Identifier
- St000367: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>0
[1,3,2,4]=>0
[1,3,4,2]=>0
[1,4,2,3]=>0
[1,4,3,2]=>1
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,3,1]=>1
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>2
[3,2,4,1]=>1
[3,4,1,2]=>0
[3,4,2,1]=>2
[4,1,2,3]=>0
[4,1,3,2]=>0
[4,2,1,3]=>1
[4,2,3,1]=>0
[4,3,1,2]=>1
[4,3,2,1]=>3
[1,2,3,4,5]=>0
[1,2,3,5,4]=>0
[1,2,4,3,5]=>0
[1,2,4,5,3]=>0
[1,2,5,3,4]=>0
[1,2,5,4,3]=>1
[1,3,2,4,5]=>0
[1,3,2,5,4]=>0
[1,3,4,2,5]=>0
[1,3,4,5,2]=>0
[1,3,5,2,4]=>0
[1,3,5,4,2]=>1
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>2
[1,4,3,5,2]=>1
[1,4,5,2,3]=>0
[1,4,5,3,2]=>2
[1,5,2,3,4]=>0
[1,5,2,4,3]=>0
[1,5,3,2,4]=>1
[1,5,3,4,2]=>0
[1,5,4,2,3]=>1
[1,5,4,3,2]=>3
[2,1,3,4,5]=>0
[2,1,3,5,4]=>0
[2,1,4,3,5]=>0
[2,1,4,5,3]=>0
[2,1,5,3,4]=>0
[2,1,5,4,3]=>1
[2,3,1,4,5]=>0
[2,3,1,5,4]=>0
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>0
[2,3,5,4,1]=>1
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>2
[2,4,3,5,1]=>1
[2,4,5,1,3]=>0
[2,4,5,3,1]=>2
[2,5,1,3,4]=>0
[2,5,1,4,3]=>0
[2,5,3,1,4]=>1
[2,5,3,4,1]=>0
[2,5,4,1,3]=>1
[2,5,4,3,1]=>3
[3,1,2,4,5]=>0
[3,1,2,5,4]=>0
[3,1,4,2,5]=>0
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,4,2]=>1
[3,2,1,4,5]=>3
[3,2,1,5,4]=>3
[3,2,4,1,5]=>1
[3,2,4,5,1]=>1
[3,2,5,1,4]=>2
[3,2,5,4,1]=>2
[3,4,1,2,5]=>0
[3,4,1,5,2]=>0
[3,4,2,1,5]=>3
[3,4,2,5,1]=>2
[3,4,5,1,2]=>0
[3,4,5,2,1]=>3
[3,5,1,2,4]=>0
[3,5,1,4,2]=>0
[3,5,2,1,4]=>3
[3,5,2,4,1]=>1
[3,5,4,1,2]=>1
[3,5,4,2,1]=>4
[4,1,2,3,5]=>0
[4,1,2,5,3]=>0
[4,1,3,2,5]=>0
[4,1,3,5,2]=>0
[4,1,5,2,3]=>0
[4,1,5,3,2]=>1
[4,2,1,3,5]=>2
[4,2,1,5,3]=>2
[4,2,3,1,5]=>0
[4,2,3,5,1]=>0
[4,2,5,1,3]=>1
[4,2,5,3,1]=>1
[4,3,1,2,5]=>2
[4,3,1,5,2]=>2
[4,3,2,1,5]=>5
[4,3,2,5,1]=>4
[4,3,5,1,2]=>1
[4,3,5,2,1]=>4
[4,5,1,2,3]=>0
[4,5,1,3,2]=>0
[4,5,2,1,3]=>2
[4,5,2,3,1]=>0
[4,5,3,1,2]=>2
[4,5,3,2,1]=>5
[5,1,2,3,4]=>0
[5,1,2,4,3]=>0
[5,1,3,2,4]=>0
[5,1,3,4,2]=>0
[5,1,4,2,3]=>0
[5,1,4,3,2]=>2
[5,2,1,3,4]=>1
[5,2,1,4,3]=>1
[5,2,3,1,4]=>0
[5,2,3,4,1]=>0
[5,2,4,1,3]=>0
[5,2,4,3,1]=>2
[5,3,1,2,4]=>1
[5,3,1,4,2]=>1
[5,3,2,1,4]=>4
[5,3,2,4,1]=>2
[5,3,4,1,2]=>0
[5,3,4,2,1]=>3
[5,4,1,2,3]=>1
[5,4,1,3,2]=>1
[5,4,2,1,3]=>3
[5,4,2,3,1]=>1
[5,4,3,1,2]=>3
[5,4,3,2,1]=>6
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>0
[1,2,3,5,4,6]=>0
[1,2,3,5,6,4]=>0
[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>1
[1,2,4,3,5,6]=>0
[1,2,4,3,6,5]=>0
[1,2,4,5,3,6]=>0
[1,2,4,5,6,3]=>0
[1,2,4,6,3,5]=>0
[1,2,4,6,5,3]=>1
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>1
[1,2,5,6,3,4]=>0
[1,2,5,6,4,3]=>2
[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>0
[1,2,6,4,3,5]=>1
[1,2,6,4,5,3]=>0
[1,2,6,5,3,4]=>1
[1,2,6,5,4,3]=>3
[1,3,2,4,5,6]=>0
[1,3,2,4,6,5]=>0
[1,3,2,5,4,6]=>0
[1,3,2,5,6,4]=>0
[1,3,2,6,4,5]=>0
[1,3,2,6,5,4]=>1
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>0
[1,3,4,5,2,6]=>0
[1,3,4,5,6,2]=>0
[1,3,4,6,2,5]=>0
[1,3,4,6,5,2]=>1
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>2
[1,3,5,4,6,2]=>1
[1,3,5,6,2,4]=>0
[1,3,5,6,4,2]=>2
[1,3,6,2,4,5]=>0
[1,3,6,2,5,4]=>0
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>0
[1,3,6,5,2,4]=>1
[1,3,6,5,4,2]=>3
[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>0
[1,4,2,5,3,6]=>0
[1,4,2,5,6,3]=>0
[1,4,2,6,3,5]=>0
[1,4,2,6,5,3]=>1
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>3
[1,4,3,5,2,6]=>1
[1,4,3,5,6,2]=>1
[1,4,3,6,2,5]=>2
[1,4,3,6,5,2]=>2
[1,4,5,2,3,6]=>0
[1,4,5,2,6,3]=>0
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>0
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>0
[1,4,6,2,5,3]=>0
[1,4,6,3,2,5]=>3
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>1
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>0
[1,5,2,4,3,6]=>0
[1,5,2,4,6,3]=>0
[1,5,2,6,3,4]=>0
[1,5,2,6,4,3]=>1
[1,5,3,2,4,6]=>2
[1,5,3,2,6,4]=>2
[1,5,3,4,2,6]=>0
[1,5,3,4,6,2]=>0
[1,5,3,6,2,4]=>1
[1,5,3,6,4,2]=>1
[1,5,4,2,3,6]=>2
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>5
[1,5,4,3,6,2]=>4
[1,5,4,6,2,3]=>1
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>0
[1,5,6,2,4,3]=>0
[1,5,6,3,2,4]=>2
[1,5,6,3,4,2]=>0
[1,5,6,4,2,3]=>2
[1,5,6,4,3,2]=>5
[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>0
[1,6,2,4,3,5]=>0
[1,6,2,4,5,3]=>0
[1,6,2,5,3,4]=>0
[1,6,2,5,4,3]=>2
[1,6,3,2,4,5]=>1
[1,6,3,2,5,4]=>1
[1,6,3,4,2,5]=>0
[1,6,3,4,5,2]=>0
[1,6,3,5,2,4]=>0
[1,6,3,5,4,2]=>2
[1,6,4,2,3,5]=>1
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>0
[1,6,4,5,3,2]=>3
[1,6,5,2,3,4]=>1
[1,6,5,2,4,3]=>1
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>1
[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>0
[2,1,3,5,4,6]=>0
[2,1,3,5,6,4]=>0
[2,1,3,6,4,5]=>0
[2,1,3,6,5,4]=>1
[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>0
[2,1,4,5,6,3]=>0
[2,1,4,6,3,5]=>0
[2,1,4,6,5,3]=>1
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>0
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>1
[2,1,5,6,3,4]=>0
[2,1,5,6,4,3]=>2
[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>0
[2,1,6,4,3,5]=>1
[2,1,6,4,5,3]=>0
[2,1,6,5,3,4]=>1
[2,1,6,5,4,3]=>3
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>0
[2,3,1,5,4,6]=>0
[2,3,1,5,6,4]=>0
[2,3,1,6,4,5]=>0
[2,3,1,6,5,4]=>1
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>0
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>0
[2,3,4,6,5,1]=>1
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>1
[2,3,5,6,1,4]=>0
[2,3,5,6,4,1]=>2
[2,3,6,1,4,5]=>0
[2,3,6,1,5,4]=>0
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>0
[2,3,6,5,1,4]=>1
[2,3,6,5,4,1]=>3
[2,4,1,3,5,6]=>0
[2,4,1,3,6,5]=>0
[2,4,1,5,3,6]=>0
[2,4,1,5,6,3]=>0
[2,4,1,6,3,5]=>0
[2,4,1,6,5,3]=>1
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>3
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>2
[2,4,3,6,5,1]=>2
[2,4,5,1,3,6]=>0
[2,4,5,1,6,3]=>0
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>2
[2,4,5,6,1,3]=>0
[2,4,5,6,3,1]=>3
[2,4,6,1,3,5]=>0
[2,4,6,1,5,3]=>0
[2,4,6,3,1,5]=>3
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>1
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>0
[2,5,1,3,6,4]=>0
[2,5,1,4,3,6]=>0
[2,5,1,4,6,3]=>0
[2,5,1,6,3,4]=>0
[2,5,1,6,4,3]=>1
[2,5,3,1,4,6]=>2
[2,5,3,1,6,4]=>2
[2,5,3,4,1,6]=>0
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>1
[2,5,3,6,4,1]=>1
[2,5,4,1,3,6]=>2
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>5
[2,5,4,3,6,1]=>4
[2,5,4,6,1,3]=>1
[2,5,4,6,3,1]=>4
[2,5,6,1,3,4]=>0
[2,5,6,1,4,3]=>0
[2,5,6,3,1,4]=>2
[2,5,6,3,4,1]=>0
[2,5,6,4,1,3]=>2
[2,5,6,4,3,1]=>5
[2,6,1,3,4,5]=>0
[2,6,1,3,5,4]=>0
[2,6,1,4,3,5]=>0
[2,6,1,4,5,3]=>0
[2,6,1,5,3,4]=>0
[2,6,1,5,4,3]=>2
[2,6,3,1,4,5]=>1
[2,6,3,1,5,4]=>1
[2,6,3,4,1,5]=>0
[2,6,3,4,5,1]=>0
[2,6,3,5,1,4]=>0
[2,6,3,5,4,1]=>2
[2,6,4,1,3,5]=>1
[2,6,4,1,5,3]=>1
[2,6,4,3,1,5]=>4
[2,6,4,3,5,1]=>2
[2,6,4,5,1,3]=>0
[2,6,4,5,3,1]=>3
[2,6,5,1,3,4]=>1
[2,6,5,1,4,3]=>1
[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>1
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>6
[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>0
[3,1,2,5,4,6]=>0
[3,1,2,5,6,4]=>0
[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>1
[3,1,4,2,5,6]=>0
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>0
[3,1,4,5,6,2]=>0
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>2
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>0
[3,1,5,6,4,2]=>2
[3,1,6,2,4,5]=>0
[3,1,6,2,5,4]=>0
[3,1,6,4,2,5]=>1
[3,1,6,4,5,2]=>0
[3,1,6,5,2,4]=>1
[3,1,6,5,4,2]=>3
[3,2,1,4,5,6]=>4
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>4
[3,2,1,6,4,5]=>4
[3,2,1,6,5,4]=>5
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>1
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>1
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>2
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>2
[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]=>2
[3,2,6,4,5,1]=>1
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>0
[3,4,1,2,6,5]=>0
[3,4,1,5,2,6]=>0
[3,4,1,5,6,2]=>0
[3,4,1,6,2,5]=>0
[3,4,1,6,5,2]=>1
[3,4,2,1,5,6]=>4
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>2
[3,4,2,5,6,1]=>2
[3,4,2,6,1,5]=>3
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>0
[3,4,5,1,6,2]=>0
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>3
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>4
[3,4,6,1,2,5]=>0
[3,4,6,1,5,2]=>0
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>1
[3,4,6,5,2,1]=>5
[3,5,1,2,4,6]=>0
[3,5,1,2,6,4]=>0
[3,5,1,4,2,6]=>0
[3,5,1,4,6,2]=>0
[3,5,1,6,2,4]=>0
[3,5,1,6,4,2]=>1
[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]=>1
[3,5,2,6,1,4]=>3
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>6
[3,5,4,2,6,1]=>5
[3,5,4,6,1,2]=>1
[3,5,4,6,2,1]=>5
[3,5,6,1,2,4]=>0
[3,5,6,1,4,2]=>0
[3,5,6,2,1,4]=>4
[3,5,6,2,4,1]=>1
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>6
[3,6,1,2,4,5]=>0
[3,6,1,2,5,4]=>0
[3,6,1,4,2,5]=>0
[3,6,1,4,5,2]=>0
[3,6,1,5,2,4]=>0
[3,6,1,5,4,2]=>2
[3,6,2,1,4,5]=>4
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>1
[3,6,2,4,5,1]=>1
[3,6,2,5,1,4]=>2
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>1
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>5
[3,6,4,2,5,1]=>3
[3,6,4,5,1,2]=>0
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>1
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>2
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>7
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>0
[4,1,2,5,3,6]=>0
[4,1,2,5,6,3]=>0
[4,1,2,6,3,5]=>0
[4,1,2,6,5,3]=>1
[4,1,3,2,5,6]=>0
[4,1,3,2,6,5]=>0
[4,1,3,5,2,6]=>0
[4,1,3,5,6,2]=>0
[4,1,3,6,2,5]=>0
[4,1,3,6,5,2]=>1
[4,1,5,2,3,6]=>0
[4,1,5,2,6,3]=>0
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>1
[4,1,5,6,2,3]=>0
[4,1,5,6,3,2]=>2
[4,1,6,2,3,5]=>0
[4,1,6,2,5,3]=>0
[4,1,6,3,2,5]=>1
[4,1,6,3,5,2]=>0
[4,1,6,5,2,3]=>1
[4,1,6,5,3,2]=>3
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>3
[4,2,1,5,3,6]=>3
[4,2,1,5,6,3]=>3
[4,2,1,6,3,5]=>3
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>0
[4,2,3,1,6,5]=>0
[4,2,3,5,1,6]=>0
[4,2,3,5,6,1]=>0
[4,2,3,6,1,5]=>0
[4,2,3,6,5,1]=>1
[4,2,5,1,3,6]=>1
[4,2,5,1,6,3]=>1
[4,2,5,3,1,6]=>2
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>1
[4,2,5,6,3,1]=>2
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>2
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>0
[4,2,6,5,1,3]=>2
[4,2,6,5,3,1]=>3
[4,3,1,2,5,6]=>3
[4,3,1,2,6,5]=>3
[4,3,1,5,2,6]=>3
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>3
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>7
[4,3,2,1,6,5]=>7
[4,3,2,5,1,6]=>5
[4,3,2,5,6,1]=>5
[4,3,2,6,1,5]=>6
[4,3,2,6,5,1]=>6
[4,3,5,1,2,6]=>1
[4,3,5,1,6,2]=>1
[4,3,5,2,1,6]=>5
[4,3,5,2,6,1]=>4
[4,3,5,6,1,2]=>1
[4,3,5,6,2,1]=>5
[4,3,6,1,2,5]=>2
[4,3,6,1,5,2]=>2
[4,3,6,2,1,5]=>6
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>2
[4,3,6,5,2,1]=>6
[4,5,1,2,3,6]=>0
[4,5,1,2,6,3]=>0
[4,5,1,3,2,6]=>0
[4,5,1,3,6,2]=>0
[4,5,1,6,2,3]=>0
[4,5,1,6,3,2]=>1
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>0
[4,5,2,3,6,1]=>0
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>1
[4,5,3,1,2,6]=>3
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>7
[4,5,3,2,6,1]=>6
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>6
[4,5,6,1,2,3]=>0
[4,5,6,1,3,2]=>0
[4,5,6,2,1,3]=>3
[4,5,6,2,3,1]=>0
[4,5,6,3,1,2]=>3
[4,5,6,3,2,1]=>7
[4,6,1,2,3,5]=>0
[4,6,1,2,5,3]=>0
[4,6,1,3,2,5]=>0
[4,6,1,3,5,2]=>0
[4,6,1,5,2,3]=>0
[4,6,1,5,3,2]=>2
[4,6,2,1,3,5]=>3
[4,6,2,1,5,3]=>3
[4,6,2,3,1,5]=>0
[4,6,2,3,5,1]=>0
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>2
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>7
[4,6,3,2,5,1]=>5
[4,6,3,5,1,2]=>1
[4,6,3,5,2,1]=>5
[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>1
[4,6,5,2,1,3]=>4
[4,6,5,2,3,1]=>1
[4,6,5,3,1,2]=>4
[4,6,5,3,2,1]=>8
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>0
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>0
[5,1,2,6,3,4]=>0
[5,1,2,6,4,3]=>1
[5,1,3,2,4,6]=>0
[5,1,3,2,6,4]=>0
[5,1,3,4,2,6]=>0
[5,1,3,4,6,2]=>0
[5,1,3,6,2,4]=>0
[5,1,3,6,4,2]=>1
[5,1,4,2,3,6]=>0
[5,1,4,2,6,3]=>0
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>2
[5,1,4,6,2,3]=>0
[5,1,4,6,3,2]=>3
[5,1,6,2,3,4]=>0
[5,1,6,2,4,3]=>0
[5,1,6,3,2,4]=>1
[5,1,6,3,4,2]=>0
[5,1,6,4,2,3]=>1
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>2
[5,2,1,3,6,4]=>2
[5,2,1,4,3,6]=>2
[5,2,1,4,6,3]=>2
[5,2,1,6,3,4]=>2
[5,2,1,6,4,3]=>3
[5,2,3,1,4,6]=>0
[5,2,3,1,6,4]=>0
[5,2,3,4,1,6]=>0
[5,2,3,4,6,1]=>0
[5,2,3,6,1,4]=>0
[5,2,3,6,4,1]=>1
[5,2,4,1,3,6]=>0
[5,2,4,1,6,3]=>0
[5,2,4,3,1,6]=>3
[5,2,4,3,6,1]=>2
[5,2,4,6,1,3]=>0
[5,2,4,6,3,1]=>3
[5,2,6,1,3,4]=>1
[5,2,6,1,4,3]=>1
[5,2,6,3,1,4]=>1
[5,2,6,3,4,1]=>0
[5,2,6,4,1,3]=>1
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>2
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>2
[5,3,1,4,6,2]=>2
[5,3,1,6,2,4]=>2
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>6
[5,3,2,1,6,4]=>6
[5,3,2,4,1,6]=>3
[5,3,2,4,6,1]=>3
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>0
[5,3,4,1,6,2]=>0
[5,3,4,2,1,6]=>4
[5,3,4,2,6,1]=>3
[5,3,4,6,1,2]=>0
[5,3,4,6,2,1]=>4
[5,3,6,1,2,4]=>1
[5,3,6,1,4,2]=>1
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>1
[5,3,6,4,2,1]=>5
[5,4,1,2,3,6]=>2
[5,4,1,2,6,3]=>2
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>2
[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]=>5
[5,4,2,3,1,6]=>2
[5,4,2,3,6,1]=>2
[5,4,2,6,1,3]=>4
[5,4,2,6,3,1]=>3
[5,4,3,1,2,6]=>5
[5,4,3,1,6,2]=>5
[5,4,3,2,1,6]=>9
[5,4,3,2,6,1]=>8
[5,4,3,6,1,2]=>4
[5,4,3,6,2,1]=>8
[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>1
[5,4,6,2,1,3]=>4
[5,4,6,2,3,1]=>1
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>8
[5,6,1,2,3,4]=>0
[5,6,1,2,4,3]=>0
[5,6,1,3,2,4]=>0
[5,6,1,3,4,2]=>0
[5,6,1,4,2,3]=>0
[5,6,1,4,3,2]=>3
[5,6,2,1,3,4]=>2
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>0
[5,6,2,3,4,1]=>0
[5,6,2,4,1,3]=>0
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>2
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>6
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>0
[5,6,3,4,2,1]=>4
[5,6,4,1,2,3]=>2
[5,6,4,1,3,2]=>2
[5,6,4,2,1,3]=>5
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>5
[5,6,4,3,2,1]=>9
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>0
[6,1,2,4,3,5]=>0
[6,1,2,4,5,3]=>0
[6,1,2,5,3,4]=>0
[6,1,2,5,4,3]=>2
[6,1,3,2,4,5]=>0
[6,1,3,2,5,4]=>0
[6,1,3,4,2,5]=>0
[6,1,3,4,5,2]=>0
[6,1,3,5,2,4]=>0
[6,1,3,5,4,2]=>2
[6,1,4,2,3,5]=>0
[6,1,4,2,5,3]=>0
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>0
[6,1,4,5,3,2]=>3
[6,1,5,2,3,4]=>0
[6,1,5,2,4,3]=>0
[6,1,5,3,2,4]=>2
[6,1,5,3,4,2]=>0
[6,1,5,4,2,3]=>2
[6,1,5,4,3,2]=>5
[6,2,1,3,4,5]=>1
[6,2,1,3,5,4]=>1
[6,2,1,4,3,5]=>1
[6,2,1,4,5,3]=>1
[6,2,1,5,3,4]=>1
[6,2,1,5,4,3]=>3
[6,2,3,1,4,5]=>0
[6,2,3,1,5,4]=>0
[6,2,3,4,1,5]=>0
[6,2,3,4,5,1]=>0
[6,2,3,5,1,4]=>0
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>0
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>3
[6,2,4,3,5,1]=>1
[6,2,4,5,1,3]=>0
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>0
[6,2,5,1,4,3]=>0
[6,2,5,3,1,4]=>2
[6,2,5,3,4,1]=>0
[6,2,5,4,1,3]=>2
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>1
[6,3,1,2,5,4]=>1
[6,3,1,4,2,5]=>1
[6,3,1,4,5,2]=>1
[6,3,1,5,2,4]=>1
[6,3,1,5,4,2]=>3
[6,3,2,1,4,5]=>5
[6,3,2,1,5,4]=>5
[6,3,2,4,1,5]=>2
[6,3,2,4,5,1]=>2
[6,3,2,5,1,4]=>3
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>0
[6,3,4,1,5,2]=>0
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>2
[6,3,4,5,1,2]=>0
[6,3,4,5,2,1]=>4
[6,3,5,1,2,4]=>0
[6,3,5,1,4,2]=>0
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>2
[6,3,5,4,2,1]=>6
[6,4,1,2,3,5]=>1
[6,4,1,2,5,3]=>1
[6,4,1,3,2,5]=>1
[6,4,1,3,5,2]=>1
[6,4,1,5,2,3]=>1
[6,4,1,5,3,2]=>3
[6,4,2,1,3,5]=>4
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>1
[6,4,2,5,1,3]=>2
[6,4,2,5,3,1]=>3
[6,4,3,1,2,5]=>4
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>8
[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]=>0
[6,4,5,1,3,2]=>0
[6,4,5,2,1,3]=>3
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>3
[6,4,5,3,2,1]=>7
[6,5,1,2,3,4]=>1
[6,5,1,2,4,3]=>1
[6,5,1,3,2,4]=>1
[6,5,1,3,4,2]=>1
[6,5,1,4,2,3]=>1
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>1
[6,5,2,3,4,1]=>1
[6,5,2,4,1,3]=>1
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>3
[6,5,3,2,1,4]=>7
[6,5,3,2,4,1]=>4
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>5
[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]=>6
[6,5,4,3,2,1]=>10
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>0
[1,2,3,4,6,5,7]=>0
[1,2,3,4,6,7,5]=>0
[1,2,3,4,7,5,6]=>0
[1,2,3,4,7,6,5]=>1
[1,2,3,5,4,6,7]=>0
[1,2,3,5,4,7,6]=>0
[1,2,3,5,6,4,7]=>0
[1,2,3,5,6,7,4]=>0
[1,2,3,5,7,4,6]=>0
[1,2,3,5,7,6,4]=>1
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,3,6,5,4,7]=>2
[1,2,3,6,5,7,4]=>1
[1,2,3,6,7,4,5]=>0
[1,2,3,6,7,5,4]=>2
[1,2,3,7,4,5,6]=>0
[1,2,3,7,4,6,5]=>0
[1,2,3,7,5,4,6]=>1
[1,2,3,7,5,6,4]=>0
[1,2,3,7,6,4,5]=>1
[1,2,3,7,6,5,4]=>3
[1,2,4,3,5,6,7]=>0
[1,2,4,3,5,7,6]=>0
[1,2,4,3,6,5,7]=>0
[1,2,4,3,6,7,5]=>0
[1,2,4,3,7,5,6]=>0
[1,2,4,3,7,6,5]=>1
[1,2,4,5,3,6,7]=>0
[1,2,4,5,3,7,6]=>0
[1,2,4,5,6,3,7]=>0
[1,2,4,5,6,7,3]=>0
[1,2,4,5,7,3,6]=>0
[1,2,4,5,7,6,3]=>1
[1,2,4,6,3,5,7]=>0
[1,2,4,6,3,7,5]=>0
[1,2,4,6,5,3,7]=>2
[1,2,4,6,5,7,3]=>1
[1,2,4,6,7,3,5]=>0
[1,2,4,6,7,5,3]=>2
[1,2,4,7,3,5,6]=>0
[1,2,4,7,3,6,5]=>0
[1,2,4,7,5,3,6]=>1
[1,2,4,7,5,6,3]=>0
[1,2,4,7,6,3,5]=>1
[1,2,4,7,6,5,3]=>3
[1,2,5,3,4,6,7]=>0
[1,2,5,3,4,7,6]=>0
[1,2,5,3,6,4,7]=>0
[1,2,5,3,6,7,4]=>0
[1,2,5,3,7,4,6]=>0
[1,2,5,3,7,6,4]=>1
[1,2,5,4,3,6,7]=>3
[1,2,5,4,3,7,6]=>3
[1,2,5,4,6,3,7]=>1
[1,2,5,4,6,7,3]=>1
[1,2,5,4,7,3,6]=>2
[1,2,5,4,7,6,3]=>2
[1,2,5,6,3,4,7]=>0
[1,2,5,6,3,7,4]=>0
[1,2,5,6,4,3,7]=>3
[1,2,5,6,4,7,3]=>2
[1,2,5,6,7,3,4]=>0
[1,2,5,6,7,4,3]=>3
[1,2,5,7,3,4,6]=>0
[1,2,5,7,3,6,4]=>0
[1,2,5,7,4,3,6]=>3
[1,2,5,7,4,6,3]=>1
[1,2,5,7,6,3,4]=>1
[1,2,5,7,6,4,3]=>4
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>0
[1,2,6,3,5,4,7]=>0
[1,2,6,3,5,7,4]=>0
[1,2,6,3,7,4,5]=>0
[1,2,6,3,7,5,4]=>1
[1,2,6,4,3,5,7]=>2
[1,2,6,4,3,7,5]=>2
[1,2,6,4,5,3,7]=>0
[1,2,6,4,5,7,3]=>0
[1,2,6,4,7,3,5]=>1
[1,2,6,4,7,5,3]=>1
[1,2,6,5,3,4,7]=>2
[1,2,6,5,3,7,4]=>2
[1,2,6,5,4,3,7]=>5
[1,2,6,5,4,7,3]=>4
[1,2,6,5,7,3,4]=>1
[1,2,6,5,7,4,3]=>4
[1,2,6,7,3,4,5]=>0
[1,2,6,7,3,5,4]=>0
[1,2,6,7,4,3,5]=>2
[1,2,6,7,4,5,3]=>0
[1,2,6,7,5,3,4]=>2
[1,2,6,7,5,4,3]=>5
[1,2,7,3,4,5,6]=>0
[1,2,7,3,4,6,5]=>0
[1,2,7,3,5,4,6]=>0
[1,2,7,3,5,6,4]=>0
[1,2,7,3,6,4,5]=>0
[1,2,7,3,6,5,4]=>2
[1,2,7,4,3,5,6]=>1
[1,2,7,4,3,6,5]=>1
[1,2,7,4,5,3,6]=>0
[1,2,7,4,5,6,3]=>0
[1,2,7,4,6,3,5]=>0
[1,2,7,4,6,5,3]=>2
[1,2,7,5,3,4,6]=>1
[1,2,7,5,3,6,4]=>1
[1,2,7,5,4,3,6]=>4
[1,2,7,5,4,6,3]=>2
[1,2,7,5,6,3,4]=>0
[1,2,7,5,6,4,3]=>3
[1,2,7,6,3,4,5]=>1
[1,2,7,6,3,5,4]=>1
[1,2,7,6,4,3,5]=>3
[1,2,7,6,4,5,3]=>1
[1,2,7,6,5,3,4]=>3
[1,2,7,6,5,4,3]=>6
[1,3,2,4,5,6,7]=>0
[1,3,2,4,5,7,6]=>0
[1,3,2,4,6,5,7]=>0
[1,3,2,4,6,7,5]=>0
[1,3,2,4,7,5,6]=>0
[1,3,2,4,7,6,5]=>1
[1,3,2,5,4,6,7]=>0
[1,3,2,5,4,7,6]=>0
[1,3,2,5,6,4,7]=>0
[1,3,2,5,6,7,4]=>0
[1,3,2,5,7,4,6]=>0
[1,3,2,5,7,6,4]=>1
[1,3,2,6,4,5,7]=>0
[1,3,2,6,4,7,5]=>0
[1,3,2,6,5,4,7]=>2
[1,3,2,6,5,7,4]=>1
[1,3,2,6,7,4,5]=>0
[1,3,2,6,7,5,4]=>2
[1,3,2,7,4,5,6]=>0
[1,3,2,7,4,6,5]=>0
[1,3,2,7,5,4,6]=>1
[1,3,2,7,5,6,4]=>0
[1,3,2,7,6,4,5]=>1
[1,3,2,7,6,5,4]=>3
[1,3,4,2,5,6,7]=>0
[1,3,4,2,5,7,6]=>0
[1,3,4,2,6,5,7]=>0
[1,3,4,2,6,7,5]=>0
[1,3,4,2,7,5,6]=>0
[1,3,4,2,7,6,5]=>1
[1,3,4,5,2,6,7]=>0
[1,3,4,5,2,7,6]=>0
[1,3,4,5,6,2,7]=>0
[1,3,4,5,6,7,2]=>0
[1,3,4,5,7,2,6]=>0
[1,3,4,5,7,6,2]=>1
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>0
[1,3,4,6,5,2,7]=>2
[1,3,4,6,5,7,2]=>1
[1,3,4,6,7,2,5]=>0
[1,3,4,6,7,5,2]=>2
[1,3,4,7,2,5,6]=>0
[1,3,4,7,2,6,5]=>0
[1,3,4,7,5,2,6]=>1
[1,3,4,7,5,6,2]=>0
[1,3,4,7,6,2,5]=>1
[1,3,4,7,6,5,2]=>3
[1,3,5,2,4,6,7]=>0
[1,3,5,2,4,7,6]=>0
[1,3,5,2,6,4,7]=>0
[1,3,5,2,6,7,4]=>0
[1,3,5,2,7,4,6]=>0
[1,3,5,2,7,6,4]=>1
[1,3,5,4,2,6,7]=>3
[1,3,5,4,2,7,6]=>3
[1,3,5,4,6,2,7]=>1
[1,3,5,4,6,7,2]=>1
[1,3,5,4,7,2,6]=>2
[1,3,5,4,7,6,2]=>2
[1,3,5,6,2,4,7]=>0
[1,3,5,6,2,7,4]=>0
[1,3,5,6,4,2,7]=>3
[1,3,5,6,4,7,2]=>2
[1,3,5,6,7,2,4]=>0
[1,3,5,6,7,4,2]=>3
[1,3,5,7,2,4,6]=>0
[1,3,5,7,2,6,4]=>0
[1,3,5,7,4,2,6]=>3
[1,3,5,7,4,6,2]=>1
[1,3,5,7,6,2,4]=>1
[1,3,5,7,6,4,2]=>4
[1,3,6,2,4,5,7]=>0
[1,3,6,2,4,7,5]=>0
[1,3,6,2,5,4,7]=>0
[1,3,6,2,5,7,4]=>0
[1,3,6,2,7,4,5]=>0
[1,3,6,2,7,5,4]=>1
[1,3,6,4,2,5,7]=>2
[1,3,6,4,2,7,5]=>2
[1,3,6,4,5,2,7]=>0
[1,3,6,4,5,7,2]=>0
[1,3,6,4,7,2,5]=>1
[1,3,6,4,7,5,2]=>1
[1,3,6,5,2,4,7]=>2
[1,3,6,5,2,7,4]=>2
[1,3,6,5,4,2,7]=>5
[1,3,6,5,4,7,2]=>4
[1,3,6,5,7,2,4]=>1
[1,3,6,5,7,4,2]=>4
[1,3,6,7,2,4,5]=>0
[1,3,6,7,2,5,4]=>0
[1,3,6,7,4,2,5]=>2
[1,3,6,7,4,5,2]=>0
[1,3,6,7,5,2,4]=>2
[1,3,6,7,5,4,2]=>5
[1,3,7,2,4,5,6]=>0
[1,3,7,2,4,6,5]=>0
[1,3,7,2,5,4,6]=>0
[1,3,7,2,5,6,4]=>0
[1,3,7,2,6,4,5]=>0
[1,3,7,2,6,5,4]=>2
[1,3,7,4,2,5,6]=>1
[1,3,7,4,2,6,5]=>1
[1,3,7,4,5,2,6]=>0
[1,3,7,4,5,6,2]=>0
[1,3,7,4,6,2,5]=>0
[1,3,7,4,6,5,2]=>2
[1,3,7,5,2,4,6]=>1
[1,3,7,5,2,6,4]=>1
[1,3,7,5,4,2,6]=>4
[1,3,7,5,4,6,2]=>2
[1,3,7,5,6,2,4]=>0
[1,3,7,5,6,4,2]=>3
[1,3,7,6,2,4,5]=>1
[1,3,7,6,2,5,4]=>1
[1,3,7,6,4,2,5]=>3
[1,3,7,6,4,5,2]=>1
[1,3,7,6,5,2,4]=>3
[1,3,7,6,5,4,2]=>6
[1,4,2,3,5,6,7]=>0
[1,4,2,3,5,7,6]=>0
[1,4,2,3,6,5,7]=>0
[1,4,2,3,6,7,5]=>0
[1,4,2,3,7,5,6]=>0
[1,4,2,3,7,6,5]=>1
[1,4,2,5,3,6,7]=>0
[1,4,2,5,3,7,6]=>0
[1,4,2,5,6,3,7]=>0
[1,4,2,5,6,7,3]=>0
[1,4,2,5,7,3,6]=>0
[1,4,2,5,7,6,3]=>1
[1,4,2,6,3,5,7]=>0
[1,4,2,6,3,7,5]=>0
[1,4,2,6,5,3,7]=>2
[1,4,2,6,5,7,3]=>1
[1,4,2,6,7,3,5]=>0
[1,4,2,6,7,5,3]=>2
[1,4,2,7,3,5,6]=>0
[1,4,2,7,3,6,5]=>0
[1,4,2,7,5,3,6]=>1
[1,4,2,7,5,6,3]=>0
[1,4,2,7,6,3,5]=>1
[1,4,2,7,6,5,3]=>3
[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]=>5
[1,4,3,5,2,6,7]=>1
[1,4,3,5,2,7,6]=>1
[1,4,3,5,6,2,7]=>1
[1,4,3,5,6,7,2]=>1
[1,4,3,5,7,2,6]=>1
[1,4,3,5,7,6,2]=>2
[1,4,3,6,2,5,7]=>2
[1,4,3,6,2,7,5]=>2
[1,4,3,6,5,2,7]=>3
[1,4,3,6,5,7,2]=>2
[1,4,3,6,7,2,5]=>2
[1,4,3,6,7,5,2]=>3
[1,4,3,7,2,5,6]=>3
[1,4,3,7,2,6,5]=>3
[1,4,3,7,5,2,6]=>2
[1,4,3,7,5,6,2]=>1
[1,4,3,7,6,2,5]=>3
[1,4,3,7,6,5,2]=>4
[1,4,5,2,3,6,7]=>0
[1,4,5,2,3,7,6]=>0
[1,4,5,2,6,3,7]=>0
[1,4,5,2,6,7,3]=>0
[1,4,5,2,7,3,6]=>0
[1,4,5,2,7,6,3]=>1
[1,4,5,3,2,6,7]=>4
[1,4,5,3,2,7,6]=>4
[1,4,5,3,6,2,7]=>2
[1,4,5,3,6,7,2]=>2
[1,4,5,3,7,2,6]=>3
[1,4,5,3,7,6,2]=>3
[1,4,5,6,2,3,7]=>0
[1,4,5,6,2,7,3]=>0
[1,4,5,6,3,2,7]=>4
[1,4,5,6,3,7,2]=>3
[1,4,5,6,7,2,3]=>0
[1,4,5,6,7,3,2]=>4
[1,4,5,7,2,3,6]=>0
[1,4,5,7,2,6,3]=>0
[1,4,5,7,3,2,6]=>4
[1,4,5,7,3,6,2]=>2
[1,4,5,7,6,2,3]=>1
[1,4,5,7,6,3,2]=>5
[1,4,6,2,3,5,7]=>0
[1,4,6,2,3,7,5]=>0
[1,4,6,2,5,3,7]=>0
[1,4,6,2,5,7,3]=>0
[1,4,6,2,7,3,5]=>0
[1,4,6,2,7,5,3]=>1
[1,4,6,3,2,5,7]=>4
[1,4,6,3,2,7,5]=>4
[1,4,6,3,5,2,7]=>1
[1,4,6,3,5,7,2]=>1
[1,4,6,3,7,2,5]=>3
[1,4,6,3,7,5,2]=>2
[1,4,6,5,2,3,7]=>2
[1,4,6,5,2,7,3]=>2
[1,4,6,5,3,2,7]=>6
[1,4,6,5,3,7,2]=>5
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 simsun double descents of a permutation.
The restriction of a permutation $\pi$ to $[k] = \{1,\ldots,k\}$ is given in one-line notation by the subword of $\pi$ of letters in $[k]$.
A simsun double descent of a permutation $\pi$ is a double descent of any restriction of $\pi$ to $[1,\ldots,k]$ for some $k$. (Note here that the same double descent can appear in multiple restrictions!)
The restriction of a permutation $\pi$ to $[k] = \{1,\ldots,k\}$ is given in one-line notation by the subword of $\pi$ of letters in $[k]$.
A simsun double descent of a permutation $\pi$ is a double descent of any restriction of $\pi$ to $[1,\ldots,k]$ for some $k$. (Note here that the same double descent can appear in multiple restrictions!)
References
[1] Sundaram, S. The homology representations of the symmetric group on Cohen-Macaulay subposets of the partition lattice MathSciNet:1273390
[2] Ma, S.-M., Yeh, Y.-N. The peak statistics on simsun permutations arXiv:1601.06505
[2] Ma, S.-M., Yeh, Y.-N. The peak statistics on simsun permutations arXiv:1601.06505
Code
def restriction(pi,k):
return Permutation([pi[i] for i in range(len(pi)) if pi[i] <= k])
def double_descents(pi):
return sum( 1 for i in range(len(pi)-2) if pi[i]>pi[i+1]>pi[i+2] )
def statistic(pi):
return sum( double_descents(restriction(pi,k)) for k in [3..len(pi)] )
Created
Jan 26, 2016 at 21:14 by Christian Stump
Updated
May 10, 2019 at 17:28 by Henning Ulfarsson
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!