Identifier
- St000724: Permutations ⟶ ℤ
Values
=>
[1,2]=>2
[2,1]=>2
[1,2,3]=>3
[1,3,2]=>3
[2,1,3]=>2
[2,3,1]=>3
[3,1,2]=>2
[3,2,1]=>3
[1,2,3,4]=>4
[1,2,4,3]=>4
[1,3,2,4]=>3
[1,3,4,2]=>4
[1,4,2,3]=>3
[1,4,3,2]=>4
[2,1,3,4]=>2
[2,1,4,3]=>2
[2,3,1,4]=>3
[2,3,4,1]=>4
[2,4,1,3]=>4
[2,4,3,1]=>4
[3,1,2,4]=>4
[3,1,4,2]=>4
[3,2,1,4]=>3
[3,2,4,1]=>3
[3,4,1,2]=>2
[3,4,2,1]=>4
[4,1,2,3]=>3
[4,1,3,2]=>3
[4,2,1,3]=>4
[4,2,3,1]=>3
[4,3,1,2]=>2
[4,3,2,1]=>4
[1,2,3,4,5]=>5
[1,2,3,5,4]=>5
[1,2,4,3,5]=>4
[1,2,4,5,3]=>5
[1,2,5,3,4]=>4
[1,2,5,4,3]=>5
[1,3,2,4,5]=>3
[1,3,2,5,4]=>3
[1,3,4,2,5]=>4
[1,3,4,5,2]=>5
[1,3,5,2,4]=>5
[1,3,5,4,2]=>5
[1,4,2,3,5]=>5
[1,4,2,5,3]=>5
[1,4,3,2,5]=>4
[1,4,3,5,2]=>4
[1,4,5,2,3]=>3
[1,4,5,3,2]=>5
[1,5,2,3,4]=>4
[1,5,2,4,3]=>4
[1,5,3,2,4]=>5
[1,5,3,4,2]=>4
[1,5,4,2,3]=>3
[1,5,4,3,2]=>5
[2,1,3,4,5]=>2
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>2
[2,1,5,3,4]=>2
[2,1,5,4,3]=>2
[2,3,1,4,5]=>3
[2,3,1,5,4]=>3
[2,3,4,1,5]=>4
[2,3,4,5,1]=>5
[2,3,5,1,4]=>5
[2,3,5,4,1]=>5
[2,4,1,3,5]=>4
[2,4,1,5,3]=>4
[2,4,3,1,5]=>4
[2,4,3,5,1]=>4
[2,4,5,1,3]=>5
[2,4,5,3,1]=>5
[2,5,1,3,4]=>5
[2,5,1,4,3]=>5
[2,5,3,1,4]=>5
[2,5,3,4,1]=>4
[2,5,4,1,3]=>5
[2,5,4,3,1]=>5
[3,1,2,4,5]=>5
[3,1,2,5,4]=>5
[3,1,4,2,5]=>4
[3,1,4,5,2]=>5
[3,1,5,2,4]=>4
[3,1,5,4,2]=>5
[3,2,1,4,5]=>3
[3,2,1,5,4]=>3
[3,2,4,1,5]=>3
[3,2,4,5,1]=>3
[3,2,5,1,4]=>3
[3,2,5,4,1]=>3
[3,4,1,2,5]=>5
[3,4,1,5,2]=>5
[3,4,2,1,5]=>4
[3,4,2,5,1]=>4
[3,4,5,1,2]=>2
[3,4,5,2,1]=>5
[3,5,1,2,4]=>4
[3,5,1,4,2]=>4
[3,5,2,1,4]=>5
[3,5,2,4,1]=>5
[3,5,4,1,2]=>2
[3,5,4,2,1]=>5
[4,1,2,3,5]=>5
[4,1,2,5,3]=>5
[4,1,3,2,5]=>3
[4,1,3,5,2]=>5
[4,1,5,2,3]=>3
[4,1,5,3,2]=>5
[4,2,1,3,5]=>4
[4,2,1,5,3]=>4
[4,2,3,1,5]=>3
[4,2,3,5,1]=>5
[4,2,5,1,3]=>4
[4,2,5,3,1]=>5
[4,3,1,2,5]=>5
[4,3,1,5,2]=>5
[4,3,2,1,5]=>4
[4,3,2,5,1]=>4
[4,3,5,1,2]=>2
[4,3,5,2,1]=>4
[4,5,1,2,3]=>3
[4,5,1,3,2]=>3
[4,5,2,1,3]=>5
[4,5,2,3,1]=>3
[4,5,3,1,2]=>2
[4,5,3,2,1]=>5
[5,1,2,3,4]=>4
[5,1,2,4,3]=>4
[5,1,3,2,4]=>3
[5,1,3,4,2]=>4
[5,1,4,2,3]=>3
[5,1,4,3,2]=>4
[5,2,1,3,4]=>5
[5,2,1,4,3]=>5
[5,2,3,1,4]=>3
[5,2,3,4,1]=>4
[5,2,4,1,3]=>4
[5,2,4,3,1]=>4
[5,3,1,2,4]=>4
[5,3,1,4,2]=>4
[5,3,2,1,4]=>5
[5,3,2,4,1]=>5
[5,3,4,1,2]=>2
[5,3,4,2,1]=>4
[5,4,1,2,3]=>3
[5,4,1,3,2]=>3
[5,4,2,1,3]=>5
[5,4,2,3,1]=>3
[5,4,3,1,2]=>2
[5,4,3,2,1]=>5
[1,2,3,4,5,6]=>6
[1,2,3,4,6,5]=>6
[1,2,3,5,4,6]=>5
[1,2,3,5,6,4]=>6
[1,2,3,6,4,5]=>5
[1,2,3,6,5,4]=>6
[1,2,4,3,5,6]=>4
[1,2,4,3,6,5]=>4
[1,2,4,5,3,6]=>5
[1,2,4,5,6,3]=>6
[1,2,4,6,3,5]=>6
[1,2,4,6,5,3]=>6
[1,2,5,3,4,6]=>6
[1,2,5,3,6,4]=>6
[1,2,5,4,3,6]=>5
[1,2,5,4,6,3]=>5
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>6
[1,2,6,3,4,5]=>5
[1,2,6,3,5,4]=>5
[1,2,6,4,3,5]=>6
[1,2,6,4,5,3]=>5
[1,2,6,5,3,4]=>4
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>3
[1,3,2,4,6,5]=>3
[1,3,2,5,4,6]=>3
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>4
[1,3,4,5,2,6]=>5
[1,3,4,5,6,2]=>6
[1,3,4,6,2,5]=>6
[1,3,4,6,5,2]=>6
[1,3,5,2,4,6]=>5
[1,3,5,2,6,4]=>5
[1,3,5,4,2,6]=>5
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>6
[1,3,5,6,4,2]=>6
[1,3,6,2,4,5]=>6
[1,3,6,2,5,4]=>6
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>6
[1,3,6,5,4,2]=>6
[1,4,2,3,5,6]=>6
[1,4,2,3,6,5]=>6
[1,4,2,5,3,6]=>5
[1,4,2,5,6,3]=>6
[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>6
[1,4,3,2,5,6]=>4
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>4
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>6
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>5
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>6
[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>5
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>6
[1,5,2,3,4,6]=>6
[1,5,2,3,6,4]=>6
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>6
[1,5,2,6,3,4]=>4
[1,5,2,6,4,3]=>6
[1,5,3,2,4,6]=>5
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>4
[1,5,3,4,6,2]=>6
[1,5,3,6,2,4]=>5
[1,5,3,6,4,2]=>6
[1,5,4,2,3,6]=>6
[1,5,4,2,6,3]=>6
[1,5,4,3,2,6]=>5
[1,5,4,3,6,2]=>5
[1,5,4,6,2,3]=>3
[1,5,4,6,3,2]=>5
[1,5,6,2,3,4]=>4
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>4
[1,5,6,4,2,3]=>3
[1,5,6,4,3,2]=>6
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>5
[1,6,2,4,3,5]=>4
[1,6,2,4,5,3]=>5
[1,6,2,5,3,4]=>4
[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]=>4
[1,6,3,4,5,2]=>5
[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]=>6
[1,6,4,3,5,2]=>6
[1,6,4,5,2,3]=>3
[1,6,4,5,3,2]=>5
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>6
[1,6,5,3,4,2]=>4
[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>2
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>2
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>2
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>2
[2,1,4,5,3,6]=>2
[2,1,4,5,6,3]=>2
[2,1,4,6,3,5]=>2
[2,1,4,6,5,3]=>2
[2,1,5,3,4,6]=>2
[2,1,5,3,6,4]=>2
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>2
[2,1,5,6,3,4]=>2
[2,1,5,6,4,3]=>2
[2,1,6,3,4,5]=>2
[2,1,6,3,5,4]=>2
[2,1,6,4,3,5]=>2
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>2
[2,1,6,5,4,3]=>2
[2,3,1,4,5,6]=>3
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>3
[2,3,1,6,4,5]=>3
[2,3,1,6,5,4]=>3
[2,3,4,1,5,6]=>4
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>5
[2,3,4,5,6,1]=>6
[2,3,4,6,1,5]=>6
[2,3,4,6,5,1]=>6
[2,3,5,1,4,6]=>5
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>5
[2,3,5,4,6,1]=>5
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>6
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>5
[2,3,6,5,1,4]=>6
[2,3,6,5,4,1]=>6
[2,4,1,3,5,6]=>4
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>4
[2,4,1,5,6,3]=>4
[2,4,1,6,3,5]=>4
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>4
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>4
[2,4,3,5,6,1]=>4
[2,4,3,6,1,5]=>4
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>5
[2,4,5,3,1,6]=>5
[2,4,5,3,6,1]=>5
[2,4,5,6,1,3]=>6
[2,4,5,6,3,1]=>6
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>6
[2,4,6,3,5,1]=>6
[2,4,6,5,1,3]=>6
[2,4,6,5,3,1]=>6
[2,5,1,3,4,6]=>5
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>5
[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]=>5
[2,5,3,4,1,6]=>4
[2,5,3,4,6,1]=>6
[2,5,3,6,1,4]=>5
[2,5,3,6,4,1]=>6
[2,5,4,1,3,6]=>5
[2,5,4,1,6,3]=>5
[2,5,4,3,1,6]=>5
[2,5,4,3,6,1]=>5
[2,5,4,6,1,3]=>5
[2,5,4,6,3,1]=>5
[2,5,6,1,3,4]=>6
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>4
[2,5,6,4,1,3]=>6
[2,5,6,4,3,1]=>6
[2,6,1,3,4,5]=>6
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>6
[2,6,1,4,5,3]=>6
[2,6,1,5,3,4]=>6
[2,6,1,5,4,3]=>6
[2,6,3,1,4,5]=>6
[2,6,3,1,5,4]=>6
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>5
[2,6,3,5,1,4]=>5
[2,6,3,5,4,1]=>5
[2,6,4,1,3,5]=>6
[2,6,4,1,5,3]=>6
[2,6,4,3,1,5]=>6
[2,6,4,3,5,1]=>6
[2,6,4,5,1,3]=>5
[2,6,4,5,3,1]=>5
[2,6,5,1,3,4]=>6
[2,6,5,1,4,3]=>6
[2,6,5,3,1,4]=>6
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>6
[2,6,5,4,3,1]=>6
[3,1,2,4,5,6]=>6
[3,1,2,4,6,5]=>6
[3,1,2,5,4,6]=>5
[3,1,2,5,6,4]=>6
[3,1,2,6,4,5]=>5
[3,1,2,6,5,4]=>6
[3,1,4,2,5,6]=>4
[3,1,4,2,6,5]=>4
[3,1,4,5,2,6]=>5
[3,1,4,5,6,2]=>6
[3,1,4,6,2,5]=>6
[3,1,4,6,5,2]=>6
[3,1,5,2,4,6]=>6
[3,1,5,2,6,4]=>6
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>5
[3,1,5,6,2,4]=>4
[3,1,5,6,4,2]=>6
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>5
[3,1,6,4,2,5]=>6
[3,1,6,4,5,2]=>5
[3,1,6,5,2,4]=>4
[3,1,6,5,4,2]=>6
[3,2,1,4,5,6]=>3
[3,2,1,4,6,5]=>3
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>3
[3,2,1,6,5,4]=>3
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>3
[3,2,4,5,1,6]=>3
[3,2,4,5,6,1]=>3
[3,2,4,6,1,5]=>3
[3,2,4,6,5,1]=>3
[3,2,5,1,4,6]=>3
[3,2,5,1,6,4]=>3
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>3
[3,2,5,6,1,4]=>3
[3,2,5,6,4,1]=>3
[3,2,6,1,4,5]=>3
[3,2,6,1,5,4]=>3
[3,2,6,4,1,5]=>3
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>3
[3,4,1,2,5,6]=>6
[3,4,1,2,6,5]=>6
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>6
[3,4,1,6,2,5]=>5
[3,4,1,6,5,2]=>6
[3,4,2,1,5,6]=>4
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>4
[3,4,2,5,6,1]=>4
[3,4,2,6,1,5]=>4
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>6
[3,4,5,2,1,6]=>5
[3,4,5,2,6,1]=>5
[3,4,5,6,1,2]=>2
[3,4,5,6,2,1]=>6
[3,4,6,1,2,5]=>5
[3,4,6,1,5,2]=>5
[3,4,6,2,1,5]=>6
[3,4,6,2,5,1]=>6
[3,4,6,5,1,2]=>2
[3,4,6,5,2,1]=>6
[3,5,1,2,4,6]=>6
[3,5,1,2,6,4]=>6
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>6
[3,5,1,6,2,4]=>4
[3,5,1,6,4,2]=>6
[3,5,2,1,4,6]=>5
[3,5,2,1,6,4]=>5
[3,5,2,4,1,6]=>5
[3,5,2,4,6,1]=>5
[3,5,2,6,1,4]=>5
[3,5,2,6,4,1]=>5
[3,5,4,1,2,6]=>6
[3,5,4,1,6,2]=>6
[3,5,4,2,1,6]=>5
[3,5,4,2,6,1]=>5
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>5
[3,5,6,1,2,4]=>4
[3,5,6,1,4,2]=>4
[3,5,6,2,1,4]=>6
[3,5,6,2,4,1]=>6
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>6
[3,6,1,2,4,5]=>5
[3,6,1,2,5,4]=>5
[3,6,1,4,2,5]=>4
[3,6,1,4,5,2]=>5
[3,6,1,5,2,4]=>4
[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]=>6
[3,6,2,5,1,4]=>6
[3,6,2,5,4,1]=>6
[3,6,4,1,2,5]=>5
[3,6,4,1,5,2]=>5
[3,6,4,2,1,5]=>6
[3,6,4,2,5,1]=>6
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>5
[3,6,5,1,2,4]=>4
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>6
[3,6,5,2,4,1]=>6
[3,6,5,4,1,2]=>2
[3,6,5,4,2,1]=>6
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>6
[4,1,2,5,3,6]=>5
[4,1,2,5,6,3]=>6
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>6
[4,1,3,2,5,6]=>3
[4,1,3,2,6,5]=>3
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>6
[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]=>6
[4,1,5,3,2,6]=>5
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>6
[4,1,6,2,3,5]=>5
[4,1,6,2,5,3]=>5
[4,1,6,3,2,5]=>6
[4,1,6,3,5,2]=>5
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>6
[4,2,1,3,5,6]=>4
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>4
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>3
[4,2,3,1,6,5]=>3
[4,2,3,5,1,6]=>5
[4,2,3,5,6,1]=>6
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>6
[4,2,5,1,3,6]=>4
[4,2,5,1,6,3]=>4
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>5
[4,2,5,6,1,3]=>4
[4,2,5,6,3,1]=>6
[4,2,6,1,3,5]=>4
[4,2,6,1,5,3]=>4
[4,2,6,3,1,5]=>6
[4,2,6,3,5,1]=>5
[4,2,6,5,1,3]=>4
[4,2,6,5,3,1]=>6
[4,3,1,2,5,6]=>6
[4,3,1,2,6,5]=>6
[4,3,1,5,2,6]=>5
[4,3,1,5,6,2]=>6
[4,3,1,6,2,5]=>5
[4,3,1,6,5,2]=>6
[4,3,2,1,5,6]=>4
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>4
[4,3,2,5,6,1]=>4
[4,3,2,6,1,5]=>4
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>6
[4,3,5,1,6,2]=>6
[4,3,5,2,1,6]=>4
[4,3,5,2,6,1]=>4
[4,3,5,6,1,2]=>2
[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]=>4
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>2
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>6
[4,5,1,3,2,6]=>3
[4,5,1,3,6,2]=>6
[4,5,1,6,2,3]=>3
[4,5,1,6,3,2]=>6
[4,5,2,1,3,6]=>5
[4,5,2,1,6,3]=>5
[4,5,2,3,1,6]=>3
[4,5,2,3,6,1]=>6
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>6
[4,5,3,1,2,6]=>6
[4,5,3,1,6,2]=>6
[4,5,3,2,1,6]=>5
[4,5,3,2,6,1]=>5
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>5
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>3
[4,5,6,2,1,3]=>6
[4,5,6,2,3,1]=>3
[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>6
[4,6,1,2,3,5]=>5
[4,6,1,2,5,3]=>5
[4,6,1,3,2,5]=>3
[4,6,1,3,5,2]=>5
[4,6,1,5,2,3]=>3
[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]=>3
[4,6,2,3,5,1]=>5
[4,6,2,5,1,3]=>6
[4,6,2,5,3,1]=>5
[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>5
[4,6,3,2,1,5]=>6
[4,6,3,2,5,1]=>6
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>6
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>6
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>2
[4,6,5,3,2,1]=>6
[5,1,2,3,4,6]=>6
[5,1,2,3,6,4]=>6
[5,1,2,4,3,6]=>4
[5,1,2,4,6,3]=>6
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>6
[5,1,3,2,4,6]=>3
[5,1,3,2,6,4]=>3
[5,1,3,4,2,6]=>4
[5,1,3,4,6,2]=>6
[5,1,3,6,2,4]=>6
[5,1,3,6,4,2]=>6
[5,1,4,2,3,6]=>6
[5,1,4,2,6,3]=>6
[5,1,4,3,2,6]=>4
[5,1,4,3,6,2]=>4
[5,1,4,6,2,3]=>3
[5,1,4,6,3,2]=>6
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>6
[5,1,6,3,4,2]=>4
[5,1,6,4,2,3]=>3
[5,1,6,4,3,2]=>6
[5,2,1,3,4,6]=>5
[5,2,1,3,6,4]=>5
[5,2,1,4,3,6]=>5
[5,2,1,4,6,3]=>5
[5,2,1,6,3,4]=>5
[5,2,1,6,4,3]=>5
[5,2,3,1,4,6]=>3
[5,2,3,1,6,4]=>3
[5,2,3,4,1,6]=>4
[5,2,3,4,6,1]=>6
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>6
[5,2,4,1,3,6]=>4
[5,2,4,1,6,3]=>4
[5,2,4,3,1,6]=>4
[5,2,4,3,6,1]=>4
[5,2,4,6,1,3]=>6
[5,2,4,6,3,1]=>6
[5,2,6,1,3,4]=>5
[5,2,6,1,4,3]=>5
[5,2,6,3,1,4]=>6
[5,2,6,3,4,1]=>4
[5,2,6,4,1,3]=>6
[5,2,6,4,3,1]=>6
[5,3,1,2,4,6]=>6
[5,3,1,2,6,4]=>6
[5,3,1,4,2,6]=>4
[5,3,1,4,6,2]=>6
[5,3,1,6,2,4]=>4
[5,3,1,6,4,2]=>6
[5,3,2,1,4,6]=>5
[5,3,2,1,6,4]=>5
[5,3,2,4,1,6]=>5
[5,3,2,4,6,1]=>5
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>5
[5,3,4,1,2,6]=>6
[5,3,4,1,6,2]=>6
[5,3,4,2,1,6]=>4
[5,3,4,2,6,1]=>4
[5,3,4,6,1,2]=>2
[5,3,4,6,2,1]=>6
[5,3,6,1,2,4]=>4
[5,3,6,1,4,2]=>4
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>5
[5,3,6,4,1,2]=>2
[5,3,6,4,2,1]=>6
[5,4,1,2,3,6]=>6
[5,4,1,2,6,3]=>6
[5,4,1,3,2,6]=>3
[5,4,1,3,6,2]=>6
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>6
[5,4,2,1,3,6]=>5
[5,4,2,1,6,3]=>5
[5,4,2,3,1,6]=>3
[5,4,2,3,6,1]=>6
[5,4,2,6,1,3]=>5
[5,4,2,6,3,1]=>6
[5,4,3,1,2,6]=>6
[5,4,3,1,6,2]=>6
[5,4,3,2,1,6]=>5
[5,4,3,2,6,1]=>5
[5,4,3,6,1,2]=>2
[5,4,3,6,2,1]=>5
[5,4,6,1,2,3]=>3
[5,4,6,1,3,2]=>3
[5,4,6,2,1,3]=>5
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>2
[5,4,6,3,2,1]=>5
[5,6,1,2,3,4]=>4
[5,6,1,2,4,3]=>4
[5,6,1,3,2,4]=>3
[5,6,1,3,4,2]=>4
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>6
[5,6,2,1,4,3]=>6
[5,6,2,3,1,4]=>3
[5,6,2,3,4,1]=>4
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>4
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>6
[5,6,3,2,4,1]=>6
[5,6,3,4,1,2]=>2
[5,6,3,4,2,1]=>4
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>6
[5,6,4,2,3,1]=>3
[5,6,4,3,1,2]=>2
[5,6,4,3,2,1]=>6
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>5
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>5
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>5
[6,1,3,2,4,5]=>3
[6,1,3,2,5,4]=>3
[6,1,3,4,2,5]=>4
[6,1,3,4,5,2]=>5
[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]=>4
[6,1,4,3,5,2]=>4
[6,1,4,5,2,3]=>3
[6,1,4,5,3,2]=>5
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>4
[6,1,5,3,2,4]=>5
[6,1,5,3,4,2]=>4
[6,1,5,4,2,3]=>3
[6,1,5,4,3,2]=>5
[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]=>6
[6,2,1,5,4,3]=>6
[6,2,3,1,4,5]=>3
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>5
[6,2,3,5,1,4]=>5
[6,2,3,5,4,1]=>5
[6,2,4,1,3,5]=>4
[6,2,4,1,5,3]=>4
[6,2,4,3,1,5]=>4
[6,2,4,3,5,1]=>4
[6,2,4,5,1,3]=>5
[6,2,4,5,3,1]=>5
[6,2,5,1,3,4]=>5
[6,2,5,1,4,3]=>5
[6,2,5,3,1,4]=>5
[6,2,5,3,4,1]=>4
[6,2,5,4,1,3]=>5
[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]=>4
[6,3,1,4,5,2]=>5
[6,3,1,5,2,4]=>4
[6,3,1,5,4,2]=>5
[6,3,2,1,4,5]=>6
[6,3,2,1,5,4]=>6
[6,3,2,4,1,5]=>6
[6,3,2,4,5,1]=>6
[6,3,2,5,1,4]=>6
[6,3,2,5,4,1]=>6
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>5
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>4
[6,3,4,5,1,2]=>2
[6,3,4,5,2,1]=>5
[6,3,5,1,2,4]=>4
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>5
[6,3,5,2,4,1]=>5
[6,3,5,4,1,2]=>2
[6,3,5,4,2,1]=>5
[6,4,1,2,3,5]=>5
[6,4,1,2,5,3]=>5
[6,4,1,3,2,5]=>3
[6,4,1,3,5,2]=>5
[6,4,1,5,2,3]=>3
[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]=>3
[6,4,2,3,5,1]=>5
[6,4,2,5,1,3]=>6
[6,4,2,5,3,1]=>5
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>5
[6,4,3,2,1,5]=>6
[6,4,3,2,5,1]=>6
[6,4,3,5,1,2]=>2
[6,4,3,5,2,1]=>6
[6,4,5,1,2,3]=>3
[6,4,5,1,3,2]=>3
[6,4,5,2,1,3]=>5
[6,4,5,2,3,1]=>3
[6,4,5,3,1,2]=>2
[6,4,5,3,2,1]=>5
[6,5,1,2,3,4]=>4
[6,5,1,2,4,3]=>4
[6,5,1,3,2,4]=>3
[6,5,1,3,4,2]=>4
[6,5,1,4,2,3]=>3
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>6
[6,5,2,1,4,3]=>6
[6,5,2,3,1,4]=>3
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>4
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>4
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>6
[6,5,3,2,4,1]=>6
[6,5,3,4,1,2]=>2
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>3
[6,5,4,2,1,3]=>6
[6,5,4,2,3,1]=>3
[6,5,4,3,1,2]=>2
[6,5,4,3,2,1]=>6
[1,2,3,4,5,6,7]=>7
[1,2,3,4,5,7,6]=>7
[1,2,3,4,6,5,7]=>6
[1,2,3,4,6,7,5]=>7
[1,2,3,4,7,5,6]=>6
[1,2,3,4,7,6,5]=>7
[1,2,3,5,4,6,7]=>5
[1,2,3,5,4,7,6]=>5
[1,2,3,5,6,4,7]=>6
[1,2,3,5,6,7,4]=>7
[1,2,3,5,7,4,6]=>7
[1,2,3,5,7,6,4]=>7
[1,2,3,6,4,5,7]=>7
[1,2,3,6,4,7,5]=>7
[1,2,3,6,5,4,7]=>6
[1,2,3,6,5,7,4]=>6
[1,2,3,6,7,4,5]=>5
[1,2,3,6,7,5,4]=>7
[1,2,3,7,4,5,6]=>6
[1,2,3,7,4,6,5]=>6
[1,2,3,7,5,4,6]=>7
[1,2,3,7,5,6,4]=>6
[1,2,3,7,6,4,5]=>5
[1,2,3,7,6,5,4]=>7
[1,2,4,3,5,6,7]=>4
[1,2,4,3,5,7,6]=>4
[1,2,4,3,6,5,7]=>4
[1,2,4,3,6,7,5]=>4
[1,2,4,3,7,5,6]=>4
[1,2,4,3,7,6,5]=>4
[1,2,4,5,3,6,7]=>5
[1,2,4,5,3,7,6]=>5
[1,2,4,5,6,3,7]=>6
[1,2,4,5,6,7,3]=>7
[1,2,4,5,7,3,6]=>7
[1,2,4,5,7,6,3]=>7
[1,2,4,6,3,5,7]=>6
[1,2,4,6,3,7,5]=>6
[1,2,4,6,5,3,7]=>6
[1,2,4,6,5,7,3]=>6
[1,2,4,6,7,3,5]=>7
[1,2,4,6,7,5,3]=>7
[1,2,4,7,3,5,6]=>7
[1,2,4,7,3,6,5]=>7
[1,2,4,7,5,3,6]=>7
[1,2,4,7,5,6,3]=>6
[1,2,4,7,6,3,5]=>7
[1,2,4,7,6,5,3]=>7
[1,2,5,3,4,6,7]=>7
[1,2,5,3,4,7,6]=>7
[1,2,5,3,6,4,7]=>6
[1,2,5,3,6,7,4]=>7
[1,2,5,3,7,4,6]=>6
[1,2,5,3,7,6,4]=>7
[1,2,5,4,3,6,7]=>5
[1,2,5,4,3,7,6]=>5
[1,2,5,4,6,3,7]=>5
[1,2,5,4,6,7,3]=>5
[1,2,5,4,7,3,6]=>5
[1,2,5,4,7,6,3]=>5
[1,2,5,6,3,4,7]=>7
[1,2,5,6,3,7,4]=>7
[1,2,5,6,4,3,7]=>6
[1,2,5,6,4,7,3]=>6
[1,2,5,6,7,3,4]=>4
[1,2,5,6,7,4,3]=>7
[1,2,5,7,3,4,6]=>6
[1,2,5,7,3,6,4]=>6
[1,2,5,7,4,3,6]=>7
[1,2,5,7,4,6,3]=>7
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>7
[1,2,6,3,4,5,7]=>7
[1,2,6,3,4,7,5]=>7
[1,2,6,3,5,4,7]=>5
[1,2,6,3,5,7,4]=>7
[1,2,6,3,7,4,5]=>5
[1,2,6,3,7,5,4]=>7
[1,2,6,4,3,5,7]=>6
[1,2,6,4,3,7,5]=>6
[1,2,6,4,5,3,7]=>5
[1,2,6,4,5,7,3]=>7
[1,2,6,4,7,3,5]=>6
[1,2,6,4,7,5,3]=>7
[1,2,6,5,3,4,7]=>7
[1,2,6,5,3,7,4]=>7
[1,2,6,5,4,3,7]=>6
[1,2,6,5,4,7,3]=>6
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>6
[1,2,6,7,3,4,5]=>5
[1,2,6,7,3,5,4]=>5
[1,2,6,7,4,3,5]=>7
[1,2,6,7,4,5,3]=>5
[1,2,6,7,5,3,4]=>4
[1,2,6,7,5,4,3]=>7
[1,2,7,3,4,5,6]=>6
[1,2,7,3,4,6,5]=>6
[1,2,7,3,5,4,6]=>5
[1,2,7,3,5,6,4]=>6
[1,2,7,3,6,4,5]=>5
[1,2,7,3,6,5,4]=>6
[1,2,7,4,3,5,6]=>7
[1,2,7,4,3,6,5]=>7
[1,2,7,4,5,3,6]=>5
[1,2,7,4,5,6,3]=>6
[1,2,7,4,6,3,5]=>6
[1,2,7,4,6,5,3]=>6
[1,2,7,5,3,4,6]=>6
[1,2,7,5,3,6,4]=>6
[1,2,7,5,4,3,6]=>7
[1,2,7,5,4,6,3]=>7
[1,2,7,5,6,3,4]=>4
[1,2,7,5,6,4,3]=>6
[1,2,7,6,3,4,5]=>5
[1,2,7,6,3,5,4]=>5
[1,2,7,6,4,3,5]=>7
[1,2,7,6,4,5,3]=>5
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>7
[1,3,2,4,5,6,7]=>3
[1,3,2,4,5,7,6]=>3
[1,3,2,4,6,5,7]=>3
[1,3,2,4,6,7,5]=>3
[1,3,2,4,7,5,6]=>3
[1,3,2,4,7,6,5]=>3
[1,3,2,5,4,6,7]=>3
[1,3,2,5,4,7,6]=>3
[1,3,2,5,6,4,7]=>3
[1,3,2,5,6,7,4]=>3
[1,3,2,5,7,4,6]=>3
[1,3,2,5,7,6,4]=>3
[1,3,2,6,4,5,7]=>3
[1,3,2,6,4,7,5]=>3
[1,3,2,6,5,4,7]=>3
[1,3,2,6,5,7,4]=>3
[1,3,2,6,7,4,5]=>3
[1,3,2,6,7,5,4]=>3
[1,3,2,7,4,5,6]=>3
[1,3,2,7,4,6,5]=>3
[1,3,2,7,5,4,6]=>3
[1,3,2,7,5,6,4]=>3
[1,3,2,7,6,4,5]=>3
[1,3,2,7,6,5,4]=>3
[1,3,4,2,5,6,7]=>4
[1,3,4,2,5,7,6]=>4
[1,3,4,2,6,5,7]=>4
[1,3,4,2,6,7,5]=>4
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>4
[1,3,4,5,2,6,7]=>5
[1,3,4,5,2,7,6]=>5
[1,3,4,5,6,2,7]=>6
[1,3,4,5,6,7,2]=>7
[1,3,4,5,7,2,6]=>7
[1,3,4,5,7,6,2]=>7
[1,3,4,6,2,5,7]=>6
[1,3,4,6,2,7,5]=>6
[1,3,4,6,5,2,7]=>6
[1,3,4,6,5,7,2]=>6
[1,3,4,6,7,2,5]=>7
[1,3,4,6,7,5,2]=>7
[1,3,4,7,2,5,6]=>7
[1,3,4,7,2,6,5]=>7
[1,3,4,7,5,2,6]=>7
[1,3,4,7,5,6,2]=>6
[1,3,4,7,6,2,5]=>7
[1,3,4,7,6,5,2]=>7
[1,3,5,2,4,6,7]=>5
[1,3,5,2,4,7,6]=>5
[1,3,5,2,6,4,7]=>5
[1,3,5,2,6,7,4]=>5
[1,3,5,2,7,4,6]=>5
[1,3,5,2,7,6,4]=>5
[1,3,5,4,2,6,7]=>5
[1,3,5,4,2,7,6]=>5
[1,3,5,4,6,2,7]=>5
[1,3,5,4,6,7,2]=>5
[1,3,5,4,7,2,6]=>5
[1,3,5,4,7,6,2]=>5
[1,3,5,6,2,4,7]=>6
[1,3,5,6,2,7,4]=>6
[1,3,5,6,4,2,7]=>6
[1,3,5,6,4,7,2]=>6
[1,3,5,6,7,2,4]=>7
[1,3,5,6,7,4,2]=>7
[1,3,5,7,2,4,6]=>7
[1,3,5,7,2,6,4]=>7
[1,3,5,7,4,2,6]=>7
[1,3,5,7,4,6,2]=>7
[1,3,5,7,6,2,4]=>7
[1,3,5,7,6,4,2]=>7
[1,3,6,2,4,5,7]=>6
[1,3,6,2,4,7,5]=>6
[1,3,6,2,5,4,7]=>6
[1,3,6,2,5,7,4]=>6
[1,3,6,2,7,4,5]=>6
[1,3,6,2,7,5,4]=>6
[1,3,6,4,2,5,7]=>6
[1,3,6,4,2,7,5]=>6
[1,3,6,4,5,2,7]=>5
[1,3,6,4,5,7,2]=>7
[1,3,6,4,7,2,5]=>6
[1,3,6,4,7,5,2]=>7
[1,3,6,5,2,4,7]=>6
[1,3,6,5,2,7,4]=>6
[1,3,6,5,4,2,7]=>6
[1,3,6,5,4,7,2]=>6
[1,3,6,5,7,2,4]=>6
[1,3,6,5,7,4,2]=>6
[1,3,6,7,2,4,5]=>7
[1,3,6,7,2,5,4]=>7
[1,3,6,7,4,2,5]=>7
[1,3,6,7,4,5,2]=>5
[1,3,6,7,5,2,4]=>7
[1,3,6,7,5,4,2]=>7
[1,3,7,2,4,5,6]=>7
[1,3,7,2,4,6,5]=>7
[1,3,7,2,5,4,6]=>7
[1,3,7,2,5,6,4]=>7
[1,3,7,2,6,4,5]=>7
[1,3,7,2,6,5,4]=>7
[1,3,7,4,2,5,6]=>7
[1,3,7,4,2,6,5]=>7
[1,3,7,4,5,2,6]=>5
[1,3,7,4,5,6,2]=>6
[1,3,7,4,6,2,5]=>6
[1,3,7,4,6,5,2]=>6
[1,3,7,5,2,4,6]=>7
[1,3,7,5,2,6,4]=>7
[1,3,7,5,4,2,6]=>7
[1,3,7,5,4,6,2]=>7
[1,3,7,5,6,2,4]=>6
[1,3,7,5,6,4,2]=>6
[1,3,7,6,2,4,5]=>7
[1,3,7,6,2,5,4]=>7
[1,3,7,6,4,2,5]=>7
[1,3,7,6,4,5,2]=>5
[1,3,7,6,5,2,4]=>7
[1,3,7,6,5,4,2]=>7
[1,4,2,3,5,6,7]=>7
[1,4,2,3,5,7,6]=>7
[1,4,2,3,6,5,7]=>6
[1,4,2,3,6,7,5]=>7
[1,4,2,3,7,5,6]=>6
[1,4,2,3,7,6,5]=>7
[1,4,2,5,3,6,7]=>5
[1,4,2,5,3,7,6]=>5
[1,4,2,5,6,3,7]=>6
[1,4,2,5,6,7,3]=>7
[1,4,2,5,7,3,6]=>7
[1,4,2,5,7,6,3]=>7
[1,4,2,6,3,5,7]=>7
[1,4,2,6,3,7,5]=>7
[1,4,2,6,5,3,7]=>6
[1,4,2,6,5,7,3]=>6
[1,4,2,6,7,3,5]=>5
[1,4,2,6,7,5,3]=>7
[1,4,2,7,3,5,6]=>6
[1,4,2,7,3,6,5]=>6
[1,4,2,7,5,3,6]=>7
[1,4,2,7,5,6,3]=>6
[1,4,2,7,6,3,5]=>5
[1,4,2,7,6,5,3]=>7
[1,4,3,2,5,6,7]=>4
[1,4,3,2,5,7,6]=>4
[1,4,3,2,6,5,7]=>4
[1,4,3,2,6,7,5]=>4
[1,4,3,2,7,5,6]=>4
[1,4,3,2,7,6,5]=>4
[1,4,3,5,2,6,7]=>4
[1,4,3,5,2,7,6]=>4
[1,4,3,5,6,2,7]=>4
[1,4,3,5,6,7,2]=>4
[1,4,3,5,7,2,6]=>4
[1,4,3,5,7,6,2]=>4
[1,4,3,6,2,5,7]=>4
[1,4,3,6,2,7,5]=>4
[1,4,3,6,5,2,7]=>4
[1,4,3,6,5,7,2]=>4
[1,4,3,6,7,2,5]=>4
[1,4,3,6,7,5,2]=>4
[1,4,3,7,2,5,6]=>4
[1,4,3,7,2,6,5]=>4
[1,4,3,7,5,2,6]=>4
[1,4,3,7,5,6,2]=>4
[1,4,3,7,6,2,5]=>4
[1,4,3,7,6,5,2]=>4
[1,4,5,2,3,6,7]=>7
[1,4,5,2,3,7,6]=>7
[1,4,5,2,6,3,7]=>6
[1,4,5,2,6,7,3]=>7
[1,4,5,2,7,3,6]=>6
[1,4,5,2,7,6,3]=>7
[1,4,5,3,2,6,7]=>5
[1,4,5,3,2,7,6]=>5
[1,4,5,3,6,2,7]=>5
[1,4,5,3,6,7,2]=>5
[1,4,5,3,7,2,6]=>5
[1,4,5,3,7,6,2]=>5
[1,4,5,6,2,3,7]=>7
[1,4,5,6,2,7,3]=>7
[1,4,5,6,3,2,7]=>6
[1,4,5,6,3,7,2]=>6
[1,4,5,6,7,2,3]=>3
[1,4,5,6,7,3,2]=>7
[1,4,5,7,2,3,6]=>6
[1,4,5,7,2,6,3]=>6
[1,4,5,7,3,2,6]=>7
[1,4,5,7,3,6,2]=>7
[1,4,5,7,6,2,3]=>3
[1,4,5,7,6,3,2]=>7
[1,4,6,2,3,5,7]=>7
[1,4,6,2,3,7,5]=>7
[1,4,6,2,5,3,7]=>5
[1,4,6,2,5,7,3]=>7
[1,4,6,2,7,3,5]=>5
[1,4,6,2,7,5,3]=>7
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>6
[1,4,6,3,5,2,7]=>6
[1,4,6,3,5,7,2]=>6
[1,4,6,3,7,2,5]=>6
[1,4,6,3,7,5,2]=>6
[1,4,6,5,2,3,7]=>7
[1,4,6,5,2,7,3]=>7
[1,4,6,5,3,2,7]=>6
[1,4,6,5,3,7,2]=>6
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Description
The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation.
Associate an increasing binary tree to the permutation using Mp00061to increasing tree. Then follow the path starting at the root which always selects the child with the smaller label. This statistic is the label of the leaf in the path, see [1].
Han [2] showed that this statistic is (up to a shift) equidistributed on zigzag permutations (permutations $\pi$ such that $\pi(1) < \pi(2) > \pi(3) \cdots$) with the greater neighbor of the maximum (St000060The greater neighbor of the maximum.), see also [3].
Associate an increasing binary tree to the permutation using Mp00061to increasing tree. Then follow the path starting at the root which always selects the child with the smaller label. This statistic is the label of the leaf in the path, see [1].
Han [2] showed that this statistic is (up to a shift) equidistributed on zigzag permutations (permutations $\pi$ such that $\pi(1) < \pi(2) > \pi(3) \cdots$) with the greater neighbor of the maximum (St000060The greater neighbor of the maximum.), see also [3].
References
[1] Poupard, C. Deux propriétés des arbres binaires ordonnés stricts MathSciNet:1005843
[2] https://www.emis.de/journals/SLC/wpapers/s74vortrag/han.pdf
[3] Foata, D., Han, G.-N. Finite difference calculus for alternating permutations MathSciNet:3173528 arXiv:1304.2483
[2] https://www.emis.de/journals/SLC/wpapers/s74vortrag/han.pdf
[3] Foata, D., Han, G.-N. Finite difference calculus for alternating permutations MathSciNet:3173528 arXiv:1304.2483
Code
def statistic(pi):
pi = list(pi)
if len(pi) == 1:
return pi[0]
else:
a = min(pi)
j = pi.index(a)
b = min( x for x in pi if x != a )
if pi.index(b) < j:
return statistic(pi[:j])
else:
return statistic(pi[j+1:])
Created
Mar 28, 2017 at 11:20 by Christian Stump
Updated
Mar 28, 2017 at 11:47 by Christian Stump
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