Identifier
- St000222: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>1
[1,4,2,3]=>2
[1,4,3,2]=>2
[2,1,3,4]=>2
[2,1,4,3]=>2
[2,3,1,4]=>1
[2,3,4,1]=>0
[2,4,1,3]=>1
[2,4,3,1]=>1
[3,1,2,4]=>2
[3,1,4,2]=>1
[3,2,1,4]=>2
[3,2,4,1]=>1
[3,4,1,2]=>0
[3,4,2,1]=>1
[4,1,2,3]=>0
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>2
[4,3,1,2]=>1
[4,3,2,1]=>2
[1,2,3,4,5]=>0
[1,2,3,5,4]=>3
[1,2,4,3,5]=>3
[1,2,4,5,3]=>2
[1,2,5,3,4]=>4
[1,2,5,4,3]=>3
[1,3,2,4,5]=>3
[1,3,2,5,4]=>4
[1,3,4,2,5]=>2
[1,3,4,5,2]=>1
[1,3,5,2,4]=>3
[1,3,5,4,2]=>2
[1,4,2,3,5]=>4
[1,4,2,5,3]=>3
[1,4,3,2,5]=>3
[1,4,3,5,2]=>2
[1,4,5,2,3]=>2
[1,4,5,3,2]=>3
[1,5,2,3,4]=>3
[1,5,2,4,3]=>4
[1,5,3,2,4]=>4
[1,5,3,4,2]=>3
[1,5,4,2,3]=>3
[1,5,4,3,2]=>4
[2,1,3,4,5]=>3
[2,1,3,5,4]=>4
[2,1,4,3,5]=>4
[2,1,4,5,3]=>3
[2,1,5,3,4]=>3
[2,1,5,4,3]=>4
[2,3,1,4,5]=>2
[2,3,1,5,4]=>3
[2,3,4,1,5]=>1
[2,3,4,5,1]=>0
[2,3,5,1,4]=>2
[2,3,5,4,1]=>1
[2,4,1,3,5]=>3
[2,4,1,5,3]=>2
[2,4,3,1,5]=>2
[2,4,3,5,1]=>1
[2,4,5,1,3]=>1
[2,4,5,3,1]=>2
[2,5,1,3,4]=>2
[2,5,1,4,3]=>3
[2,5,3,1,4]=>3
[2,5,3,4,1]=>2
[2,5,4,1,3]=>2
[2,5,4,3,1]=>3
[3,1,2,4,5]=>4
[3,1,2,5,4]=>3
[3,1,4,2,5]=>3
[3,1,4,5,2]=>2
[3,1,5,2,4]=>2
[3,1,5,4,2]=>3
[3,2,1,4,5]=>3
[3,2,1,5,4]=>4
[3,2,4,1,5]=>2
[3,2,4,5,1]=>1
[3,2,5,1,4]=>3
[3,2,5,4,1]=>2
[3,4,1,2,5]=>2
[3,4,1,5,2]=>1
[3,4,2,1,5]=>3
[3,4,2,5,1]=>2
[3,4,5,1,2]=>0
[3,4,5,2,1]=>1
[3,5,1,2,4]=>1
[3,5,1,4,2]=>2
[3,5,2,1,4]=>2
[3,5,2,4,1]=>3
[3,5,4,1,2]=>1
[3,5,4,2,1]=>2
[4,1,2,3,5]=>3
[4,1,2,5,3]=>2
[4,1,3,2,5]=>4
[4,1,3,5,2]=>3
[4,1,5,2,3]=>1
[4,1,5,3,2]=>2
[4,2,1,3,5]=>4
[4,2,1,5,3]=>3
[4,2,3,1,5]=>3
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>3
[4,3,1,5,2]=>2
[4,3,2,1,5]=>4
[4,3,2,5,1]=>3
[4,3,5,1,2]=>1
[4,3,5,2,1]=>2
[4,5,1,2,3]=>0
[4,5,1,3,2]=>1
[4,5,2,1,3]=>1
[4,5,2,3,1]=>2
[4,5,3,1,2]=>2
[4,5,3,2,1]=>3
[5,1,2,3,4]=>0
[5,1,2,4,3]=>3
[5,1,3,2,4]=>3
[5,1,3,4,2]=>4
[5,1,4,2,3]=>2
[5,1,4,3,2]=>3
[5,2,1,3,4]=>3
[5,2,1,4,3]=>4
[5,2,3,1,4]=>4
[5,2,3,4,1]=>3
[5,2,4,1,3]=>3
[5,2,4,3,1]=>4
[5,3,1,2,4]=>2
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>4
[5,3,4,1,2]=>2
[5,3,4,2,1]=>3
[5,4,1,2,3]=>1
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>3
[5,4,3,1,2]=>3
[5,4,3,2,1]=>4
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>4
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>3
[1,2,3,6,4,5]=>6
[1,2,3,6,5,4]=>4
[1,2,4,3,5,6]=>4
[1,2,4,3,6,5]=>6
[1,2,4,5,3,6]=>3
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>5
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>6
[1,2,5,3,6,4]=>5
[1,2,5,4,3,6]=>4
[1,2,5,4,6,3]=>3
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>5
[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]=>4
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>4
[1,3,2,4,6,5]=>6
[1,3,2,5,4,6]=>6
[1,3,2,5,6,4]=>5
[1,3,2,6,4,5]=>6
[1,3,2,6,5,4]=>6
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>5
[1,3,4,5,2,6]=>2
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>2
[1,3,5,2,4,6]=>5
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>4
[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]=>3
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>5
[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]=>4
[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>5
[1,4,3,2,5,6]=>4
[1,4,3,2,6,5]=>6
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>2
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>3
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>4
[1,4,5,6,2,3]=>2
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>5
[1,4,6,3,5,2]=>5
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>4
[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]=>4
[1,5,2,6,4,3]=>5
[1,5,3,2,4,6]=>6
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>4
[1,5,3,4,6,2]=>3
[1,5,3,6,2,4]=>4
[1,5,3,6,4,2]=>5
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>5
[1,5,4,6,2,3]=>3
[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]=>4
[1,5,6,3,4,2]=>5
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>5
[1,6,2,3,4,5]=>4
[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]=>6
[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]=>4
[1,6,3,5,2,4]=>5
[1,6,3,5,4,2]=>6
[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]=>4
[1,6,4,5,3,2]=>5
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>5
[1,6,5,3,2,4]=>5
[1,6,5,3,4,2]=>6
[1,6,5,4,2,3]=>5
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>4
[2,1,3,4,6,5]=>6
[2,1,3,5,4,6]=>6
[2,1,3,5,6,4]=>5
[2,1,3,6,4,5]=>6
[2,1,3,6,5,4]=>6
[2,1,4,3,5,6]=>6
[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]=>5
[2,1,5,3,4,6]=>6
[2,1,5,3,6,4]=>5
[2,1,5,4,3,6]=>6
[2,1,5,4,6,3]=>5
[2,1,5,6,3,4]=>4
[2,1,5,6,4,3]=>5
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>6
[2,1,6,4,3,5]=>6
[2,1,6,4,5,3]=>6
[2,1,6,5,3,4]=>5
[2,1,6,5,4,3]=>6
[2,3,1,4,5,6]=>3
[2,3,1,4,6,5]=>5
[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]=>5
[2,3,4,1,5,6]=>2
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>1
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>1
[2,3,5,6,1,4]=>2
[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]=>2
[2,3,6,5,1,4]=>3
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>5
[2,4,1,3,6,5]=>5
[2,4,1,5,3,6]=>4
[2,4,1,5,6,3]=>3
[2,4,1,6,3,5]=>4
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>4
[2,4,3,6,5,1]=>2
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>2
[2,4,5,3,1,6]=>4
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>1
[2,4,5,6,3,1]=>2
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>3
[2,4,6,3,1,5]=>4
[2,4,6,3,5,1]=>4
[2,4,6,5,1,3]=>2
[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]=>3
[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]=>3
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>3
[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]=>5
[2,5,4,3,6,1]=>4
[2,5,4,6,1,3]=>2
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>2
[2,5,6,1,4,3]=>3
[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]=>4
[2,6,1,3,4,5]=>3
[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]=>5
[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]=>3
[2,6,3,5,1,4]=>4
[2,6,3,5,4,1]=>5
[2,6,4,1,3,5]=>4
[2,6,4,1,5,3]=>4
[2,6,4,3,1,5]=>5
[2,6,4,3,5,1]=>5
[2,6,4,5,1,3]=>3
[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]=>4
[2,6,5,3,4,1]=>5
[2,6,5,4,1,3]=>4
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>6
[3,1,2,4,6,5]=>6
[3,1,2,5,4,6]=>6
[3,1,2,5,6,4]=>5
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>6
[3,1,4,2,5,6]=>5
[3,1,4,2,6,5]=>5
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>4
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>5
[3,1,5,2,6,4]=>4
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>4
[3,1,5,6,2,4]=>3
[3,1,5,6,4,2]=>4
[3,1,6,2,4,5]=>3
[3,1,6,2,5,4]=>5
[3,1,6,4,2,5]=>5
[3,1,6,4,5,2]=>5
[3,1,6,5,2,4]=>4
[3,1,6,5,4,2]=>5
[3,2,1,4,5,6]=>4
[3,2,1,4,6,5]=>6
[3,2,1,5,4,6]=>6
[3,2,1,5,6,4]=>5
[3,2,1,6,4,5]=>6
[3,2,1,6,5,4]=>6
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>2
[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>4
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>4
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>3
[3,2,5,6,4,1]=>4
[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>5
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>5
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>4
[3,4,1,5,2,6]=>3
[3,4,1,5,6,2]=>2
[3,4,1,6,2,5]=>3
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>5
[3,4,2,5,1,6]=>4
[3,4,2,5,6,1]=>3
[3,4,2,6,1,5]=>4
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>2
[3,4,5,1,6,2]=>1
[3,4,5,2,1,6]=>3
[3,4,5,2,6,1]=>2
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>2
[3,4,6,1,5,2]=>2
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>1
[3,4,6,5,2,1]=>2
[3,5,1,2,4,6]=>4
[3,5,1,2,6,4]=>3
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>3
[3,5,1,6,2,4]=>2
[3,5,1,6,4,2]=>3
[3,5,2,1,4,6]=>5
[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]=>3
[3,5,2,6,4,1]=>4
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>4
[3,5,4,2,6,1]=>3
[3,5,4,6,1,2]=>1
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>1
[3,5,6,1,4,2]=>2
[3,5,6,2,1,4]=>2
[3,5,6,2,4,1]=>3
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>4
[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]=>3
[3,6,2,1,5,4]=>5
[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]=>5
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>4
[3,6,4,2,5,1]=>4
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>2
[3,6,5,1,4,2]=>3
[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]=>4
[4,1,2,3,5,6]=>6
[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]=>3
[4,1,2,6,5,3]=>5
[4,1,3,2,5,6]=>6
[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]=>5
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>5
[4,1,5,3,6,2]=>4
[4,1,5,6,2,3]=>2
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>4
[4,1,6,3,2,5]=>3
[4,1,6,3,5,2]=>5
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>6
[4,2,1,3,6,5]=>6
[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]=>5
[4,2,3,1,5,6]=>4
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>3
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>5
[4,2,3,6,5,1]=>3
[4,2,5,1,3,6]=>4
[4,2,5,1,6,3]=>3
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>4
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>4
[4,2,6,1,5,3]=>4
[4,2,6,3,1,5]=>5
[4,2,6,3,5,1]=>5
[4,2,6,5,1,3]=>3
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>5
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>3
[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]=>6
[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]=>5
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>4
[4,3,5,2,6,1]=>3
[4,3,5,6,1,2]=>1
[4,3,5,6,2,1]=>2
[4,3,6,1,2,5]=>3
[4,3,6,1,5,2]=>3
[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]=>3
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>2
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>1
[4,5,1,6,3,2]=>2
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>4
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>3
[4,5,3,1,2,6]=>4
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>5
[4,5,3,2,6,1]=>4
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>0
[4,5,6,1,3,2]=>1
[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>1
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>3
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>4
[4,6,2,3,1,5]=>3
[4,6,2,3,5,1]=>5
[4,6,2,5,1,3]=>3
[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]=>3
[4,6,3,5,2,1]=>4
[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>2
[4,6,5,2,1,3]=>2
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>4
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>6
[5,1,2,4,6,3]=>5
[5,1,2,6,3,4]=>2
[5,1,2,6,4,3]=>3
[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]=>4
[5,1,3,6,4,2]=>5
[5,1,4,2,3,6]=>5
[5,1,4,2,6,3]=>4
[5,1,4,3,2,6]=>6
[5,1,4,3,6,2]=>5
[5,1,4,6,2,3]=>3
[5,1,4,6,3,2]=>4
[5,1,6,2,3,4]=>1
[5,1,6,2,4,3]=>2
[5,1,6,3,2,4]=>2
[5,1,6,3,4,2]=>3
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>5
[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]=>4
[5,2,1,6,4,3]=>5
[5,2,3,1,4,6]=>6
[5,2,3,1,6,4]=>5
[5,2,3,4,1,6]=>4
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>4
[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]=>6
[5,2,4,3,6,1]=>5
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>3
[5,2,6,1,4,3]=>4
[5,2,6,3,1,4]=>4
[5,2,6,3,4,1]=>5
[5,2,6,4,1,3]=>4
[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]=>3
[5,3,1,6,4,2]=>4
[5,3,2,1,4,6]=>6
[5,3,2,1,6,4]=>5
[5,3,2,4,1,6]=>6
[5,3,2,4,6,1]=>5
[5,3,2,6,1,4]=>4
[5,3,2,6,4,1]=>5
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>5
[5,3,4,2,6,1]=>4
[5,3,4,6,1,2]=>2
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>3
[5,3,6,2,4,1]=>4
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>5
[5,4,1,3,6,2]=>4
[5,4,1,6,2,3]=>2
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>5
[5,4,2,1,6,3]=>4
[5,4,2,3,1,6]=>6
[5,4,2,3,6,1]=>5
[5,4,2,6,1,3]=>3
[5,4,2,6,3,1]=>4
[5,4,3,1,2,6]=>5
[5,4,3,1,6,2]=>4
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>5
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>2
[5,4,6,2,1,3]=>2
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>3
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>0
[5,6,1,2,4,3]=>1
[5,6,1,3,2,4]=>1
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>1
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>5
[5,6,3,1,2,4]=>3
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>4
[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]=>2
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>4
[5,6,4,3,1,2]=>4
[5,6,4,3,2,1]=>5
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>6
[6,1,2,5,3,4]=>3
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>4
[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]=>6
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>5
[6,1,4,3,2,5]=>4
[6,1,4,3,5,2]=>6
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>5
[6,1,5,2,3,4]=>2
[6,1,5,2,4,3]=>3
[6,1,5,3,2,4]=>3
[6,1,5,3,4,2]=>4
[6,1,5,4,2,3]=>5
[6,1,5,4,3,2]=>6
[6,2,1,3,4,5]=>4
[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]=>6
[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]=>4
[6,2,3,5,1,4]=>5
[6,2,3,5,4,1]=>6
[6,2,4,1,3,5]=>5
[6,2,4,1,5,3]=>5
[6,2,4,3,1,5]=>6
[6,2,4,3,5,1]=>6
[6,2,4,5,1,3]=>4
[6,2,4,5,3,1]=>5
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>5
[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]=>6
[6,3,1,2,4,5]=>3
[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]=>5
[6,3,2,1,4,5]=>4
[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]=>5
[6,3,2,5,4,1]=>6
[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]=>3
[6,3,4,5,2,1]=>4
[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]=>5
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>5
[6,4,1,2,3,5]=>2
[6,4,1,2,5,3]=>4
[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]=>4
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>5
[6,4,2,3,1,5]=>4
[6,4,2,3,5,1]=>6
[6,4,2,5,1,3]=>4
[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]=>4
[6,4,3,5,2,1]=>5
[6,4,5,1,2,3]=>2
[6,4,5,1,3,2]=>3
[6,4,5,2,1,3]=>3
[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]=>1
[6,5,1,2,4,3]=>2
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>4
[6,5,1,4,3,2]=>5
[6,5,2,1,3,4]=>2
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>3
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>5
[6,5,2,4,3,1]=>6
[6,5,3,1,2,4]=>4
[6,5,3,1,4,2]=>5
[6,5,3,2,1,4]=>5
[6,5,3,2,4,1]=>6
[6,5,3,4,1,2]=>5
[6,5,3,4,2,1]=>6
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>4
[6,5,4,2,1,3]=>4
[6,5,4,2,3,1]=>5
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>6
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of alignments in the permutation.
References
[1] Corteel, S. Crossings and alignments of permutations MathSciNet:2290808
Code
def statistic(pi):
al = 0
n = len(pi)
for i in range(n):
for j in range(n):
if j < i < pi[i] < pi[j] or pi[j] < pi[i] <= i < j or j+1 <= pi[j] < pi[i] < i+1 or pi[i] < i+1 < j+1 <= pi[j]:
al = al+1
return al
Created
Sep 26, 2014 at 11:37 by Martin Rubey
Updated
Nov 16, 2017 at 11:40 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!