Identifier
- St000863: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>2
[2,1]=>2
[1,2,3]=>3
[1,3,2]=>2
[2,1,3]=>3
[2,3,1]=>3
[3,1,2]=>2
[3,2,1]=>3
[1,2,3,4]=>4
[1,2,4,3]=>3
[1,3,2,4]=>3
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>3
[2,1,3,4]=>4
[2,1,4,3]=>3
[2,3,1,4]=>4
[2,3,4,1]=>4
[2,4,1,3]=>3
[2,4,3,1]=>3
[3,1,2,4]=>3
[3,1,4,2]=>3
[3,2,1,4]=>4
[3,2,4,1]=>4
[3,4,1,2]=>3
[3,4,2,1]=>4
[4,1,2,3]=>3
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>3
[4,3,1,2]=>3
[4,3,2,1]=>4
[1,2,3,4,5]=>5
[1,2,3,5,4]=>4
[1,2,4,3,5]=>4
[1,2,4,5,3]=>4
[1,2,5,3,4]=>4
[1,2,5,4,3]=>3
[1,3,2,4,5]=>4
[1,3,2,5,4]=>3
[1,3,4,2,5]=>4
[1,3,4,5,2]=>4
[1,3,5,2,4]=>3
[1,3,5,4,2]=>3
[1,4,2,3,5]=>4
[1,4,2,5,3]=>3
[1,4,3,2,5]=>4
[1,4,3,5,2]=>4
[1,4,5,2,3]=>3
[1,4,5,3,2]=>4
[1,5,2,3,4]=>4
[1,5,2,4,3]=>3
[1,5,3,2,4]=>3
[1,5,3,4,2]=>3
[1,5,4,2,3]=>3
[1,5,4,3,2]=>4
[2,1,3,4,5]=>5
[2,1,3,5,4]=>4
[2,1,4,3,5]=>4
[2,1,4,5,3]=>4
[2,1,5,3,4]=>4
[2,1,5,4,3]=>3
[2,3,1,4,5]=>5
[2,3,1,5,4]=>4
[2,3,4,1,5]=>5
[2,3,4,5,1]=>5
[2,3,5,1,4]=>4
[2,3,5,4,1]=>4
[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]=>4
[2,4,5,3,1]=>4
[2,5,1,3,4]=>4
[2,5,1,4,3]=>3
[2,5,3,1,4]=>4
[2,5,3,4,1]=>4
[2,5,4,1,3]=>3
[2,5,4,3,1]=>4
[3,1,2,4,5]=>4
[3,1,2,5,4]=>3
[3,1,4,2,5]=>4
[3,1,4,5,2]=>4
[3,1,5,2,4]=>3
[3,1,5,4,2]=>3
[3,2,1,4,5]=>5
[3,2,1,5,4]=>4
[3,2,4,1,5]=>5
[3,2,4,5,1]=>5
[3,2,5,1,4]=>4
[3,2,5,4,1]=>4
[3,4,1,2,5]=>4
[3,4,1,5,2]=>4
[3,4,2,1,5]=>5
[3,4,2,5,1]=>5
[3,4,5,1,2]=>4
[3,4,5,2,1]=>5
[3,5,1,2,4]=>3
[3,5,1,4,2]=>3
[3,5,2,1,4]=>4
[3,5,2,4,1]=>4
[3,5,4,1,2]=>3
[3,5,4,2,1]=>4
[4,1,2,3,5]=>4
[4,1,2,5,3]=>3
[4,1,3,2,5]=>4
[4,1,3,5,2]=>4
[4,1,5,2,3]=>3
[4,1,5,3,2]=>4
[4,2,1,3,5]=>4
[4,2,1,5,3]=>4
[4,2,3,1,5]=>4
[4,2,3,5,1]=>4
[4,2,5,1,3]=>4
[4,2,5,3,1]=>4
[4,3,1,2,5]=>4
[4,3,1,5,2]=>4
[4,3,2,1,5]=>5
[4,3,2,5,1]=>5
[4,3,5,1,2]=>4
[4,3,5,2,1]=>5
[4,5,1,2,3]=>3
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>4
[4,5,3,1,2]=>4
[4,5,3,2,1]=>5
[5,1,2,3,4]=>4
[5,1,2,4,3]=>3
[5,1,3,2,4]=>3
[5,1,3,4,2]=>3
[5,1,4,2,3]=>3
[5,1,4,3,2]=>4
[5,2,1,3,4]=>4
[5,2,1,4,3]=>3
[5,2,3,1,4]=>4
[5,2,3,4,1]=>4
[5,2,4,1,3]=>3
[5,2,4,3,1]=>4
[5,3,1,2,4]=>3
[5,3,1,4,2]=>3
[5,3,2,1,4]=>4
[5,3,2,4,1]=>4
[5,3,4,1,2]=>3
[5,3,4,2,1]=>4
[5,4,1,2,3]=>3
[5,4,1,3,2]=>4
[5,4,2,1,3]=>4
[5,4,2,3,1]=>4
[5,4,3,1,2]=>4
[5,4,3,2,1]=>5
[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]=>5
[1,2,3,6,4,5]=>5
[1,2,3,6,5,4]=>4
[1,2,4,3,5,6]=>5
[1,2,4,3,6,5]=>4
[1,2,4,5,3,6]=>5
[1,2,4,5,6,3]=>5
[1,2,4,6,3,5]=>4
[1,2,4,6,5,3]=>4
[1,2,5,3,4,6]=>5
[1,2,5,3,6,4]=>4
[1,2,5,4,3,6]=>4
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>4
[1,2,6,3,4,5]=>5
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>4
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>4
[1,2,6,5,4,3]=>4
[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]=>4
[1,3,2,6,4,5]=>4
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>5
[1,3,4,2,6,5]=>4
[1,3,4,5,2,6]=>5
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>4
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>4
[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]=>4
[1,3,6,4,5,2]=>4
[1,3,6,5,2,4]=>3
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>5
[1,4,2,3,6,5]=>4
[1,4,2,5,3,6]=>4
[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]=>5
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>5
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>4
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>4
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>5
[1,4,5,6,2,3]=>4
[1,4,5,6,3,2]=>5
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>3
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>4
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>5
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>4
[1,5,2,6,3,4]=>4
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>4
[1,5,3,2,6,4]=>4
[1,5,3,4,2,6]=>4
[1,5,3,4,6,2]=>4
[1,5,3,6,2,4]=>4
[1,5,3,6,4,2]=>4
[1,5,4,2,3,6]=>4
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>5
[1,5,4,3,6,2]=>5
[1,5,4,6,2,3]=>4
[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]=>4
[1,5,6,3,4,2]=>4
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>5
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>4
[1,6,2,4,5,3]=>4
[1,6,2,5,3,4]=>4
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>4
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>4
[1,6,3,4,5,2]=>4
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>4
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>4
[1,6,4,5,2,3]=>3
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>4
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>5
[2,1,3,4,5,6]=>6
[2,1,3,4,6,5]=>5
[2,1,3,5,4,6]=>5
[2,1,3,5,6,4]=>5
[2,1,3,6,4,5]=>5
[2,1,3,6,5,4]=>4
[2,1,4,3,5,6]=>5
[2,1,4,3,6,5]=>4
[2,1,4,5,3,6]=>5
[2,1,4,5,6,3]=>5
[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]=>4
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>4
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>5
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>4
[2,1,6,5,3,4]=>4
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>6
[2,3,1,4,6,5]=>5
[2,3,1,5,4,6]=>5
[2,3,1,5,6,4]=>5
[2,3,1,6,4,5]=>5
[2,3,1,6,5,4]=>4
[2,3,4,1,5,6]=>6
[2,3,4,1,6,5]=>5
[2,3,4,5,1,6]=>6
[2,3,4,5,6,1]=>6
[2,3,4,6,1,5]=>5
[2,3,4,6,5,1]=>5
[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]=>5
[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]=>5
[2,3,6,4,5,1]=>5
[2,3,6,5,1,4]=>4
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>5
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>4
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>5
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>5
[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]=>5
[2,4,5,6,3,1]=>5
[2,4,6,1,3,5]=>4
[2,4,6,1,5,3]=>4
[2,4,6,3,1,5]=>4
[2,4,6,3,5,1]=>4
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>5
[2,5,1,3,6,4]=>4
[2,5,1,4,3,6]=>4
[2,5,1,4,6,3]=>4
[2,5,1,6,3,4]=>4
[2,5,1,6,4,3]=>4
[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]=>5
[2,5,3,6,1,4]=>4
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>4
[2,5,4,3,1,6]=>5
[2,5,4,3,6,1]=>5
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>5
[2,5,6,1,3,4]=>4
[2,5,6,1,4,3]=>4
[2,5,6,3,1,4]=>4
[2,5,6,3,4,1]=>4
[2,5,6,4,1,3]=>4
[2,5,6,4,3,1]=>5
[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]=>4
[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]=>4
[2,6,3,4,1,5]=>5
[2,6,3,4,5,1]=>5
[2,6,3,5,1,4]=>4
[2,6,3,5,4,1]=>4
[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]=>4
[2,6,4,5,1,3]=>4
[2,6,4,5,3,1]=>4
[2,6,5,1,3,4]=>4
[2,6,5,1,4,3]=>4
[2,6,5,3,1,4]=>4
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>4
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>5
[3,1,2,4,6,5]=>4
[3,1,2,5,4,6]=>4
[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]=>5
[3,1,4,2,6,5]=>4
[3,1,4,5,2,6]=>5
[3,1,4,5,6,2]=>5
[3,1,4,6,2,5]=>4
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>4
[3,1,5,4,2,6]=>4
[3,1,5,4,6,2]=>4
[3,1,5,6,2,4]=>4
[3,1,5,6,4,2]=>4
[3,1,6,2,4,5]=>4
[3,1,6,2,5,4]=>3
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>4
[3,1,6,5,2,4]=>3
[3,1,6,5,4,2]=>4
[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]=>5
[3,2,1,6,4,5]=>5
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>6
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>6
[3,2,4,5,6,1]=>6
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>5
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>5
[3,2,5,4,1,6]=>5
[3,2,5,4,6,1]=>5
[3,2,5,6,1,4]=>5
[3,2,5,6,4,1]=>5
[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>4
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>5
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>5
[3,4,1,2,6,5]=>4
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>5
[3,4,1,6,2,5]=>4
[3,4,1,6,5,2]=>4
[3,4,2,1,5,6]=>6
[3,4,2,1,6,5]=>5
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>6
[3,4,2,6,1,5]=>5
[3,4,2,6,5,1]=>5
[3,4,5,1,2,6]=>5
[3,4,5,1,6,2]=>5
[3,4,5,2,1,6]=>6
[3,4,5,2,6,1]=>6
[3,4,5,6,1,2]=>5
[3,4,5,6,2,1]=>6
[3,4,6,1,2,5]=>4
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>5
[3,4,6,2,5,1]=>5
[3,4,6,5,1,2]=>4
[3,4,6,5,2,1]=>5
[3,5,1,2,4,6]=>4
[3,5,1,2,6,4]=>4
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>4
[3,5,1,6,2,4]=>4
[3,5,1,6,4,2]=>4
[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]=>4
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>5
[3,5,4,2,6,1]=>5
[3,5,4,6,1,2]=>4
[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]=>5
[3,5,6,2,4,1]=>5
[3,5,6,4,1,2]=>4
[3,5,6,4,2,1]=>5
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>4
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>4
[3,6,2,1,4,5]=>5
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>5
[3,6,2,4,5,1]=>5
[3,6,2,5,1,4]=>4
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>4
[3,6,4,2,1,5]=>5
[3,6,4,2,5,1]=>5
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>5
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>4
[3,6,5,2,4,1]=>4
[3,6,5,4,1,2]=>4
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>5
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>4
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>4
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>5
[4,1,3,2,6,5]=>4
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>5
[4,1,3,6,2,5]=>4
[4,1,3,6,5,2]=>4
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>4
[4,1,5,3,2,6]=>5
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>4
[4,1,5,6,3,2]=>5
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>3
[4,1,6,3,2,5]=>4
[4,1,6,3,5,2]=>4
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>5
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>5
[4,2,1,5,6,3]=>5
[4,2,1,6,3,5]=>4
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>5
[4,2,3,1,6,5]=>4
[4,2,3,5,1,6]=>5
[4,2,3,5,6,1]=>5
[4,2,3,6,1,5]=>4
[4,2,3,6,5,1]=>4
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>5
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>5
[4,2,5,6,1,3]=>5
[4,2,5,6,3,1]=>5
[4,2,6,1,3,5]=>4
[4,2,6,1,5,3]=>4
[4,2,6,3,1,5]=>4
[4,2,6,3,5,1]=>4
[4,2,6,5,1,3]=>4
[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]=>5
[4,3,1,5,6,2]=>5
[4,3,1,6,2,5]=>4
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>5
[4,3,2,5,1,6]=>6
[4,3,2,5,6,1]=>6
[4,3,2,6,1,5]=>5
[4,3,2,6,5,1]=>5
[4,3,5,1,2,6]=>5
[4,3,5,1,6,2]=>5
[4,3,5,2,1,6]=>6
[4,3,5,2,6,1]=>6
[4,3,5,6,1,2]=>5
[4,3,5,6,2,1]=>6
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>4
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>5
[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]=>4
[4,5,1,3,2,6]=>5
[4,5,1,3,6,2]=>5
[4,5,1,6,2,3]=>4
[4,5,1,6,3,2]=>5
[4,5,2,1,3,6]=>5
[4,5,2,1,6,3]=>5
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>5
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>5
[4,5,3,1,2,6]=>5
[4,5,3,1,6,2]=>5
[4,5,3,2,1,6]=>6
[4,5,3,2,6,1]=>6
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>6
[4,5,6,1,2,3]=>4
[4,5,6,1,3,2]=>5
[4,5,6,2,1,3]=>5
[4,5,6,2,3,1]=>5
[4,5,6,3,1,2]=>5
[4,5,6,3,2,1]=>6
[4,6,1,2,3,5]=>4
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>3
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>4
[4,6,2,3,1,5]=>4
[4,6,2,3,5,1]=>4
[4,6,2,5,1,3]=>4
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>4
[4,6,3,1,5,2]=>4
[4,6,3,2,1,5]=>5
[4,6,3,2,5,1]=>5
[4,6,3,5,1,2]=>4
[4,6,3,5,2,1]=>5
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>4
[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]=>5
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>4
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>4
[5,1,3,2,4,6]=>4
[5,1,3,2,6,4]=>4
[5,1,3,4,2,6]=>4
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>4
[5,1,3,6,4,2]=>4
[5,1,4,2,3,6]=>4
[5,1,4,2,6,3]=>4
[5,1,4,3,2,6]=>5
[5,1,4,3,6,2]=>5
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>4
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>5
[5,2,1,3,4,6]=>5
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>4
[5,2,1,4,6,3]=>4
[5,2,1,6,3,4]=>4
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>5
[5,2,3,1,6,4]=>4
[5,2,3,4,1,6]=>5
[5,2,3,4,6,1]=>5
[5,2,3,6,1,4]=>4
[5,2,3,6,4,1]=>4
[5,2,4,1,3,6]=>4
[5,2,4,1,6,3]=>4
[5,2,4,3,1,6]=>5
[5,2,4,3,6,1]=>5
[5,2,4,6,1,3]=>4
[5,2,4,6,3,1]=>5
[5,2,6,1,3,4]=>4
[5,2,6,1,4,3]=>4
[5,2,6,3,1,4]=>4
[5,2,6,3,4,1]=>4
[5,2,6,4,1,3]=>4
[5,2,6,4,3,1]=>5
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>4
[5,3,1,4,2,6]=>4
[5,3,1,4,6,2]=>4
[5,3,1,6,2,4]=>4
[5,3,1,6,4,2]=>4
[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]=>4
[5,3,4,1,6,2]=>4
[5,3,4,2,1,6]=>5
[5,3,4,2,6,1]=>5
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>5
[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]=>4
[5,3,6,4,2,1]=>5
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>4
[5,4,1,3,2,6]=>5
[5,4,1,3,6,2]=>5
[5,4,1,6,2,3]=>4
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>5
[5,4,2,1,6,3]=>5
[5,4,2,3,1,6]=>5
[5,4,2,3,6,1]=>5
[5,4,2,6,1,3]=>5
[5,4,2,6,3,1]=>5
[5,4,3,1,2,6]=>5
[5,4,3,1,6,2]=>5
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>6
[5,4,3,6,1,2]=>5
[5,4,3,6,2,1]=>6
[5,4,6,1,2,3]=>4
[5,4,6,1,3,2]=>5
[5,4,6,2,1,3]=>5
[5,4,6,2,3,1]=>5
[5,4,6,3,1,2]=>5
[5,4,6,3,2,1]=>6
[5,6,1,2,3,4]=>4
[5,6,1,2,4,3]=>4
[5,6,1,3,2,4]=>4
[5,6,1,3,4,2]=>4
[5,6,1,4,2,3]=>4
[5,6,1,4,3,2]=>5
[5,6,2,1,3,4]=>4
[5,6,2,1,4,3]=>4
[5,6,2,3,1,4]=>4
[5,6,2,3,4,1]=>4
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>5
[5,6,3,1,2,4]=>4
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>5
[5,6,3,2,4,1]=>5
[5,6,3,4,1,2]=>4
[5,6,3,4,2,1]=>5
[5,6,4,1,2,3]=>4
[5,6,4,1,3,2]=>5
[5,6,4,2,1,3]=>5
[5,6,4,2,3,1]=>5
[5,6,4,3,1,2]=>5
[5,6,4,3,2,1]=>6
[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]=>4
[6,1,2,5,3,4]=>4
[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]=>4
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>4
[6,1,4,2,5,3]=>3
[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]=>4
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>4
[6,1,5,3,2,4]=>4
[6,1,5,3,4,2]=>4
[6,1,5,4,2,3]=>4
[6,1,5,4,3,2]=>5
[6,2,1,3,4,5]=>5
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>4
[6,2,1,4,5,3]=>4
[6,2,1,5,3,4]=>4
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>5
[6,2,3,1,5,4]=>4
[6,2,3,4,1,5]=>5
[6,2,3,4,5,1]=>5
[6,2,3,5,1,4]=>4
[6,2,3,5,4,1]=>4
[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]=>4
[6,2,4,5,3,1]=>4
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>4
[6,2,5,3,1,4]=>4
[6,2,5,3,4,1]=>4
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>4
[6,3,1,4,5,2]=>4
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>5
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>5
[6,3,2,4,5,1]=>5
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>4
[6,3,4,1,5,2]=>4
[6,3,4,2,1,5]=>5
[6,3,4,2,5,1]=>5
[6,3,4,5,1,2]=>4
[6,3,4,5,2,1]=>5
[6,3,5,1,2,4]=>3
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>4
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>5
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>4
[6,4,1,3,5,2]=>4
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>4
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>4
[6,4,2,3,5,1]=>4
[6,4,2,5,1,3]=>4
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>4
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>5
[6,4,3,5,1,2]=>4
[6,4,3,5,2,1]=>5
[6,4,5,1,2,3]=>3
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>4
[6,4,5,2,3,1]=>4
[6,4,5,3,1,2]=>4
[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]=>4
[6,5,1,3,4,2]=>4
[6,5,1,4,2,3]=>4
[6,5,1,4,3,2]=>5
[6,5,2,1,3,4]=>4
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>4
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>4
[6,5,2,4,3,1]=>5
[6,5,3,1,2,4]=>4
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>5
[6,5,3,2,4,1]=>5
[6,5,3,4,1,2]=>4
[6,5,3,4,2,1]=>5
[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]=>5
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>6
[1,2,3,4,5,6,7]=>7
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>6
[1,2,3,4,6,7,5]=>6
[1,2,3,4,7,5,6]=>6
[1,2,3,4,7,6,5]=>5
[1,2,3,5,4,6,7]=>6
[1,2,3,5,4,7,6]=>5
[1,2,3,5,6,4,7]=>6
[1,2,3,5,6,7,4]=>6
[1,2,3,5,7,4,6]=>5
[1,2,3,5,7,6,4]=>5
[1,2,3,6,4,5,7]=>6
[1,2,3,6,4,7,5]=>5
[1,2,3,6,5,4,7]=>5
[1,2,3,6,5,7,4]=>5
[1,2,3,6,7,4,5]=>5
[1,2,3,6,7,5,4]=>5
[1,2,3,7,4,5,6]=>6
[1,2,3,7,4,6,5]=>5
[1,2,3,7,5,4,6]=>5
[1,2,3,7,5,6,4]=>5
[1,2,3,7,6,4,5]=>5
[1,2,3,7,6,5,4]=>4
[1,2,4,3,5,6,7]=>6
[1,2,4,3,5,7,6]=>5
[1,2,4,3,6,5,7]=>5
[1,2,4,3,6,7,5]=>5
[1,2,4,3,7,5,6]=>5
[1,2,4,3,7,6,5]=>4
[1,2,4,5,3,6,7]=>6
[1,2,4,5,3,7,6]=>5
[1,2,4,5,6,3,7]=>6
[1,2,4,5,6,7,3]=>6
[1,2,4,5,7,3,6]=>5
[1,2,4,5,7,6,3]=>5
[1,2,4,6,3,5,7]=>5
[1,2,4,6,3,7,5]=>5
[1,2,4,6,5,3,7]=>5
[1,2,4,6,5,7,3]=>5
[1,2,4,6,7,3,5]=>5
[1,2,4,6,7,5,3]=>5
[1,2,4,7,3,5,6]=>5
[1,2,4,7,3,6,5]=>4
[1,2,4,7,5,3,6]=>5
[1,2,4,7,5,6,3]=>5
[1,2,4,7,6,3,5]=>4
[1,2,4,7,6,5,3]=>4
[1,2,5,3,4,6,7]=>6
[1,2,5,3,4,7,6]=>5
[1,2,5,3,6,4,7]=>5
[1,2,5,3,6,7,4]=>5
[1,2,5,3,7,4,6]=>5
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>5
[1,2,5,4,3,7,6]=>4
[1,2,5,4,6,3,7]=>5
[1,2,5,4,6,7,3]=>5
[1,2,5,4,7,3,6]=>4
[1,2,5,4,7,6,3]=>4
[1,2,5,6,3,4,7]=>5
[1,2,5,6,3,7,4]=>5
[1,2,5,6,4,3,7]=>5
[1,2,5,6,4,7,3]=>5
[1,2,5,6,7,3,4]=>5
[1,2,5,6,7,4,3]=>5
[1,2,5,7,3,4,6]=>5
[1,2,5,7,3,6,4]=>4
[1,2,5,7,4,3,6]=>4
[1,2,5,7,4,6,3]=>4
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>4
[1,2,6,3,4,5,7]=>6
[1,2,6,3,4,7,5]=>5
[1,2,6,3,5,4,7]=>5
[1,2,6,3,5,7,4]=>5
[1,2,6,3,7,4,5]=>5
[1,2,6,3,7,5,4]=>4
[1,2,6,4,3,5,7]=>5
[1,2,6,4,3,7,5]=>4
[1,2,6,4,5,3,7]=>5
[1,2,6,4,5,7,3]=>5
[1,2,6,4,7,3,5]=>4
[1,2,6,4,7,5,3]=>4
[1,2,6,5,3,4,7]=>5
[1,2,6,5,3,7,4]=>4
[1,2,6,5,4,3,7]=>5
[1,2,6,5,4,7,3]=>5
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>5
[1,2,6,7,3,4,5]=>5
[1,2,6,7,3,5,4]=>4
[1,2,6,7,4,3,5]=>4
[1,2,6,7,4,5,3]=>4
[1,2,6,7,5,3,4]=>4
[1,2,6,7,5,4,3]=>5
[1,2,7,3,4,5,6]=>6
[1,2,7,3,4,6,5]=>5
[1,2,7,3,5,4,6]=>5
[1,2,7,3,5,6,4]=>5
[1,2,7,3,6,4,5]=>5
[1,2,7,3,6,5,4]=>4
[1,2,7,4,3,5,6]=>5
[1,2,7,4,3,6,5]=>4
[1,2,7,4,5,3,6]=>5
[1,2,7,4,5,6,3]=>5
[1,2,7,4,6,3,5]=>4
[1,2,7,4,6,5,3]=>4
[1,2,7,5,3,4,6]=>5
[1,2,7,5,3,6,4]=>4
[1,2,7,5,4,3,6]=>4
[1,2,7,5,4,6,3]=>4
[1,2,7,5,6,3,4]=>4
[1,2,7,5,6,4,3]=>4
[1,2,7,6,3,4,5]=>5
[1,2,7,6,3,5,4]=>4
[1,2,7,6,4,3,5]=>4
[1,2,7,6,4,5,3]=>4
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>5
[1,3,2,4,5,6,7]=>6
[1,3,2,4,5,7,6]=>5
[1,3,2,4,6,5,7]=>5
[1,3,2,4,6,7,5]=>5
[1,3,2,4,7,5,6]=>5
[1,3,2,4,7,6,5]=>4
[1,3,2,5,4,6,7]=>5
[1,3,2,5,4,7,6]=>4
[1,3,2,5,6,4,7]=>5
[1,3,2,5,6,7,4]=>5
[1,3,2,5,7,4,6]=>4
[1,3,2,5,7,6,4]=>4
[1,3,2,6,4,5,7]=>5
[1,3,2,6,4,7,5]=>4
[1,3,2,6,5,4,7]=>4
[1,3,2,6,5,7,4]=>4
[1,3,2,6,7,4,5]=>4
[1,3,2,6,7,5,4]=>4
[1,3,2,7,4,5,6]=>5
[1,3,2,7,4,6,5]=>4
[1,3,2,7,5,4,6]=>4
[1,3,2,7,5,6,4]=>4
[1,3,2,7,6,4,5]=>4
[1,3,2,7,6,5,4]=>4
[1,3,4,2,5,6,7]=>6
[1,3,4,2,5,7,6]=>5
[1,3,4,2,6,5,7]=>5
[1,3,4,2,6,7,5]=>5
[1,3,4,2,7,5,6]=>5
[1,3,4,2,7,6,5]=>4
[1,3,4,5,2,6,7]=>6
[1,3,4,5,2,7,6]=>5
[1,3,4,5,6,2,7]=>6
[1,3,4,5,6,7,2]=>6
[1,3,4,5,7,2,6]=>5
[1,3,4,5,7,6,2]=>5
[1,3,4,6,2,5,7]=>5
[1,3,4,6,2,7,5]=>5
[1,3,4,6,5,2,7]=>5
[1,3,4,6,5,7,2]=>5
[1,3,4,6,7,2,5]=>5
[1,3,4,6,7,5,2]=>5
[1,3,4,7,2,5,6]=>5
[1,3,4,7,2,6,5]=>4
[1,3,4,7,5,2,6]=>5
[1,3,4,7,5,6,2]=>5
[1,3,4,7,6,2,5]=>4
[1,3,4,7,6,5,2]=>4
[1,3,5,2,4,6,7]=>5
[1,3,5,2,4,7,6]=>4
[1,3,5,2,6,4,7]=>5
[1,3,5,2,6,7,4]=>5
[1,3,5,2,7,4,6]=>4
[1,3,5,2,7,6,4]=>4
[1,3,5,4,2,6,7]=>5
[1,3,5,4,2,7,6]=>4
[1,3,5,4,6,2,7]=>5
[1,3,5,4,6,7,2]=>5
[1,3,5,4,7,2,6]=>4
[1,3,5,4,7,6,2]=>4
[1,3,5,6,2,4,7]=>5
[1,3,5,6,2,7,4]=>5
[1,3,5,6,4,2,7]=>5
[1,3,5,6,4,7,2]=>5
[1,3,5,6,7,2,4]=>5
[1,3,5,6,7,4,2]=>5
[1,3,5,7,2,4,6]=>4
[1,3,5,7,2,6,4]=>4
[1,3,5,7,4,2,6]=>4
[1,3,5,7,4,6,2]=>4
[1,3,5,7,6,2,4]=>4
[1,3,5,7,6,4,2]=>4
[1,3,6,2,4,5,7]=>5
[1,3,6,2,4,7,5]=>4
[1,3,6,2,5,4,7]=>4
[1,3,6,2,5,7,4]=>4
[1,3,6,2,7,4,5]=>4
[1,3,6,2,7,5,4]=>4
[1,3,6,4,2,5,7]=>5
[1,3,6,4,2,7,5]=>4
[1,3,6,4,5,2,7]=>5
[1,3,6,4,5,7,2]=>5
[1,3,6,4,7,2,5]=>4
[1,3,6,4,7,5,2]=>4
[1,3,6,5,2,4,7]=>4
[1,3,6,5,2,7,4]=>4
[1,3,6,5,4,2,7]=>5
[1,3,6,5,4,7,2]=>5
[1,3,6,5,7,2,4]=>4
[1,3,6,5,7,4,2]=>5
[1,3,6,7,2,4,5]=>4
[1,3,6,7,2,5,4]=>4
[1,3,6,7,4,2,5]=>4
[1,3,6,7,4,5,2]=>4
[1,3,6,7,5,2,4]=>4
[1,3,6,7,5,4,2]=>5
[1,3,7,2,4,5,6]=>5
[1,3,7,2,4,6,5]=>4
[1,3,7,2,5,4,6]=>4
[1,3,7,2,5,6,4]=>4
[1,3,7,2,6,4,5]=>4
[1,3,7,2,6,5,4]=>4
[1,3,7,4,2,5,6]=>5
[1,3,7,4,2,6,5]=>4
[1,3,7,4,5,2,6]=>5
[1,3,7,4,5,6,2]=>5
[1,3,7,4,6,2,5]=>4
[1,3,7,4,6,5,2]=>4
[1,3,7,5,2,4,6]=>4
[1,3,7,5,2,6,4]=>4
[1,3,7,5,4,2,6]=>4
[1,3,7,5,4,6,2]=>4
[1,3,7,5,6,2,4]=>4
[1,3,7,5,6,4,2]=>4
[1,3,7,6,2,4,5]=>4
[1,3,7,6,2,5,4]=>4
[1,3,7,6,4,2,5]=>4
[1,3,7,6,4,5,2]=>4
[1,3,7,6,5,2,4]=>4
[1,3,7,6,5,4,2]=>5
[1,4,2,3,5,6,7]=>6
[1,4,2,3,5,7,6]=>5
[1,4,2,3,6,5,7]=>5
[1,4,2,3,6,7,5]=>5
[1,4,2,3,7,5,6]=>5
[1,4,2,3,7,6,5]=>4
[1,4,2,5,3,6,7]=>5
[1,4,2,5,3,7,6]=>4
[1,4,2,5,6,3,7]=>5
[1,4,2,5,6,7,3]=>5
[1,4,2,5,7,3,6]=>4
[1,4,2,5,7,6,3]=>4
[1,4,2,6,3,5,7]=>5
[1,4,2,6,3,7,5]=>4
[1,4,2,6,5,3,7]=>4
[1,4,2,6,5,7,3]=>4
[1,4,2,6,7,3,5]=>4
[1,4,2,6,7,5,3]=>4
[1,4,2,7,3,5,6]=>5
[1,4,2,7,3,6,5]=>4
[1,4,2,7,5,3,6]=>4
[1,4,2,7,5,6,3]=>4
[1,4,2,7,6,3,5]=>4
[1,4,2,7,6,5,3]=>4
[1,4,3,2,5,6,7]=>6
[1,4,3,2,5,7,6]=>5
[1,4,3,2,6,5,7]=>5
[1,4,3,2,6,7,5]=>5
[1,4,3,2,7,5,6]=>5
[1,4,3,2,7,6,5]=>4
[1,4,3,5,2,6,7]=>6
[1,4,3,5,2,7,6]=>5
[1,4,3,5,6,2,7]=>6
[1,4,3,5,6,7,2]=>6
[1,4,3,5,7,2,6]=>5
[1,4,3,5,7,6,2]=>5
[1,4,3,6,2,5,7]=>5
[1,4,3,6,2,7,5]=>5
[1,4,3,6,5,2,7]=>5
[1,4,3,6,5,7,2]=>5
[1,4,3,6,7,2,5]=>5
[1,4,3,6,7,5,2]=>5
[1,4,3,7,2,5,6]=>5
[1,4,3,7,2,6,5]=>4
[1,4,3,7,5,2,6]=>5
[1,4,3,7,5,6,2]=>5
[1,4,3,7,6,2,5]=>4
[1,4,3,7,6,5,2]=>4
[1,4,5,2,3,6,7]=>5
[1,4,5,2,3,7,6]=>4
[1,4,5,2,6,3,7]=>5
[1,4,5,2,6,7,3]=>5
[1,4,5,2,7,3,6]=>4
[1,4,5,2,7,6,3]=>4
[1,4,5,3,2,6,7]=>6
[1,4,5,3,2,7,6]=>5
[1,4,5,3,6,2,7]=>6
[1,4,5,3,6,7,2]=>6
[1,4,5,3,7,2,6]=>5
[1,4,5,3,7,6,2]=>5
[1,4,5,6,2,3,7]=>5
[1,4,5,6,2,7,3]=>5
[1,4,5,6,3,2,7]=>6
[1,4,5,6,3,7,2]=>6
[1,4,5,6,7,2,3]=>5
[1,4,5,6,7,3,2]=>6
[1,4,5,7,2,3,6]=>4
[1,4,5,7,2,6,3]=>4
[1,4,5,7,3,2,6]=>5
[1,4,5,7,3,6,2]=>5
[1,4,5,7,6,2,3]=>4
[1,4,5,7,6,3,2]=>5
[1,4,6,2,3,5,7]=>5
[1,4,6,2,3,7,5]=>4
[1,4,6,2,5,3,7]=>4
[1,4,6,2,5,7,3]=>4
[1,4,6,2,7,3,5]=>4
[1,4,6,2,7,5,3]=>4
[1,4,6,3,2,5,7]=>5
[1,4,6,3,2,7,5]=>5
[1,4,6,3,5,2,7]=>5
[1,4,6,3,5,7,2]=>5
[1,4,6,3,7,2,5]=>5
[1,4,6,3,7,5,2]=>5
[1,4,6,5,2,3,7]=>4
[1,4,6,5,2,7,3]=>4
[1,4,6,5,3,2,7]=>5
[1,4,6,5,3,7,2]=>5
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Description
The length of the first row of the shifted shape of a permutation.
The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing.
The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled.
This statistic records the length of the first row of $P$ and $Q$.
The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing.
The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled.
This statistic records the length of the first row of $P$ and $Q$.
References
[1] Sagan, B. E. Shifted tableaux, Schur $Q$-functions, and a conjecture of R. Stanley MathSciNet:0883894
[2] Worley, D. R. A THEORY OF SHIFTED YOUNG TABLEAUX MathSciNet:2941073
[3] Haiman, M. D. On mixed insertion, symmetry, and shifted Young tableaux MathSciNet:0989194
[2] Worley, D. R. A THEORY OF SHIFTED YOUNG TABLEAUX MathSciNet:2941073
[3] Haiman, M. D. On mixed insertion, symmetry, and shifted Young tableaux MathSciNet:0989194
Code
def statistic(pi):
return GrowthDiagram.rules.ShiftedShapes()(pi).P_chain()[-1][0]
Created
Jun 25, 2017 at 20:09 by Martin Rubey
Updated
Feb 09, 2021 at 14:57 by Martin Rubey
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