Identifier
- St000060: Permutations ⟶ ℤ
Values
=>
[1,2]=>1
[2,1]=>1
[1,2,3]=>2
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>1
[3,2,1]=>2
[1,2,3,4]=>3
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>3
[1,4,2,3]=>2
[1,4,3,2]=>3
[2,1,3,4]=>3
[2,1,4,3]=>3
[2,3,1,4]=>1
[2,3,4,1]=>3
[2,4,1,3]=>2
[2,4,3,1]=>3
[3,1,2,4]=>2
[3,1,4,2]=>2
[3,2,1,4]=>1
[3,2,4,1]=>2
[3,4,1,2]=>3
[3,4,2,1]=>3
[4,1,2,3]=>1
[4,1,3,2]=>1
[4,2,1,3]=>2
[4,2,3,1]=>2
[4,3,1,2]=>3
[4,3,2,1]=>3
[1,2,3,4,5]=>4
[1,2,3,5,4]=>4
[1,2,4,3,5]=>3
[1,2,4,5,3]=>4
[1,2,5,3,4]=>3
[1,2,5,4,3]=>4
[1,3,2,4,5]=>4
[1,3,2,5,4]=>4
[1,3,4,2,5]=>2
[1,3,4,5,2]=>4
[1,3,5,2,4]=>3
[1,3,5,4,2]=>4
[1,4,2,3,5]=>3
[1,4,2,5,3]=>3
[1,4,3,2,5]=>2
[1,4,3,5,2]=>3
[1,4,5,2,3]=>4
[1,4,5,3,2]=>4
[1,5,2,3,4]=>2
[1,5,2,4,3]=>2
[1,5,3,2,4]=>3
[1,5,3,4,2]=>3
[1,5,4,2,3]=>4
[1,5,4,3,2]=>4
[2,1,3,4,5]=>4
[2,1,3,5,4]=>4
[2,1,4,3,5]=>3
[2,1,4,5,3]=>4
[2,1,5,3,4]=>3
[2,1,5,4,3]=>4
[2,3,1,4,5]=>4
[2,3,1,5,4]=>4
[2,3,4,1,5]=>1
[2,3,4,5,1]=>4
[2,3,5,1,4]=>3
[2,3,5,4,1]=>4
[2,4,1,3,5]=>3
[2,4,1,5,3]=>3
[2,4,3,1,5]=>1
[2,4,3,5,1]=>3
[2,4,5,1,3]=>4
[2,4,5,3,1]=>4
[2,5,1,3,4]=>2
[2,5,1,4,3]=>2
[2,5,3,1,4]=>3
[2,5,3,4,1]=>3
[2,5,4,1,3]=>4
[2,5,4,3,1]=>4
[3,1,2,4,5]=>4
[3,1,2,5,4]=>4
[3,1,4,2,5]=>2
[3,1,4,5,2]=>4
[3,1,5,2,4]=>2
[3,1,5,4,2]=>4
[3,2,1,4,5]=>4
[3,2,1,5,4]=>4
[3,2,4,1,5]=>1
[3,2,4,5,1]=>4
[3,2,5,1,4]=>2
[3,2,5,4,1]=>4
[3,4,1,2,5]=>2
[3,4,1,5,2]=>2
[3,4,2,1,5]=>1
[3,4,2,5,1]=>2
[3,4,5,1,2]=>4
[3,4,5,2,1]=>4
[3,5,1,2,4]=>3
[3,5,1,4,2]=>3
[3,5,2,1,4]=>3
[3,5,2,4,1]=>3
[3,5,4,1,2]=>4
[3,5,4,2,1]=>4
[4,1,2,3,5]=>3
[4,1,2,5,3]=>3
[4,1,3,2,5]=>2
[4,1,3,5,2]=>3
[4,1,5,2,3]=>2
[4,1,5,3,2]=>3
[4,2,1,3,5]=>3
[4,2,1,5,3]=>3
[4,2,3,1,5]=>1
[4,2,3,5,1]=>3
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>2
[4,3,1,5,2]=>2
[4,3,2,1,5]=>1
[4,3,2,5,1]=>2
[4,3,5,1,2]=>3
[4,3,5,2,1]=>3
[4,5,1,2,3]=>4
[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]=>4
[5,1,2,3,4]=>1
[5,1,2,4,3]=>1
[5,1,3,2,4]=>1
[5,1,3,4,2]=>1
[5,1,4,2,3]=>1
[5,1,4,3,2]=>1
[5,2,1,3,4]=>2
[5,2,1,4,3]=>2
[5,2,3,1,4]=>2
[5,2,3,4,1]=>2
[5,2,4,1,3]=>2
[5,2,4,3,1]=>2
[5,3,1,2,4]=>3
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>3
[5,3,4,1,2]=>3
[5,3,4,2,1]=>3
[5,4,1,2,3]=>4
[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]=>4
[1,2,3,4,5,6]=>5
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>5
[1,2,3,6,4,5]=>4
[1,2,3,6,5,4]=>5
[1,2,4,3,5,6]=>5
[1,2,4,3,6,5]=>5
[1,2,4,5,3,6]=>3
[1,2,4,5,6,3]=>5
[1,2,4,6,3,5]=>4
[1,2,4,6,5,3]=>5
[1,2,5,3,4,6]=>4
[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]=>5
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>4
[1,2,6,4,5,3]=>4
[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]=>5
[1,3,2,5,4,6]=>4
[1,3,2,5,6,4]=>5
[1,3,2,6,4,5]=>4
[1,3,2,6,5,4]=>5
[1,3,4,2,5,6]=>5
[1,3,4,2,6,5]=>5
[1,3,4,5,2,6]=>2
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>4
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>2
[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]=>3
[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]=>5
[1,3,6,5,4,2]=>5
[1,4,2,3,5,6]=>5
[1,4,2,3,6,5]=>5
[1,4,2,5,3,6]=>3
[1,4,2,5,6,3]=>5
[1,4,2,6,3,5]=>3
[1,4,2,6,5,3]=>5
[1,4,3,2,5,6]=>5
[1,4,3,2,6,5]=>5
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>3
[1,4,3,6,5,2]=>5
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>2
[1,4,5,3,6,2]=>3
[1,4,5,6,2,3]=>5
[1,4,5,6,3,2]=>5
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>4
[1,4,6,5,2,3]=>5
[1,4,6,5,3,2]=>5
[1,5,2,3,4,6]=>4
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>4
[1,5,2,6,3,4]=>3
[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]=>2
[1,5,3,4,6,2]=>4
[1,5,3,6,2,4]=>3
[1,5,3,6,4,2]=>4
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>3
[1,5,4,3,2,6]=>2
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>4
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>5
[1,5,6,2,4,3]=>5
[1,5,6,3,2,4]=>5
[1,5,6,3,4,2]=>5
[1,5,6,4,2,3]=>5
[1,5,6,4,3,2]=>5
[1,6,2,3,4,5]=>2
[1,6,2,3,5,4]=>2
[1,6,2,4,3,5]=>2
[1,6,2,4,5,3]=>2
[1,6,2,5,3,4]=>2
[1,6,2,5,4,3]=>2
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>3
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>3
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>4
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>4
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>5
[1,6,5,2,4,3]=>5
[1,6,5,3,2,4]=>5
[1,6,5,3,4,2]=>5
[1,6,5,4,2,3]=>5
[1,6,5,4,3,2]=>5
[2,1,3,4,5,6]=>5
[2,1,3,4,6,5]=>5
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>5
[2,1,3,6,4,5]=>4
[2,1,3,6,5,4]=>5
[2,1,4,3,5,6]=>5
[2,1,4,3,6,5]=>5
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>5
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>5
[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>3
[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]=>3
[2,1,6,3,5,4]=>3
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>4
[2,1,6,5,3,4]=>5
[2,1,6,5,4,3]=>5
[2,3,1,4,5,6]=>5
[2,3,1,4,6,5]=>5
[2,3,1,5,4,6]=>4
[2,3,1,5,6,4]=>5
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>5
[2,3,4,1,5,6]=>5
[2,3,4,1,6,5]=>5
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>4
[2,3,4,6,5,1]=>5
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>4
[2,3,5,4,1,6]=>1
[2,3,5,4,6,1]=>4
[2,3,5,6,1,4]=>5
[2,3,5,6,4,1]=>5
[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>3
[2,3,6,4,1,5]=>4
[2,3,6,4,5,1]=>4
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>5
[2,4,1,3,5,6]=>5
[2,4,1,3,6,5]=>5
[2,4,1,5,3,6]=>3
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>3
[2,4,1,6,5,3]=>5
[2,4,3,1,5,6]=>5
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>5
[2,4,3,6,1,5]=>3
[2,4,3,6,5,1]=>5
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>3
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>3
[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]=>5
[2,4,6,5,3,1]=>5
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>4
[2,5,1,4,3,6]=>3
[2,5,1,4,6,3]=>4
[2,5,1,6,3,4]=>3
[2,5,1,6,4,3]=>4
[2,5,3,1,4,6]=>4
[2,5,3,1,6,4]=>4
[2,5,3,4,1,6]=>1
[2,5,3,4,6,1]=>4
[2,5,3,6,1,4]=>3
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>3
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>1
[2,5,4,3,6,1]=>3
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>4
[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]=>5
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>5
[2,6,1,3,4,5]=>2
[2,6,1,3,5,4]=>2
[2,6,1,4,3,5]=>2
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>2
[2,6,3,1,4,5]=>3
[2,6,3,1,5,4]=>3
[2,6,3,4,1,5]=>3
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>3
[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]=>4
[2,6,4,5,1,3]=>4
[2,6,4,5,3,1]=>4
[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]=>5
[2,6,5,4,1,3]=>5
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>5
[3,1,2,4,6,5]=>5
[3,1,2,5,4,6]=>4
[3,1,2,5,6,4]=>5
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>5
[3,1,4,2,5,6]=>5
[3,1,4,2,6,5]=>5
[3,1,4,5,2,6]=>2
[3,1,4,5,6,2]=>5
[3,1,4,6,2,5]=>4
[3,1,4,6,5,2]=>5
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>4
[3,1,5,4,2,6]=>2
[3,1,5,4,6,2]=>4
[3,1,5,6,2,4]=>5
[3,1,5,6,4,2]=>5
[3,1,6,2,4,5]=>2
[3,1,6,2,5,4]=>2
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>4
[3,1,6,5,2,4]=>5
[3,1,6,5,4,2]=>5
[3,2,1,4,5,6]=>5
[3,2,1,4,6,5]=>5
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>5
[3,2,1,6,4,5]=>4
[3,2,1,6,5,4]=>5
[3,2,4,1,5,6]=>5
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>5
[3,2,4,6,1,5]=>4
[3,2,4,6,5,1]=>5
[3,2,5,1,4,6]=>4
[3,2,5,1,6,4]=>4
[3,2,5,4,1,6]=>1
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>5
[3,2,5,6,4,1]=>5
[3,2,6,1,4,5]=>2
[3,2,6,1,5,4]=>2
[3,2,6,4,1,5]=>4
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>5
[3,2,6,5,4,1]=>5
[3,4,1,2,5,6]=>5
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>5
[3,4,1,6,2,5]=>2
[3,4,1,6,5,2]=>5
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>5
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>5
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>5
[3,4,5,1,2,6]=>2
[3,4,5,1,6,2]=>2
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>2
[3,4,5,6,1,2]=>5
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>4
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>4
[3,4,6,5,1,2]=>5
[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]=>2
[3,5,1,4,6,2]=>4
[3,5,1,6,2,4]=>2
[3,5,1,6,4,2]=>4
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>4
[3,5,2,4,1,6]=>1
[3,5,2,4,6,1]=>4
[3,5,2,6,1,4]=>2
[3,5,2,6,4,1]=>4
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>4
[3,5,4,6,2,1]=>4
[3,5,6,1,2,4]=>5
[3,5,6,1,4,2]=>5
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>5
[3,5,6,4,1,2]=>5
[3,5,6,4,2,1]=>5
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>3
[3,6,1,4,5,2]=>3
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>3
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>3
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>4
[3,6,4,2,1,5]=>4
[3,6,4,2,5,1]=>4
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>5
[3,6,5,1,4,2]=>5
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>5
[3,6,5,4,1,2]=>5
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>5
[4,1,2,3,6,5]=>5
[4,1,2,5,3,6]=>3
[4,1,2,5,6,3]=>5
[4,1,2,6,3,5]=>3
[4,1,2,6,5,3]=>5
[4,1,3,2,5,6]=>5
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>2
[4,1,3,5,6,2]=>5
[4,1,3,6,2,5]=>3
[4,1,3,6,5,2]=>5
[4,1,5,2,3,6]=>3
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>3
[4,1,5,6,2,3]=>5
[4,1,5,6,3,2]=>5
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>2
[4,1,6,3,2,5]=>3
[4,1,6,3,5,2]=>3
[4,1,6,5,2,3]=>5
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>5
[4,2,1,3,6,5]=>5
[4,2,1,5,3,6]=>3
[4,2,1,5,6,3]=>5
[4,2,1,6,3,5]=>3
[4,2,1,6,5,3]=>5
[4,2,3,1,5,6]=>5
[4,2,3,1,6,5]=>5
[4,2,3,5,1,6]=>1
[4,2,3,5,6,1]=>5
[4,2,3,6,1,5]=>3
[4,2,3,6,5,1]=>5
[4,2,5,1,3,6]=>3
[4,2,5,1,6,3]=>3
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>3
[4,2,5,6,1,3]=>5
[4,2,5,6,3,1]=>5
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>2
[4,2,6,3,1,5]=>3
[4,2,6,3,5,1]=>3
[4,2,6,5,1,3]=>5
[4,2,6,5,3,1]=>5
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>5
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>5
[4,3,1,6,2,5]=>2
[4,3,1,6,5,2]=>5
[4,3,2,1,5,6]=>5
[4,3,2,1,6,5]=>5
[4,3,2,5,1,6]=>1
[4,3,2,5,6,1]=>5
[4,3,2,6,1,5]=>2
[4,3,2,6,5,1]=>5
[4,3,5,1,2,6]=>2
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>2
[4,3,5,6,1,2]=>5
[4,3,5,6,2,1]=>5
[4,3,6,1,2,5]=>3
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>3
[4,3,6,2,5,1]=>3
[4,3,6,5,1,2]=>5
[4,3,6,5,2,1]=>5
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>2
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>3
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>3
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>2
[4,5,3,6,1,2]=>3
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>5
[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]=>5
[4,6,1,2,3,5]=>4
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>4
[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]=>4
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>4
[4,6,3,5,2,1]=>4
[4,6,5,1,2,3]=>5
[4,6,5,1,3,2]=>5
[4,6,5,2,1,3]=>5
[4,6,5,2,3,1]=>5
[4,6,5,3,1,2]=>5
[4,6,5,3,2,1]=>5
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>3
[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]=>2
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>3
[5,1,3,6,4,2]=>4
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>3
[5,1,4,3,2,6]=>2
[5,1,4,3,6,2]=>3
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>4
[5,1,6,2,3,4]=>2
[5,1,6,2,4,3]=>2
[5,1,6,3,2,4]=>3
[5,1,6,3,4,2]=>3
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>4
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>3
[5,2,1,4,6,3]=>4
[5,2,1,6,3,4]=>3
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>4
[5,2,3,1,6,4]=>4
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>3
[5,2,3,6,4,1]=>4
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>3
[5,2,4,3,1,6]=>1
[5,2,4,3,6,1]=>3
[5,2,4,6,1,3]=>4
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>2
[5,2,6,3,1,4]=>3
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>4
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>4
[5,3,1,4,2,6]=>2
[5,3,1,4,6,2]=>4
[5,3,1,6,2,4]=>2
[5,3,1,6,4,2]=>4
[5,3,2,1,4,6]=>4
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>1
[5,3,2,4,6,1]=>4
[5,3,2,6,1,4]=>2
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>2
[5,3,4,1,6,2]=>2
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>2
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>4
[5,3,6,1,2,4]=>3
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>3
[5,3,6,2,4,1]=>3
[5,3,6,4,1,2]=>4
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>3
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>3
[5,4,1,6,2,3]=>2
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>1
[5,4,2,3,6,1]=>3
[5,4,2,6,1,3]=>2
[5,4,2,6,3,1]=>3
[5,4,3,1,2,6]=>2
[5,4,3,1,6,2]=>2
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>2
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>3
[5,4,6,1,2,3]=>4
[5,4,6,1,3,2]=>4
[5,4,6,2,1,3]=>4
[5,4,6,2,3,1]=>4
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>5
[5,6,1,2,4,3]=>5
[5,6,1,3,2,4]=>5
[5,6,1,3,4,2]=>5
[5,6,1,4,2,3]=>5
[5,6,1,4,3,2]=>5
[5,6,2,1,3,4]=>5
[5,6,2,1,4,3]=>5
[5,6,2,3,1,4]=>5
[5,6,2,3,4,1]=>5
[5,6,2,4,1,3]=>5
[5,6,2,4,3,1]=>5
[5,6,3,1,2,4]=>5
[5,6,3,1,4,2]=>5
[5,6,3,2,1,4]=>5
[5,6,3,2,4,1]=>5
[5,6,3,4,1,2]=>5
[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]=>5
[5,6,4,3,1,2]=>5
[5,6,4,3,2,1]=>5
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>1
[6,1,2,4,3,5]=>1
[6,1,2,4,5,3]=>1
[6,1,2,5,3,4]=>1
[6,1,2,5,4,3]=>1
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>1
[6,1,3,4,2,5]=>1
[6,1,3,4,5,2]=>1
[6,1,3,5,2,4]=>1
[6,1,3,5,4,2]=>1
[6,1,4,2,3,5]=>1
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>1
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>1
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>1
[6,1,5,2,4,3]=>1
[6,1,5,3,2,4]=>1
[6,1,5,3,4,2]=>1
[6,1,5,4,2,3]=>1
[6,1,5,4,3,2]=>1
[6,2,1,3,4,5]=>2
[6,2,1,3,5,4]=>2
[6,2,1,4,3,5]=>2
[6,2,1,4,5,3]=>2
[6,2,1,5,3,4]=>2
[6,2,1,5,4,3]=>2
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>2
[6,2,3,4,1,5]=>2
[6,2,3,4,5,1]=>2
[6,2,3,5,1,4]=>2
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>2
[6,2,4,1,5,3]=>2
[6,2,4,3,1,5]=>2
[6,2,4,3,5,1]=>2
[6,2,4,5,1,3]=>2
[6,2,4,5,3,1]=>2
[6,2,5,1,3,4]=>2
[6,2,5,1,4,3]=>2
[6,2,5,3,1,4]=>2
[6,2,5,3,4,1]=>2
[6,2,5,4,1,3]=>2
[6,2,5,4,3,1]=>2
[6,3,1,2,4,5]=>3
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>3
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>3
[6,3,2,4,1,5]=>3
[6,3,2,4,5,1]=>3
[6,3,2,5,1,4]=>3
[6,3,2,5,4,1]=>3
[6,3,4,1,2,5]=>3
[6,3,4,1,5,2]=>3
[6,3,4,2,1,5]=>3
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>3
[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>3
[6,3,5,1,4,2]=>3
[6,3,5,2,1,4]=>3
[6,3,5,2,4,1]=>3
[6,3,5,4,1,2]=>3
[6,3,5,4,2,1]=>3
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>4
[6,4,1,3,5,2]=>4
[6,4,1,5,2,3]=>4
[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]=>4
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>4
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>4
[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]=>4
[6,5,1,2,3,4]=>5
[6,5,1,2,4,3]=>5
[6,5,1,3,2,4]=>5
[6,5,1,3,4,2]=>5
[6,5,1,4,2,3]=>5
[6,5,1,4,3,2]=>5
[6,5,2,1,3,4]=>5
[6,5,2,1,4,3]=>5
[6,5,2,3,1,4]=>5
[6,5,2,3,4,1]=>5
[6,5,2,4,1,3]=>5
[6,5,2,4,3,1]=>5
[6,5,3,1,2,4]=>5
[6,5,3,1,4,2]=>5
[6,5,3,2,1,4]=>5
[6,5,3,2,4,1]=>5
[6,5,3,4,1,2]=>5
[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]=>5
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>5
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Description
The greater neighbor of the maximum.
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 smallest path leaf label of the binary tree associated to a permutation (St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation.), see also [3].
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 smallest path leaf label of the binary tree associated to a permutation (St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation.), see also [3].
References
[1] 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] Poupard, C. Deux propriétés des arbres binaires ordonnés stricts MathSciNet:1005843
[2] https://www.emis.de/journals/SLC/wpapers/s74vortrag/han.pdf
[3] Poupard, C. Deux propriétés des arbres binaires ordonnés stricts MathSciNet:1005843
Code
def statistic(pi):
n = pi.size()
pi = [0]+list(pi)+[0]
i = pi.index(n)
return max(pi[i-1],pi[i+1])
Created
Apr 10, 2013 at 10:30 by Christian Stump
Updated
Mar 28, 2017 at 11:45 by Christian Stump
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