Identifier
- St000235: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>2
[2,1]=>0
[1,2,3]=>3
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>0
[3,1,2]=>3
[3,2,1]=>2
[1,2,3,4]=>4
[1,2,4,3]=>3
[1,3,2,4]=>3
[1,3,4,2]=>2
[1,4,2,3]=>4
[1,4,3,2]=>4
[2,1,3,4]=>3
[2,1,4,3]=>2
[2,3,1,4]=>2
[2,3,4,1]=>0
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>4
[3,1,4,2]=>3
[3,2,1,4]=>4
[3,2,4,1]=>2
[3,4,1,2]=>4
[3,4,2,1]=>3
[4,1,2,3]=>4
[4,1,3,2]=>4
[4,2,1,3]=>4
[4,2,3,1]=>3
[4,3,1,2]=>3
[4,3,2,1]=>2
[1,2,3,4,5]=>5
[1,2,3,5,4]=>4
[1,2,4,3,5]=>4
[1,2,4,5,3]=>3
[1,2,5,3,4]=>5
[1,2,5,4,3]=>5
[1,3,2,4,5]=>4
[1,3,2,5,4]=>3
[1,3,4,2,5]=>3
[1,3,4,5,2]=>2
[1,3,5,2,4]=>4
[1,3,5,4,2]=>4
[1,4,2,3,5]=>5
[1,4,2,5,3]=>4
[1,4,3,2,5]=>5
[1,4,3,5,2]=>4
[1,4,5,2,3]=>5
[1,4,5,3,2]=>5
[1,5,2,3,4]=>5
[1,5,2,4,3]=>5
[1,5,3,2,4]=>5
[1,5,3,4,2]=>5
[1,5,4,2,3]=>4
[1,5,4,3,2]=>4
[2,1,3,4,5]=>4
[2,1,3,5,4]=>3
[2,1,4,3,5]=>3
[2,1,4,5,3]=>2
[2,1,5,3,4]=>4
[2,1,5,4,3]=>4
[2,3,1,4,5]=>3
[2,3,1,5,4]=>2
[2,3,4,1,5]=>2
[2,3,4,5,1]=>0
[2,3,5,1,4]=>3
[2,3,5,4,1]=>2
[2,4,1,3,5]=>4
[2,4,1,5,3]=>3
[2,4,3,1,5]=>4
[2,4,3,5,1]=>2
[2,4,5,1,3]=>4
[2,4,5,3,1]=>3
[2,5,1,3,4]=>4
[2,5,1,4,3]=>4
[2,5,3,1,4]=>4
[2,5,3,4,1]=>3
[2,5,4,1,3]=>3
[2,5,4,3,1]=>2
[3,1,2,4,5]=>5
[3,1,2,5,4]=>4
[3,1,4,2,5]=>4
[3,1,4,5,2]=>3
[3,1,5,2,4]=>5
[3,1,5,4,2]=>5
[3,2,1,4,5]=>5
[3,2,1,5,4]=>4
[3,2,4,1,5]=>4
[3,2,4,5,1]=>2
[3,2,5,1,4]=>5
[3,2,5,4,1]=>4
[3,4,1,2,5]=>5
[3,4,1,5,2]=>4
[3,4,2,1,5]=>5
[3,4,2,5,1]=>3
[3,4,5,1,2]=>5
[3,4,5,2,1]=>4
[3,5,1,2,4]=>5
[3,5,1,4,2]=>5
[3,5,2,1,4]=>5
[3,5,2,4,1]=>4
[3,5,4,1,2]=>4
[3,5,4,2,1]=>3
[4,1,2,3,5]=>5
[4,1,2,5,3]=>4
[4,1,3,2,5]=>5
[4,1,3,5,2]=>4
[4,1,5,2,3]=>5
[4,1,5,3,2]=>5
[4,2,1,3,5]=>5
[4,2,1,5,3]=>4
[4,2,3,1,5]=>5
[4,2,3,5,1]=>3
[4,2,5,1,3]=>5
[4,2,5,3,1]=>4
[4,3,1,2,5]=>4
[4,3,1,5,2]=>3
[4,3,2,1,5]=>4
[4,3,2,5,1]=>2
[4,3,5,1,2]=>4
[4,3,5,2,1]=>3
[4,5,1,2,3]=>5
[4,5,1,3,2]=>5
[4,5,2,1,3]=>5
[4,5,2,3,1]=>4
[4,5,3,1,2]=>5
[4,5,3,2,1]=>4
[5,1,2,3,4]=>5
[5,1,2,4,3]=>5
[5,1,3,2,4]=>5
[5,1,3,4,2]=>5
[5,1,4,2,3]=>4
[5,1,4,3,2]=>4
[5,2,1,3,4]=>5
[5,2,1,4,3]=>5
[5,2,3,1,4]=>5
[5,2,3,4,1]=>4
[5,2,4,1,3]=>4
[5,2,4,3,1]=>3
[5,3,1,2,4]=>4
[5,3,1,4,2]=>4
[5,3,2,1,4]=>4
[5,3,2,4,1]=>3
[5,3,4,1,2]=>3
[5,3,4,2,1]=>2
[5,4,1,2,3]=>5
[5,4,1,3,2]=>5
[5,4,2,1,3]=>5
[5,4,2,3,1]=>4
[5,4,3,1,2]=>5
[5,4,3,2,1]=>4
[1,2,3,4,5,6]=>6
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>5
[1,2,3,5,6,4]=>4
[1,2,3,6,4,5]=>6
[1,2,3,6,5,4]=>6
[1,2,4,3,5,6]=>5
[1,2,4,3,6,5]=>4
[1,2,4,5,3,6]=>4
[1,2,4,5,6,3]=>3
[1,2,4,6,3,5]=>5
[1,2,4,6,5,3]=>5
[1,2,5,3,4,6]=>6
[1,2,5,3,6,4]=>5
[1,2,5,4,3,6]=>6
[1,2,5,4,6,3]=>5
[1,2,5,6,3,4]=>6
[1,2,5,6,4,3]=>6
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>6
[1,2,6,4,3,5]=>6
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>5
[1,3,2,4,5,6]=>5
[1,3,2,4,6,5]=>4
[1,3,2,5,4,6]=>4
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>5
[1,3,2,6,5,4]=>5
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>2
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>5
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>5
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>5
[1,3,6,2,4,5]=>5
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>5
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>6
[1,4,2,3,6,5]=>5
[1,4,2,5,3,6]=>5
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>6
[1,4,2,6,5,3]=>6
[1,4,3,2,5,6]=>6
[1,4,3,2,6,5]=>5
[1,4,3,5,2,6]=>5
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>6
[1,4,3,6,5,2]=>6
[1,4,5,2,3,6]=>6
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>6
[1,4,5,3,6,2]=>5
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>6
[1,4,6,2,3,5]=>6
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>5
[1,4,6,5,3,2]=>5
[1,5,2,3,4,6]=>6
[1,5,2,3,6,4]=>5
[1,5,2,4,3,6]=>6
[1,5,2,4,6,3]=>5
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>6
[1,5,3,2,4,6]=>6
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>5
[1,5,3,6,2,4]=>6
[1,5,3,6,4,2]=>6
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>5
[1,5,4,3,6,2]=>4
[1,5,4,6,2,3]=>5
[1,5,4,6,3,2]=>5
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>6
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>6
[1,5,6,4,3,2]=>6
[1,6,2,3,4,5]=>6
[1,6,2,3,5,4]=>6
[1,6,2,4,3,5]=>6
[1,6,2,4,5,3]=>6
[1,6,2,5,3,4]=>5
[1,6,2,5,4,3]=>5
[1,6,3,2,4,5]=>6
[1,6,3,2,5,4]=>6
[1,6,3,4,2,5]=>6
[1,6,3,4,5,2]=>6
[1,6,3,5,2,4]=>5
[1,6,3,5,4,2]=>5
[1,6,4,2,3,5]=>5
[1,6,4,2,5,3]=>5
[1,6,4,3,2,5]=>5
[1,6,4,3,5,2]=>5
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>6
[1,6,5,2,4,3]=>6
[1,6,5,3,2,4]=>6
[1,6,5,3,4,2]=>6
[1,6,5,4,2,3]=>6
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>5
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>5
[2,1,3,6,5,4]=>5
[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>2
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>5
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>5
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>5
[2,1,5,6,4,3]=>5
[2,1,6,3,4,5]=>5
[2,1,6,3,5,4]=>5
[2,1,6,4,3,5]=>5
[2,1,6,4,5,3]=>5
[2,1,6,5,3,4]=>4
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>4
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>2
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>4
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>2
[2,3,4,5,1,6]=>2
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>2
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>4
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>3
[2,3,6,1,4,5]=>4
[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]=>3
[2,3,6,5,4,1]=>2
[2,4,1,3,5,6]=>5
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>4
[2,4,1,5,6,3]=>3
[2,4,1,6,3,5]=>5
[2,4,1,6,5,3]=>5
[2,4,3,1,5,6]=>5
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>4
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>5
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>5
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>5
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>5
[2,4,6,1,5,3]=>5
[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]=>3
[2,5,1,3,4,6]=>5
[2,5,1,3,6,4]=>4
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>4
[2,5,1,6,3,4]=>5
[2,5,1,6,4,3]=>5
[2,5,3,1,4,6]=>5
[2,5,3,1,6,4]=>4
[2,5,3,4,1,6]=>5
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>5
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>4
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>5
[2,5,6,1,4,3]=>5
[2,5,6,3,1,4]=>5
[2,5,6,3,4,1]=>4
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>5
[2,6,1,3,5,4]=>5
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>5
[2,6,1,5,3,4]=>4
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>5
[2,6,3,4,1,5]=>5
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>4
[2,6,3,5,4,1]=>3
[2,6,4,1,3,5]=>4
[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]=>3
[2,6,4,5,3,1]=>2
[2,6,5,1,3,4]=>5
[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]=>5
[2,6,5,4,3,1]=>4
[3,1,2,4,5,6]=>6
[3,1,2,4,6,5]=>5
[3,1,2,5,4,6]=>5
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>6
[3,1,2,6,5,4]=>6
[3,1,4,2,5,6]=>5
[3,1,4,2,6,5]=>4
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>5
[3,1,5,2,4,6]=>6
[3,1,5,2,6,4]=>5
[3,1,5,4,2,6]=>6
[3,1,5,4,6,2]=>5
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>6
[3,1,6,2,4,5]=>6
[3,1,6,2,5,4]=>6
[3,1,6,4,2,5]=>6
[3,1,6,4,5,2]=>6
[3,1,6,5,2,4]=>5
[3,1,6,5,4,2]=>5
[3,2,1,4,5,6]=>6
[3,2,1,4,6,5]=>5
[3,2,1,5,4,6]=>5
[3,2,1,5,6,4]=>4
[3,2,1,6,4,5]=>6
[3,2,1,6,5,4]=>6
[3,2,4,1,5,6]=>5
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>4
[3,2,4,5,6,1]=>2
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>6
[3,2,5,1,6,4]=>5
[3,2,5,4,1,6]=>6
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>6
[3,2,5,6,4,1]=>5
[3,2,6,1,4,5]=>6
[3,2,6,1,5,4]=>6
[3,2,6,4,1,5]=>6
[3,2,6,4,5,1]=>5
[3,2,6,5,1,4]=>5
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>6
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>6
[3,4,1,6,5,2]=>6
[3,4,2,1,5,6]=>6
[3,4,2,1,6,5]=>5
[3,4,2,5,1,6]=>5
[3,4,2,5,6,1]=>3
[3,4,2,6,1,5]=>6
[3,4,2,6,5,1]=>5
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>5
[3,4,5,2,1,6]=>6
[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]=>6
[3,4,6,2,1,5]=>6
[3,4,6,2,5,1]=>5
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>4
[3,5,1,2,4,6]=>6
[3,5,1,2,6,4]=>5
[3,5,1,4,2,6]=>6
[3,5,1,4,6,2]=>5
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>6
[3,5,2,1,4,6]=>6
[3,5,2,1,6,4]=>5
[3,5,2,4,1,6]=>6
[3,5,2,4,6,1]=>4
[3,5,2,6,1,4]=>6
[3,5,2,6,4,1]=>5
[3,5,4,1,2,6]=>5
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>5
[3,5,4,2,6,1]=>3
[3,5,4,6,1,2]=>5
[3,5,4,6,2,1]=>4
[3,5,6,1,2,4]=>6
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>6
[3,5,6,2,4,1]=>5
[3,5,6,4,1,2]=>6
[3,5,6,4,2,1]=>5
[3,6,1,2,4,5]=>6
[3,6,1,2,5,4]=>6
[3,6,1,4,2,5]=>6
[3,6,1,4,5,2]=>6
[3,6,1,5,2,4]=>5
[3,6,1,5,4,2]=>5
[3,6,2,1,4,5]=>6
[3,6,2,1,5,4]=>6
[3,6,2,4,1,5]=>6
[3,6,2,4,5,1]=>5
[3,6,2,5,1,4]=>5
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>5
[3,6,4,1,5,2]=>5
[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]=>3
[3,6,5,1,2,4]=>6
[3,6,5,1,4,2]=>6
[3,6,5,2,1,4]=>6
[3,6,5,2,4,1]=>5
[3,6,5,4,1,2]=>6
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>5
[4,1,2,5,3,6]=>5
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>6
[4,1,2,6,5,3]=>6
[4,1,3,2,5,6]=>6
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>6
[4,1,3,6,5,2]=>6
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>5
[4,1,5,3,2,6]=>6
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>6
[4,1,6,2,3,5]=>6
[4,1,6,2,5,3]=>6
[4,1,6,3,2,5]=>6
[4,1,6,3,5,2]=>6
[4,1,6,5,2,3]=>5
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>6
[4,2,1,3,6,5]=>5
[4,2,1,5,3,6]=>5
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>6
[4,2,1,6,5,3]=>6
[4,2,3,1,5,6]=>6
[4,2,3,1,6,5]=>5
[4,2,3,5,1,6]=>5
[4,2,3,5,6,1]=>3
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>5
[4,2,5,1,3,6]=>6
[4,2,5,1,6,3]=>5
[4,2,5,3,1,6]=>6
[4,2,5,3,6,1]=>4
[4,2,5,6,1,3]=>6
[4,2,5,6,3,1]=>5
[4,2,6,1,3,5]=>6
[4,2,6,1,5,3]=>6
[4,2,6,3,1,5]=>6
[4,2,6,3,5,1]=>5
[4,2,6,5,1,3]=>5
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>4
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>5
[4,3,1,6,5,2]=>5
[4,3,2,1,5,6]=>5
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>4
[4,3,2,5,6,1]=>2
[4,3,2,6,1,5]=>5
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>5
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>5
[4,3,5,2,6,1]=>3
[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]=>5
[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]=>3
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>5
[4,5,1,3,2,6]=>6
[4,5,1,3,6,2]=>5
[4,5,1,6,2,3]=>6
[4,5,1,6,3,2]=>6
[4,5,2,1,3,6]=>6
[4,5,2,1,6,3]=>5
[4,5,2,3,1,6]=>6
[4,5,2,3,6,1]=>4
[4,5,2,6,1,3]=>6
[4,5,2,6,3,1]=>5
[4,5,3,1,2,6]=>6
[4,5,3,1,6,2]=>5
[4,5,3,2,1,6]=>6
[4,5,3,2,6,1]=>4
[4,5,3,6,1,2]=>6
[4,5,3,6,2,1]=>5
[4,5,6,1,2,3]=>6
[4,5,6,1,3,2]=>6
[4,5,6,2,1,3]=>6
[4,5,6,2,3,1]=>5
[4,5,6,3,1,2]=>6
[4,5,6,3,2,1]=>5
[4,6,1,2,3,5]=>6
[4,6,1,2,5,3]=>6
[4,6,1,3,2,5]=>6
[4,6,1,3,5,2]=>6
[4,6,1,5,2,3]=>5
[4,6,1,5,3,2]=>5
[4,6,2,1,3,5]=>6
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>6
[4,6,2,3,5,1]=>5
[4,6,2,5,1,3]=>5
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>6
[4,6,3,1,5,2]=>6
[4,6,3,2,1,5]=>6
[4,6,3,2,5,1]=>5
[4,6,3,5,1,2]=>5
[4,6,3,5,2,1]=>4
[4,6,5,1,2,3]=>6
[4,6,5,1,3,2]=>6
[4,6,5,2,1,3]=>6
[4,6,5,2,3,1]=>5
[4,6,5,3,1,2]=>6
[4,6,5,3,2,1]=>5
[5,1,2,3,4,6]=>6
[5,1,2,3,6,4]=>5
[5,1,2,4,3,6]=>6
[5,1,2,4,6,3]=>5
[5,1,2,6,3,4]=>6
[5,1,2,6,4,3]=>6
[5,1,3,2,4,6]=>6
[5,1,3,2,6,4]=>5
[5,1,3,4,2,6]=>6
[5,1,3,4,6,2]=>5
[5,1,3,6,2,4]=>6
[5,1,3,6,4,2]=>6
[5,1,4,2,3,6]=>5
[5,1,4,2,6,3]=>4
[5,1,4,3,2,6]=>5
[5,1,4,3,6,2]=>4
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>6
[5,1,6,2,4,3]=>6
[5,1,6,3,2,4]=>6
[5,1,6,3,4,2]=>6
[5,1,6,4,2,3]=>6
[5,1,6,4,3,2]=>6
[5,2,1,3,4,6]=>6
[5,2,1,3,6,4]=>5
[5,2,1,4,3,6]=>6
[5,2,1,4,6,3]=>5
[5,2,1,6,3,4]=>6
[5,2,1,6,4,3]=>6
[5,2,3,1,4,6]=>6
[5,2,3,1,6,4]=>5
[5,2,3,4,1,6]=>6
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>5
[5,2,4,1,3,6]=>5
[5,2,4,1,6,3]=>4
[5,2,4,3,1,6]=>5
[5,2,4,3,6,1]=>3
[5,2,4,6,1,3]=>5
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>6
[5,2,6,1,4,3]=>6
[5,2,6,3,1,4]=>6
[5,2,6,3,4,1]=>5
[5,2,6,4,1,3]=>6
[5,2,6,4,3,1]=>5
[5,3,1,2,4,6]=>5
[5,3,1,2,6,4]=>4
[5,3,1,4,2,6]=>5
[5,3,1,4,6,2]=>4
[5,3,1,6,2,4]=>5
[5,3,1,6,4,2]=>5
[5,3,2,1,4,6]=>5
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>5
[5,3,2,4,6,1]=>3
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>4
[5,3,4,2,6,1]=>2
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>5
[5,3,6,1,4,2]=>5
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>4
[5,3,6,4,1,2]=>5
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>6
[5,4,1,2,6,3]=>5
[5,4,1,3,2,6]=>6
[5,4,1,3,6,2]=>5
[5,4,1,6,2,3]=>6
[5,4,1,6,3,2]=>6
[5,4,2,1,3,6]=>6
[5,4,2,1,6,3]=>5
[5,4,2,3,1,6]=>6
[5,4,2,3,6,1]=>4
[5,4,2,6,1,3]=>6
[5,4,2,6,3,1]=>5
[5,4,3,1,2,6]=>6
[5,4,3,1,6,2]=>5
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>4
[5,4,3,6,1,2]=>6
[5,4,3,6,2,1]=>5
[5,4,6,1,2,3]=>6
[5,4,6,1,3,2]=>6
[5,4,6,2,1,3]=>6
[5,4,6,2,3,1]=>5
[5,4,6,3,1,2]=>6
[5,4,6,3,2,1]=>5
[5,6,1,2,3,4]=>6
[5,6,1,2,4,3]=>6
[5,6,1,3,2,4]=>6
[5,6,1,3,4,2]=>6
[5,6,1,4,2,3]=>6
[5,6,1,4,3,2]=>6
[5,6,2,1,3,4]=>6
[5,6,2,1,4,3]=>6
[5,6,2,3,1,4]=>6
[5,6,2,3,4,1]=>5
[5,6,2,4,1,3]=>6
[5,6,2,4,3,1]=>5
[5,6,3,1,2,4]=>6
[5,6,3,1,4,2]=>6
[5,6,3,2,1,4]=>6
[5,6,3,2,4,1]=>5
[5,6,3,4,1,2]=>6
[5,6,3,4,2,1]=>5
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>5
[5,6,4,2,1,3]=>5
[5,6,4,2,3,1]=>4
[5,6,4,3,1,2]=>5
[5,6,4,3,2,1]=>4
[6,1,2,3,4,5]=>6
[6,1,2,3,5,4]=>6
[6,1,2,4,3,5]=>6
[6,1,2,4,5,3]=>6
[6,1,2,5,3,4]=>5
[6,1,2,5,4,3]=>5
[6,1,3,2,4,5]=>6
[6,1,3,2,5,4]=>6
[6,1,3,4,2,5]=>6
[6,1,3,4,5,2]=>6
[6,1,3,5,2,4]=>5
[6,1,3,5,4,2]=>5
[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>5
[6,1,4,3,2,5]=>5
[6,1,4,3,5,2]=>5
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>6
[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>6
[6,1,5,3,4,2]=>6
[6,1,5,4,2,3]=>6
[6,1,5,4,3,2]=>6
[6,2,1,3,4,5]=>6
[6,2,1,3,5,4]=>6
[6,2,1,4,3,5]=>6
[6,2,1,4,5,3]=>6
[6,2,1,5,3,4]=>5
[6,2,1,5,4,3]=>5
[6,2,3,1,4,5]=>6
[6,2,3,1,5,4]=>6
[6,2,3,4,1,5]=>6
[6,2,3,4,5,1]=>5
[6,2,3,5,1,4]=>5
[6,2,3,5,4,1]=>4
[6,2,4,1,3,5]=>5
[6,2,4,1,5,3]=>5
[6,2,4,3,1,5]=>5
[6,2,4,3,5,1]=>4
[6,2,4,5,1,3]=>4
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>6
[6,2,5,1,4,3]=>6
[6,2,5,3,1,4]=>6
[6,2,5,3,4,1]=>5
[6,2,5,4,1,3]=>6
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>5
[6,3,1,2,5,4]=>5
[6,3,1,4,2,5]=>5
[6,3,1,4,5,2]=>5
[6,3,1,5,2,4]=>4
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>5
[6,3,2,1,5,4]=>5
[6,3,2,4,1,5]=>5
[6,3,2,4,5,1]=>4
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>3
[6,3,4,1,2,5]=>4
[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]=>3
[6,3,4,5,2,1]=>2
[6,3,5,1,2,4]=>5
[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]=>5
[6,3,5,4,2,1]=>4
[6,4,1,2,3,5]=>6
[6,4,1,2,5,3]=>6
[6,4,1,3,2,5]=>6
[6,4,1,3,5,2]=>6
[6,4,1,5,2,3]=>5
[6,4,1,5,3,2]=>5
[6,4,2,1,3,5]=>6
[6,4,2,1,5,3]=>6
[6,4,2,3,1,5]=>6
[6,4,2,3,5,1]=>5
[6,4,2,5,1,3]=>5
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>6
[6,4,3,1,5,2]=>6
[6,4,3,2,1,5]=>6
[6,4,3,2,5,1]=>5
[6,4,3,5,1,2]=>5
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>6
[6,4,5,1,3,2]=>6
[6,4,5,2,1,3]=>6
[6,4,5,2,3,1]=>5
[6,4,5,3,1,2]=>6
[6,4,5,3,2,1]=>5
[6,5,1,2,3,4]=>6
[6,5,1,2,4,3]=>6
[6,5,1,3,2,4]=>6
[6,5,1,3,4,2]=>6
[6,5,1,4,2,3]=>6
[6,5,1,4,3,2]=>6
[6,5,2,1,3,4]=>6
[6,5,2,1,4,3]=>6
[6,5,2,3,1,4]=>6
[6,5,2,3,4,1]=>5
[6,5,2,4,1,3]=>6
[6,5,2,4,3,1]=>5
[6,5,3,1,2,4]=>6
[6,5,3,1,4,2]=>6
[6,5,3,2,1,4]=>6
[6,5,3,2,4,1]=>5
[6,5,3,4,1,2]=>6
[6,5,3,4,2,1]=>5
[6,5,4,1,2,3]=>5
[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]=>5
[6,5,4,3,2,1]=>4
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Description
The number of indices that are not cyclical small weak excedances.
A cyclical small weak excedance is an index $i < n$ such that $\pi_i = i+1$, or the index $i = n$ if $\pi_n = 1$.
A cyclical small weak excedance is an index $i < n$ such that $\pi_i = i+1$, or the index $i = n$ if $\pi_n = 1$.
References
[1] Li, Y. Ménage Numbers and Ménage Permutations arXiv:1502.06068
Code
def statistic(pi):
n = len(pi)
return sum(1 for i in range(n) if pi[i] != ((i+1) % n) + 1)
Created
Feb 24, 2015 at 13:16 by Christian Stump
Updated
Sep 08, 2023 at 11:45 by Martin Rubey
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