Identifier
- St000638: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>1
[2,1]=>2
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>3
[2,3,1]=>2
[3,1,2]=>3
[3,2,1]=>2
[1,2,3,4]=>1
[1,2,4,3]=>2
[1,3,2,4]=>3
[1,3,4,2]=>2
[1,4,2,3]=>3
[1,4,3,2]=>2
[2,1,3,4]=>3
[2,1,4,3]=>4
[2,3,1,4]=>3
[2,3,4,1]=>2
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>3
[3,1,4,2]=>4
[3,2,1,4]=>3
[3,2,4,1]=>4
[3,4,1,2]=>3
[3,4,2,1]=>2
[4,1,2,3]=>3
[4,1,3,2]=>4
[4,2,1,3]=>3
[4,2,3,1]=>4
[4,3,1,2]=>3
[4,3,2,1]=>2
[1,2,3,4,5]=>1
[1,2,3,5,4]=>2
[1,2,4,3,5]=>3
[1,2,4,5,3]=>2
[1,2,5,3,4]=>3
[1,2,5,4,3]=>2
[1,3,2,4,5]=>3
[1,3,2,5,4]=>4
[1,3,4,2,5]=>3
[1,3,4,5,2]=>2
[1,3,5,2,4]=>3
[1,3,5,4,2]=>2
[1,4,2,3,5]=>3
[1,4,2,5,3]=>4
[1,4,3,2,5]=>3
[1,4,3,5,2]=>4
[1,4,5,2,3]=>3
[1,4,5,3,2]=>2
[1,5,2,3,4]=>3
[1,5,2,4,3]=>4
[1,5,3,2,4]=>3
[1,5,3,4,2]=>4
[1,5,4,2,3]=>3
[1,5,4,3,2]=>2
[2,1,3,4,5]=>3
[2,1,3,5,4]=>4
[2,1,4,3,5]=>5
[2,1,4,5,3]=>4
[2,1,5,3,4]=>5
[2,1,5,4,3]=>4
[2,3,1,4,5]=>3
[2,3,1,5,4]=>4
[2,3,4,1,5]=>3
[2,3,4,5,1]=>2
[2,3,5,1,4]=>3
[2,3,5,4,1]=>2
[2,4,1,3,5]=>3
[2,4,1,5,3]=>4
[2,4,3,1,5]=>3
[2,4,3,5,1]=>4
[2,4,5,1,3]=>3
[2,4,5,3,1]=>2
[2,5,1,3,4]=>3
[2,5,1,4,3]=>4
[2,5,3,1,4]=>3
[2,5,3,4,1]=>4
[2,5,4,1,3]=>3
[2,5,4,3,1]=>2
[3,1,2,4,5]=>3
[3,1,2,5,4]=>4
[3,1,4,2,5]=>5
[3,1,4,5,2]=>4
[3,1,5,2,4]=>5
[3,1,5,4,2]=>4
[3,2,1,4,5]=>3
[3,2,1,5,4]=>4
[3,2,4,1,5]=>5
[3,2,4,5,1]=>4
[3,2,5,1,4]=>5
[3,2,5,4,1]=>4
[3,4,1,2,5]=>3
[3,4,1,5,2]=>4
[3,4,2,1,5]=>3
[3,4,2,5,1]=>4
[3,4,5,1,2]=>3
[3,4,5,2,1]=>2
[3,5,1,2,4]=>3
[3,5,1,4,2]=>4
[3,5,2,1,4]=>3
[3,5,2,4,1]=>4
[3,5,4,1,2]=>3
[3,5,4,2,1]=>2
[4,1,2,3,5]=>3
[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]=>4
[4,2,1,3,5]=>3
[4,2,1,5,3]=>4
[4,2,3,1,5]=>5
[4,2,3,5,1]=>4
[4,2,5,1,3]=>5
[4,2,5,3,1]=>4
[4,3,1,2,5]=>3
[4,3,1,5,2]=>4
[4,3,2,1,5]=>3
[4,3,2,5,1]=>4
[4,3,5,1,2]=>5
[4,3,5,2,1]=>4
[4,5,1,2,3]=>3
[4,5,1,3,2]=>4
[4,5,2,1,3]=>3
[4,5,2,3,1]=>4
[4,5,3,1,2]=>3
[4,5,3,2,1]=>2
[5,1,2,3,4]=>3
[5,1,2,4,3]=>4
[5,1,3,2,4]=>5
[5,1,3,4,2]=>4
[5,1,4,2,3]=>5
[5,1,4,3,2]=>4
[5,2,1,3,4]=>3
[5,2,1,4,3]=>4
[5,2,3,1,4]=>5
[5,2,3,4,1]=>4
[5,2,4,1,3]=>5
[5,2,4,3,1]=>4
[5,3,1,2,4]=>3
[5,3,1,4,2]=>4
[5,3,2,1,4]=>3
[5,3,2,4,1]=>4
[5,3,4,1,2]=>5
[5,3,4,2,1]=>4
[5,4,1,2,3]=>3
[5,4,1,3,2]=>4
[5,4,2,1,3]=>3
[5,4,2,3,1]=>4
[5,4,3,1,2]=>3
[5,4,3,2,1]=>2
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>2
[1,2,3,5,4,6]=>3
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>3
[1,2,3,6,5,4]=>2
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>4
[1,2,4,5,3,6]=>3
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>2
[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>4
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>3
[1,2,5,6,4,3]=>2
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>2
[1,3,2,4,5,6]=>3
[1,3,2,4,6,5]=>4
[1,3,2,5,4,6]=>5
[1,3,2,5,6,4]=>4
[1,3,2,6,4,5]=>5
[1,3,2,6,5,4]=>4
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>4
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>2
[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>2
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>2
[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>4
[1,3,6,4,2,5]=>3
[1,3,6,4,5,2]=>4
[1,3,6,5,2,4]=>3
[1,3,6,5,4,2]=>2
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>4
[1,4,2,5,3,6]=>5
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>5
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>4
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>4
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>2
[1,4,6,2,3,5]=>3
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>3
[1,4,6,3,5,2]=>4
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>2
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>5
[1,5,2,4,6,3]=>4
[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>4
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>4
[1,5,3,6,2,4]=>5
[1,5,3,6,4,2]=>4
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>4
[1,5,4,6,2,3]=>5
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>3
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>3
[1,5,6,3,4,2]=>4
[1,5,6,4,2,3]=>3
[1,5,6,4,3,2]=>2
[1,6,2,3,4,5]=>3
[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>4
[1,6,2,5,3,4]=>5
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>4
[1,6,3,5,2,4]=>5
[1,6,3,5,4,2]=>4
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>4
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>4
[1,6,4,5,2,3]=>5
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>4
[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>2
[2,1,3,4,5,6]=>3
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>5
[2,1,3,5,6,4]=>4
[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]=>6
[2,1,4,5,3,6]=>5
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>5
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>5
[2,1,5,3,6,4]=>6
[2,1,5,4,3,6]=>5
[2,1,5,4,6,3]=>6
[2,1,5,6,3,4]=>5
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>5
[2,1,6,3,5,4]=>6
[2,1,6,4,3,5]=>5
[2,1,6,4,5,3]=>6
[2,1,6,5,3,4]=>5
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>3
[2,3,1,4,6,5]=>4
[2,3,1,5,4,6]=>5
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>5
[2,3,1,6,5,4]=>4
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>3
[2,3,4,5,6,1]=>2
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>2
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>4
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>4
[2,3,5,6,1,4]=>3
[2,3,5,6,4,1]=>2
[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>4
[2,3,6,4,1,5]=>3
[2,3,6,4,5,1]=>4
[2,3,6,5,1,4]=>3
[2,3,6,5,4,1]=>2
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>4
[2,4,1,6,3,5]=>5
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>4
[2,4,3,6,1,5]=>5
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>4
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>2
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>4
[2,4,6,3,1,5]=>3
[2,4,6,3,5,1]=>4
[2,4,6,5,1,3]=>3
[2,4,6,5,3,1]=>2
[2,5,1,3,4,6]=>3
[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]=>4
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>4
[2,5,3,4,1,6]=>5
[2,5,3,4,6,1]=>4
[2,5,3,6,1,4]=>5
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>3
[2,5,4,1,6,3]=>4
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>4
[2,5,4,6,1,3]=>5
[2,5,4,6,3,1]=>4
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>4
[2,5,6,3,1,4]=>3
[2,5,6,3,4,1]=>4
[2,5,6,4,1,3]=>3
[2,5,6,4,3,1]=>2
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>4
[2,6,1,5,3,4]=>5
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>3
[2,6,3,1,5,4]=>4
[2,6,3,4,1,5]=>5
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>5
[2,6,3,5,4,1]=>4
[2,6,4,1,3,5]=>3
[2,6,4,1,5,3]=>4
[2,6,4,3,1,5]=>3
[2,6,4,3,5,1]=>4
[2,6,4,5,1,3]=>5
[2,6,4,5,3,1]=>4
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>4
[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>2
[3,1,2,4,5,6]=>3
[3,1,2,4,6,5]=>4
[3,1,2,5,4,6]=>5
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>5
[3,1,2,6,5,4]=>4
[3,1,4,2,5,6]=>5
[3,1,4,2,6,5]=>6
[3,1,4,5,2,6]=>5
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>5
[3,1,5,2,6,4]=>6
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>6
[3,1,5,6,2,4]=>5
[3,1,5,6,4,2]=>4
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>6
[3,1,6,4,2,5]=>5
[3,1,6,4,5,2]=>6
[3,1,6,5,2,4]=>5
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>3
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>5
[3,2,1,5,6,4]=>4
[3,2,1,6,4,5]=>5
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>5
[3,2,4,1,6,5]=>6
[3,2,4,5,1,6]=>5
[3,2,4,5,6,1]=>4
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>6
[3,2,5,4,1,6]=>5
[3,2,5,4,6,1]=>6
[3,2,5,6,1,4]=>5
[3,2,5,6,4,1]=>4
[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>6
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>6
[3,2,6,5,1,4]=>5
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>3
[3,4,1,2,6,5]=>4
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>5
[3,4,1,6,5,2]=>4
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>5
[3,4,2,5,6,1]=>4
[3,4,2,6,1,5]=>5
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>3
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>3
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>3
[3,4,5,6,2,1]=>2
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>4
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>2
[3,5,1,2,4,6]=>3
[3,5,1,2,6,4]=>4
[3,5,1,4,2,6]=>5
[3,5,1,4,6,2]=>4
[3,5,1,6,2,4]=>5
[3,5,1,6,4,2]=>4
[3,5,2,1,4,6]=>3
[3,5,2,1,6,4]=>4
[3,5,2,4,1,6]=>5
[3,5,2,4,6,1]=>4
[3,5,2,6,1,4]=>5
[3,5,2,6,4,1]=>4
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>4
[3,5,4,6,1,2]=>5
[3,5,4,6,2,1]=>4
[3,5,6,1,2,4]=>3
[3,5,6,1,4,2]=>4
[3,5,6,2,1,4]=>3
[3,5,6,2,4,1]=>4
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>2
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>4
[3,6,1,4,2,5]=>5
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>5
[3,6,1,5,4,2]=>4
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>5
[3,6,2,4,5,1]=>4
[3,6,2,5,1,4]=>5
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>4
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>4
[3,6,4,5,1,2]=>5
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>4
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>2
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>5
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>4
[4,1,3,2,5,6]=>5
[4,1,3,2,6,5]=>6
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>5
[4,1,3,6,5,2]=>4
[4,1,5,2,3,6]=>5
[4,1,5,2,6,3]=>6
[4,1,5,3,2,6]=>5
[4,1,5,3,6,2]=>6
[4,1,5,6,2,3]=>5
[4,1,5,6,3,2]=>4
[4,1,6,2,3,5]=>5
[4,1,6,2,5,3]=>6
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>6
[4,1,6,5,2,3]=>5
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>5
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>5
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>5
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>5
[4,2,3,5,6,1]=>4
[4,2,3,6,1,5]=>5
[4,2,3,6,5,1]=>4
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>6
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>6
[4,2,5,6,1,3]=>5
[4,2,5,6,3,1]=>4
[4,2,6,1,3,5]=>5
[4,2,6,1,5,3]=>6
[4,2,6,3,1,5]=>5
[4,2,6,3,5,1]=>6
[4,2,6,5,1,3]=>5
[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]=>5
[4,3,1,5,6,2]=>4
[4,3,1,6,2,5]=>5
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>3
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>5
[4,3,2,5,6,1]=>4
[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]=>6
[4,3,5,2,1,6]=>5
[4,3,5,2,6,1]=>6
[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]=>6
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>6
[4,3,6,5,1,2]=>5
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>4
[4,5,1,3,2,6]=>5
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>5
[4,5,1,6,3,2]=>4
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>4
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>4
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>4
[4,5,3,1,2,6]=>3
[4,5,3,1,6,2]=>4
[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>4
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>4
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>4
[4,5,6,2,1,3]=>3
[4,5,6,2,3,1]=>4
[4,5,6,3,1,2]=>3
[4,5,6,3,2,1]=>2
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>5
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>5
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>3
[4,6,2,1,5,3]=>4
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>4
[4,6,2,5,1,3]=>5
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>4
[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>5
[4,6,3,5,2,1]=>4
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>3
[4,6,5,2,3,1]=>4
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>3
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>5
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>5
[5,1,2,6,4,3]=>4
[5,1,3,2,4,6]=>5
[5,1,3,2,6,4]=>6
[5,1,3,4,2,6]=>5
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>5
[5,1,3,6,4,2]=>4
[5,1,4,2,3,6]=>5
[5,1,4,2,6,3]=>6
[5,1,4,3,2,6]=>5
[5,1,4,3,6,2]=>6
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>4
[5,1,6,2,3,4]=>5
[5,1,6,2,4,3]=>6
[5,1,6,3,2,4]=>5
[5,1,6,3,4,2]=>6
[5,1,6,4,2,3]=>5
[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]=>5
[5,2,1,4,6,3]=>4
[5,2,1,6,3,4]=>5
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>5
[5,2,3,1,6,4]=>6
[5,2,3,4,1,6]=>5
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>5
[5,2,3,6,4,1]=>4
[5,2,4,1,3,6]=>5
[5,2,4,1,6,3]=>6
[5,2,4,3,1,6]=>5
[5,2,4,3,6,1]=>6
[5,2,4,6,1,3]=>5
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>5
[5,2,6,1,4,3]=>6
[5,2,6,3,1,4]=>5
[5,2,6,3,4,1]=>6
[5,2,6,4,1,3]=>5
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>3
[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]=>4
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>5
[5,3,2,4,6,1]=>4
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>5
[5,3,4,1,6,2]=>6
[5,3,4,2,1,6]=>5
[5,3,4,2,6,1]=>6
[5,3,4,6,1,2]=>5
[5,3,4,6,2,1]=>4
[5,3,6,1,2,4]=>5
[5,3,6,1,4,2]=>6
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>6
[5,3,6,4,1,2]=>5
[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]=>5
[5,4,1,3,6,2]=>4
[5,4,1,6,2,3]=>5
[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>4
[5,4,2,3,1,6]=>5
[5,4,2,3,6,1]=>4
[5,4,2,6,1,3]=>5
[5,4,2,6,3,1]=>4
[5,4,3,1,2,6]=>3
[5,4,3,1,6,2]=>4
[5,4,3,2,1,6]=>3
[5,4,3,2,6,1]=>4
[5,4,3,6,1,2]=>5
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>5
[5,4,6,1,3,2]=>6
[5,4,6,2,1,3]=>5
[5,4,6,2,3,1]=>6
[5,4,6,3,1,2]=>5
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>3
[5,6,1,2,4,3]=>4
[5,6,1,3,2,4]=>5
[5,6,1,3,4,2]=>4
[5,6,1,4,2,3]=>5
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>4
[5,6,2,3,1,4]=>5
[5,6,2,3,4,1]=>4
[5,6,2,4,1,3]=>5
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>3
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>5
[5,6,3,4,2,1]=>4
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>4
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>2
[6,1,2,3,4,5]=>3
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>5
[6,1,2,4,5,3]=>4
[6,1,2,5,3,4]=>5
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>5
[6,1,3,2,5,4]=>6
[6,1,3,4,2,5]=>5
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>5
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>6
[6,1,4,3,2,5]=>5
[6,1,4,3,5,2]=>6
[6,1,4,5,2,3]=>5
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>5
[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>5
[6,1,5,3,4,2]=>6
[6,1,5,4,2,3]=>5
[6,1,5,4,3,2]=>4
[6,2,1,3,4,5]=>3
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>5
[6,2,1,4,5,3]=>4
[6,2,1,5,3,4]=>5
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>5
[6,2,3,1,5,4]=>6
[6,2,3,4,1,5]=>5
[6,2,3,4,5,1]=>4
[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]=>6
[6,2,4,3,1,5]=>5
[6,2,4,3,5,1]=>6
[6,2,4,5,1,3]=>5
[6,2,4,5,3,1]=>4
[6,2,5,1,3,4]=>5
[6,2,5,1,4,3]=>6
[6,2,5,3,1,4]=>5
[6,2,5,3,4,1]=>6
[6,2,5,4,1,3]=>5
[6,2,5,4,3,1]=>4
[6,3,1,2,4,5]=>3
[6,3,1,2,5,4]=>4
[6,3,1,4,2,5]=>5
[6,3,1,4,5,2]=>4
[6,3,1,5,2,4]=>5
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>5
[6,3,2,4,5,1]=>4
[6,3,2,5,1,4]=>5
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>6
[6,3,4,2,1,5]=>5
[6,3,4,2,5,1]=>6
[6,3,4,5,1,2]=>5
[6,3,4,5,2,1]=>4
[6,3,5,1,2,4]=>5
[6,3,5,1,4,2]=>6
[6,3,5,2,1,4]=>5
[6,3,5,2,4,1]=>6
[6,3,5,4,1,2]=>5
[6,3,5,4,2,1]=>4
[6,4,1,2,3,5]=>3
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>5
[6,4,1,3,5,2]=>4
[6,4,1,5,2,3]=>5
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>5
[6,4,2,3,5,1]=>4
[6,4,2,5,1,3]=>5
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>3
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>3
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>5
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>5
[6,4,5,1,3,2]=>6
[6,4,5,2,1,3]=>5
[6,4,5,2,3,1]=>6
[6,4,5,3,1,2]=>5
[6,4,5,3,2,1]=>4
[6,5,1,2,3,4]=>3
[6,5,1,2,4,3]=>4
[6,5,1,3,2,4]=>5
[6,5,1,3,4,2]=>4
[6,5,1,4,2,3]=>5
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>5
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>5
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>3
[6,5,3,2,4,1]=>4
[6,5,3,4,1,2]=>5
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>4
[6,5,4,2,1,3]=>3
[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>3
[6,5,4,3,2,1]=>2
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Description
The number of up-down runs of a permutation.
An up-down run of a permutation $\pi=\pi_{1}\pi_{2}\cdots\pi_{n}$ is either a maximal monotone consecutive subsequence or $\pi_{1}$ if 1 is a descent of $\pi$.
For example, the up-down runs of $\pi=85712643$ are $8$, $85$, $57$, $71$, $126$, and
$643$.
An up-down run of a permutation $\pi=\pi_{1}\pi_{2}\cdots\pi_{n}$ is either a maximal monotone consecutive subsequence or $\pi_{1}$ if 1 is a descent of $\pi$.
For example, the up-down runs of $\pi=85712643$ are $8$, $85$, $57$, $71$, $126$, and
$643$.
References
[1] Zhuang, Y. Counting permutations by runs MathSciNet:3499494
[2] Zhuang, Y. Eulerian polynomials and descent statistics arXiv:1610.07218
[2] Zhuang, Y. Eulerian polynomials and descent statistics arXiv:1610.07218
Code
def statistic(x):
if len(x)>1 and x[0]>x[1]:
return x.number_of_peaks() + x.complement().number_of_peaks() + 2
elif len(x)>0:
return x.number_of_peaks() + x.complement().number_of_peaks() + 1
else:
return 0
Created
Oct 27, 2016 at 21:11 by Yan Zhuang
Updated
Oct 27, 2016 at 21:11 by Yan Zhuang
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