,3,1,4]=>4
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>3
[6,2,5,4,3,1]=>2
[6,3,1,2,4,5]=>5
[6,3,1,2,5,4]=>4
[6,3,1,4,2,5]=>4
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>5
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>4
[6,3,2,1,5,4]=>3
[6,3,2,4,1,5]=>3
[6,3,2,4,5,1]=>2
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>3
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>4
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>5
[6,3,4,5,2,1]=>4
[6,3,5,1,2,4]=>4
[6,3,5,1,4,2]=>5
[6,3,5,2,1,4]=>5
[6,3,5,2,4,1]=>4
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>3
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>5
[6,4,1,3,5,2]=>4
[6,4,1,5,2,3]=>4
[6,4,1,5,3,2]=>5
[6,4,2,1,3,5]=>5
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>4
[6,4,2,3,5,1]=>3
[6,4,2,5,1,3]=>5
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>4
[6,4,3,1,5,2]=>3
[6,4,3,2,1,5]=>3
[6,4,3,2,5,1]=>2
[6,4,3,5,1,2]=>4
[6,4,3,5,2,1]=>3
[6,4,5,1,2,3]=>5
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>4
[6,4,5,2,3,1]=>3
[6,4,5,3,1,2]=>5
[6,4,5,3,2,1]=>4
[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]=>5
[6,5,1,4,2,3]=>3
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>4
[6,5,2,1,4,3]=>5
[6,5,2,3,1,4]=>5
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>4
[6,5,2,4,3,1]=>3
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>4
[6,5,3,2,4,1]=>3
[6,5,3,4,1,2]=>3
[6,5,3,4,2,1]=>2
[6,5,4,1,2,3]=>4
[6,5,4,1,3,2]=>5
[6,5,4,2,1,3]=>5
[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>4
[6,5,4,3,2,1]=>3
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Description
The absolute length of a permutation.
The absolute length of a permutation $\sigma$ of length $n$ is the shortest $k$ such that $\sigma = t_1 \dots t_k$ for transpositions $t_i$. Also, this is equal to $n$ minus the number of cycles of $\sigma$.
The absolute length of a permutation $\sigma$ of length $n$ is the shortest $k$ such that $\sigma = t_1 \dots t_k$ for transpositions $t_i$. Also, this is equal to $n$ minus the number of cycles of $\sigma$.
References
[1] Triangle read by rows: T(n,k) = |s(n,n+1-k)|, where s(n,k) are the signed Stirling numbers of the first kind (1<=k<=n; in other words, the unsigned Stirling numbers of the first kind in reverse order). OEIS:A094638
Code
def statistic(pi):
return len(pi) - len(pi.cycle_tuples())
Created
Aug 29, 2014 at 22:28 by Martin Rubey
Updated
Jul 03, 2019 at 19:02 by Christian Stump
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