Identifier
- St000124: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>2
[3,2,1]=>0
[1,2,3,4]=>1
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>1
[1,4,2,3]=>2
[1,4,3,2]=>0
[2,1,3,4]=>1
[2,1,4,3]=>1
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>2
[2,4,3,1]=>0
[3,1,2,4]=>2
[3,1,4,2]=>2
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>2
[3,4,2,1]=>0
[4,1,2,3]=>6
[4,1,3,2]=>0
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,2,3,4,5]=>1
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>1
[1,2,5,3,4]=>2
[1,2,5,4,3]=>0
[1,3,2,4,5]=>1
[1,3,2,5,4]=>1
[1,3,4,2,5]=>1
[1,3,4,5,2]=>1
[1,3,5,2,4]=>2
[1,3,5,4,2]=>0
[1,4,2,3,5]=>2
[1,4,2,5,3]=>2
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>2
[1,4,5,3,2]=>0
[1,5,2,3,4]=>6
[1,5,2,4,3]=>0
[1,5,3,2,4]=>0
[1,5,3,4,2]=>0
[1,5,4,2,3]=>0
[1,5,4,3,2]=>0
[2,1,3,4,5]=>1
[2,1,3,5,4]=>1
[2,1,4,3,5]=>1
[2,1,4,5,3]=>1
[2,1,5,3,4]=>2
[2,1,5,4,3]=>0
[2,3,1,4,5]=>1
[2,3,1,5,4]=>1
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>2
[2,3,5,4,1]=>0
[2,4,1,3,5]=>2
[2,4,1,5,3]=>2
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>2
[2,4,5,3,1]=>0
[2,5,1,3,4]=>6
[2,5,1,4,3]=>0
[2,5,3,1,4]=>0
[2,5,3,4,1]=>0
[2,5,4,1,3]=>0
[2,5,4,3,1]=>0
[3,1,2,4,5]=>2
[3,1,2,5,4]=>2
[3,1,4,2,5]=>2
[3,1,4,5,2]=>2
[3,1,5,2,4]=>4
[3,1,5,4,2]=>0
[3,2,1,4,5]=>0
[3,2,1,5,4]=>0
[3,2,4,1,5]=>0
[3,2,4,5,1]=>0
[3,2,5,1,4]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>2
[3,4,1,5,2]=>2
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[3,4,5,1,2]=>2
[3,4,5,2,1]=>0
[3,5,1,2,4]=>6
[3,5,1,4,2]=>0
[3,5,2,1,4]=>0
[3,5,2,4,1]=>0
[3,5,4,1,2]=>0
[3,5,4,2,1]=>0
[4,1,2,3,5]=>6
[4,1,2,5,3]=>6
[4,1,3,2,5]=>0
[4,1,3,5,2]=>0
[4,1,5,2,3]=>6
[4,1,5,3,2]=>0
[4,2,1,3,5]=>0
[4,2,1,5,3]=>0
[4,2,3,1,5]=>0
[4,2,3,5,1]=>0
[4,2,5,1,3]=>0
[4,2,5,3,1]=>0
[4,3,1,2,5]=>0
[4,3,1,5,2]=>0
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>0
[4,3,5,2,1]=>0
[4,5,1,2,3]=>6
[4,5,1,3,2]=>0
[4,5,2,1,3]=>0
[4,5,2,3,1]=>0
[4,5,3,1,2]=>0
[4,5,3,2,1]=>0
[5,1,2,3,4]=>24
[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]=>0
[5,2,1,3,4]=>0
[5,2,1,4,3]=>0
[5,2,3,1,4]=>0
[5,2,3,4,1]=>0
[5,2,4,1,3]=>0
[5,2,4,3,1]=>0
[5,3,1,2,4]=>0
[5,3,1,4,2]=>0
[5,3,2,1,4]=>0
[5,3,2,4,1]=>0
[5,3,4,1,2]=>0
[5,3,4,2,1]=>0
[5,4,1,2,3]=>0
[5,4,1,3,2]=>0
[5,4,2,1,3]=>0
[5,4,2,3,1]=>0
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>1
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>0
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>1
[1,2,4,5,3,6]=>1
[1,2,4,5,6,3]=>1
[1,2,4,6,3,5]=>2
[1,2,4,6,5,3]=>0
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>0
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>0
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>0
[1,2,6,4,3,5]=>0
[1,2,6,4,5,3]=>0
[1,2,6,5,3,4]=>0
[1,2,6,5,4,3]=>0
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>1
[1,3,2,5,4,6]=>1
[1,3,2,5,6,4]=>1
[1,3,2,6,4,5]=>2
[1,3,2,6,5,4]=>0
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>1
[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>2
[1,3,4,6,5,2]=>0
[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>2
[1,3,5,4,2,6]=>0
[1,3,5,4,6,2]=>0
[1,3,5,6,2,4]=>2
[1,3,5,6,4,2]=>0
[1,3,6,2,4,5]=>6
[1,3,6,2,5,4]=>0
[1,3,6,4,2,5]=>0
[1,3,6,4,5,2]=>0
[1,3,6,5,2,4]=>0
[1,3,6,5,4,2]=>0
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>2
[1,4,2,5,3,6]=>2
[1,4,2,5,6,3]=>2
[1,4,2,6,3,5]=>4
[1,4,2,6,5,3]=>0
[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>0
[1,4,3,5,2,6]=>0
[1,4,3,5,6,2]=>0
[1,4,3,6,2,5]=>0
[1,4,3,6,5,2]=>0
[1,4,5,2,3,6]=>2
[1,4,5,2,6,3]=>2
[1,4,5,3,2,6]=>0
[1,4,5,3,6,2]=>0
[1,4,5,6,2,3]=>2
[1,4,5,6,3,2]=>0
[1,4,6,2,3,5]=>6
[1,4,6,2,5,3]=>0
[1,4,6,3,2,5]=>0
[1,4,6,3,5,2]=>0
[1,4,6,5,2,3]=>0
[1,4,6,5,3,2]=>0
[1,5,2,3,4,6]=>6
[1,5,2,3,6,4]=>6
[1,5,2,4,3,6]=>0
[1,5,2,4,6,3]=>0
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>0
[1,5,3,2,4,6]=>0
[1,5,3,2,6,4]=>0
[1,5,3,4,2,6]=>0
[1,5,3,4,6,2]=>0
[1,5,3,6,2,4]=>0
[1,5,3,6,4,2]=>0
[1,5,4,2,3,6]=>0
[1,5,4,2,6,3]=>0
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>0
[1,5,4,6,2,3]=>0
[1,5,4,6,3,2]=>0
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>0
[1,5,6,3,2,4]=>0
[1,5,6,3,4,2]=>0
[1,5,6,4,2,3]=>0
[1,5,6,4,3,2]=>0
[1,6,2,3,4,5]=>24
[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]=>0
[1,6,3,2,4,5]=>0
[1,6,3,2,5,4]=>0
[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]=>0
[1,6,4,2,3,5]=>0
[1,6,4,2,5,3]=>0
[1,6,4,3,2,5]=>0
[1,6,4,3,5,2]=>0
[1,6,4,5,2,3]=>0
[1,6,4,5,3,2]=>0
[1,6,5,2,3,4]=>0
[1,6,5,2,4,3]=>0
[1,6,5,3,2,4]=>0
[1,6,5,3,4,2]=>0
[1,6,5,4,2,3]=>0
[1,6,5,4,3,2]=>0
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>1
[2,1,3,5,4,6]=>1
[2,1,3,5,6,4]=>1
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>0
[2,1,4,3,5,6]=>1
[2,1,4,3,6,5]=>1
[2,1,4,5,3,6]=>1
[2,1,4,5,6,3]=>1
[2,1,4,6,3,5]=>2
[2,1,4,6,5,3]=>0
[2,1,5,3,4,6]=>2
[2,1,5,3,6,4]=>2
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>0
[2,1,5,6,3,4]=>2
[2,1,5,6,4,3]=>0
[2,1,6,3,4,5]=>6
[2,1,6,3,5,4]=>0
[2,1,6,4,3,5]=>0
[2,1,6,4,5,3]=>0
[2,1,6,5,3,4]=>0
[2,1,6,5,4,3]=>0
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>1
[2,3,1,5,4,6]=>1
[2,3,1,5,6,4]=>1
[2,3,1,6,4,5]=>2
[2,3,1,6,5,4]=>0
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>1
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>2
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>2
[2,3,5,1,6,4]=>2
[2,3,5,4,1,6]=>0
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>2
[2,3,5,6,4,1]=>0
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>0
[2,3,6,4,1,5]=>0
[2,3,6,4,5,1]=>0
[2,3,6,5,1,4]=>0
[2,3,6,5,4,1]=>0
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>2
[2,4,1,5,3,6]=>2
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>4
[2,4,1,6,5,3]=>0
[2,4,3,1,5,6]=>0
[2,4,3,1,6,5]=>0
[2,4,3,5,1,6]=>0
[2,4,3,5,6,1]=>0
[2,4,3,6,1,5]=>0
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>2
[2,4,5,1,6,3]=>2
[2,4,5,3,1,6]=>0
[2,4,5,3,6,1]=>0
[2,4,5,6,1,3]=>2
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>0
[2,4,6,3,1,5]=>0
[2,4,6,3,5,1]=>0
[2,4,6,5,1,3]=>0
[2,4,6,5,3,1]=>0
[2,5,1,3,4,6]=>6
[2,5,1,3,6,4]=>6
[2,5,1,4,3,6]=>0
[2,5,1,4,6,3]=>0
[2,5,1,6,3,4]=>6
[2,5,1,6,4,3]=>0
[2,5,3,1,4,6]=>0
[2,5,3,1,6,4]=>0
[2,5,3,4,1,6]=>0
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>0
[2,5,3,6,4,1]=>0
[2,5,4,1,3,6]=>0
[2,5,4,1,6,3]=>0
[2,5,4,3,1,6]=>0
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>0
[2,5,4,6,3,1]=>0
[2,5,6,1,3,4]=>6
[2,5,6,1,4,3]=>0
[2,5,6,3,1,4]=>0
[2,5,6,3,4,1]=>0
[2,5,6,4,1,3]=>0
[2,5,6,4,3,1]=>0
[2,6,1,3,4,5]=>24
[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]=>0
[2,6,3,1,4,5]=>0
[2,6,3,1,5,4]=>0
[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]=>0
[2,6,4,1,3,5]=>0
[2,6,4,1,5,3]=>0
[2,6,4,3,1,5]=>0
[2,6,4,3,5,1]=>0
[2,6,4,5,1,3]=>0
[2,6,4,5,3,1]=>0
[2,6,5,1,3,4]=>0
[2,6,5,1,4,3]=>0
[2,6,5,3,1,4]=>0
[2,6,5,3,4,1]=>0
[2,6,5,4,1,3]=>0
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>2
[3,1,2,5,4,6]=>2
[3,1,2,5,6,4]=>2
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>0
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>2
[3,1,4,5,2,6]=>2
[3,1,4,5,6,2]=>2
[3,1,4,6,2,5]=>4
[3,1,4,6,5,2]=>0
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>4
[3,1,5,4,2,6]=>0
[3,1,5,4,6,2]=>0
[3,1,5,6,2,4]=>4
[3,1,5,6,4,2]=>0
[3,1,6,2,4,5]=>12
[3,1,6,2,5,4]=>0
[3,1,6,4,2,5]=>0
[3,1,6,4,5,2]=>0
[3,1,6,5,2,4]=>0
[3,1,6,5,4,2]=>0
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>0
[3,2,1,5,4,6]=>0
[3,2,1,5,6,4]=>0
[3,2,1,6,4,5]=>0
[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>0
[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>0
[3,2,4,6,5,1]=>0
[3,2,5,1,4,6]=>0
[3,2,5,1,6,4]=>0
[3,2,5,4,1,6]=>0
[3,2,5,4,6,1]=>0
[3,2,5,6,1,4]=>0
[3,2,5,6,4,1]=>0
[3,2,6,1,4,5]=>0
[3,2,6,1,5,4]=>0
[3,2,6,4,1,5]=>0
[3,2,6,4,5,1]=>0
[3,2,6,5,1,4]=>0
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>2
[3,4,1,6,2,5]=>4
[3,4,1,6,5,2]=>0
[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>0
[3,4,2,5,1,6]=>0
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>0
[3,4,2,6,5,1]=>0
[3,4,5,1,2,6]=>2
[3,4,5,1,6,2]=>2
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>2
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>6
[3,4,6,1,5,2]=>0
[3,4,6,2,1,5]=>0
[3,4,6,2,5,1]=>0
[3,4,6,5,1,2]=>0
[3,4,6,5,2,1]=>0
[3,5,1,2,4,6]=>6
[3,5,1,2,6,4]=>6
[3,5,1,4,2,6]=>0
[3,5,1,4,6,2]=>0
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>0
[3,5,2,1,4,6]=>0
[3,5,2,1,6,4]=>0
[3,5,2,4,1,6]=>0
[3,5,2,4,6,1]=>0
[3,5,2,6,1,4]=>0
[3,5,2,6,4,1]=>0
[3,5,4,1,2,6]=>0
[3,5,4,1,6,2]=>0
[3,5,4,2,1,6]=>0
[3,5,4,2,6,1]=>0
[3,5,4,6,1,2]=>0
[3,5,4,6,2,1]=>0
[3,5,6,1,2,4]=>6
[3,5,6,1,4,2]=>0
[3,5,6,2,1,4]=>0
[3,5,6,2,4,1]=>0
[3,5,6,4,1,2]=>0
[3,5,6,4,2,1]=>0
[3,6,1,2,4,5]=>24
[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]=>0
[3,6,2,1,4,5]=>0
[3,6,2,1,5,4]=>0
[3,6,2,4,1,5]=>0
[3,6,2,4,5,1]=>0
[3,6,2,5,1,4]=>0
[3,6,2,5,4,1]=>0
[3,6,4,1,2,5]=>0
[3,6,4,1,5,2]=>0
[3,6,4,2,1,5]=>0
[3,6,4,2,5,1]=>0
[3,6,4,5,1,2]=>0
[3,6,4,5,2,1]=>0
[3,6,5,1,2,4]=>0
[3,6,5,1,4,2]=>0
[3,6,5,2,1,4]=>0
[3,6,5,2,4,1]=>0
[3,6,5,4,1,2]=>0
[3,6,5,4,2,1]=>0
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>6
[4,1,2,5,3,6]=>6
[4,1,2,5,6,3]=>6
[4,1,2,6,3,5]=>12
[4,1,2,6,5,3]=>0
[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]=>0
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>6
[4,1,5,3,2,6]=>0
[4,1,5,3,6,2]=>0
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>0
[4,1,6,2,3,5]=>18
[4,1,6,2,5,3]=>0
[4,1,6,3,2,5]=>0
[4,1,6,3,5,2]=>0
[4,1,6,5,2,3]=>0
[4,1,6,5,3,2]=>0
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>0
[4,2,1,5,3,6]=>0
[4,2,1,5,6,3]=>0
[4,2,1,6,3,5]=>0
[4,2,1,6,5,3]=>0
[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]=>0
[4,2,5,1,3,6]=>0
[4,2,5,1,6,3]=>0
[4,2,5,3,1,6]=>0
[4,2,5,3,6,1]=>0
[4,2,5,6,1,3]=>0
[4,2,5,6,3,1]=>0
[4,2,6,1,3,5]=>0
[4,2,6,1,5,3]=>0
[4,2,6,3,1,5]=>0
[4,2,6,3,5,1]=>0
[4,2,6,5,1,3]=>0
[4,2,6,5,3,1]=>0
[4,3,1,2,5,6]=>0
[4,3,1,2,6,5]=>0
[4,3,1,5,2,6]=>0
[4,3,1,5,6,2]=>0
[4,3,1,6,2,5]=>0
[4,3,1,6,5,2]=>0
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>0
[4,3,2,5,1,6]=>0
[4,3,2,5,6,1]=>0
[4,3,2,6,1,5]=>0
[4,3,2,6,5,1]=>0
[4,3,5,1,2,6]=>0
[4,3,5,1,6,2]=>0
[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>0
[4,3,5,6,1,2]=>0
[4,3,5,6,2,1]=>0
[4,3,6,1,2,5]=>0
[4,3,6,1,5,2]=>0
[4,3,6,2,1,5]=>0
[4,3,6,2,5,1]=>0
[4,3,6,5,1,2]=>0
[4,3,6,5,2,1]=>0
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>6
[4,5,1,3,2,6]=>0
[4,5,1,3,6,2]=>0
[4,5,1,6,2,3]=>6
[4,5,1,6,3,2]=>0
[4,5,2,1,3,6]=>0
[4,5,2,1,6,3]=>0
[4,5,2,3,1,6]=>0
[4,5,2,3,6,1]=>0
[4,5,2,6,1,3]=>0
[4,5,2,6,3,1]=>0
[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>0
[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>0
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>6
[4,5,6,1,3,2]=>0
[4,5,6,2,1,3]=>0
[4,5,6,2,3,1]=>0
[4,5,6,3,1,2]=>0
[4,5,6,3,2,1]=>0
[4,6,1,2,3,5]=>24
[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]=>0
[4,6,2,1,3,5]=>0
[4,6,2,1,5,3]=>0
[4,6,2,3,1,5]=>0
[4,6,2,3,5,1]=>0
[4,6,2,5,1,3]=>0
[4,6,2,5,3,1]=>0
[4,6,3,1,2,5]=>0
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>0
[4,6,3,2,5,1]=>0
[4,6,3,5,1,2]=>0
[4,6,3,5,2,1]=>0
[4,6,5,1,2,3]=>0
[4,6,5,1,3,2]=>0
[4,6,5,2,1,3]=>0
[4,6,5,2,3,1]=>0
[4,6,5,3,1,2]=>0
[4,6,5,3,2,1]=>0
[5,1,2,3,4,6]=>24
[5,1,2,3,6,4]=>24
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>0
[5,1,2,6,3,4]=>24
[5,1,2,6,4,3]=>0
[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]=>0
[5,1,4,2,3,6]=>0
[5,1,4,2,6,3]=>0
[5,1,4,3,2,6]=>0
[5,1,4,3,6,2]=>0
[5,1,4,6,2,3]=>0
[5,1,4,6,3,2]=>0
[5,1,6,2,3,4]=>24
[5,1,6,2,4,3]=>0
[5,1,6,3,2,4]=>0
[5,1,6,3,4,2]=>0
[5,1,6,4,2,3]=>0
[5,1,6,4,3,2]=>0
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>0
[5,2,1,4,3,6]=>0
[5,2,1,4,6,3]=>0
[5,2,1,6,3,4]=>0
[5,2,1,6,4,3]=>0
[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]=>0
[5,2,4,1,3,6]=>0
[5,2,4,1,6,3]=>0
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>0
[5,2,4,6,3,1]=>0
[5,2,6,1,3,4]=>0
[5,2,6,1,4,3]=>0
[5,2,6,3,1,4]=>0
[5,2,6,3,4,1]=>0
[5,2,6,4,1,3]=>0
[5,2,6,4,3,1]=>0
[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>0
[5,3,1,4,2,6]=>0
[5,3,1,4,6,2]=>0
[5,3,1,6,2,4]=>0
[5,3,1,6,4,2]=>0
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>0
[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>0
[5,3,2,6,1,4]=>0
[5,3,2,6,4,1]=>0
[5,3,4,1,2,6]=>0
[5,3,4,1,6,2]=>0
[5,3,4,2,1,6]=>0
[5,3,4,2,6,1]=>0
[5,3,4,6,1,2]=>0
[5,3,4,6,2,1]=>0
[5,3,6,1,2,4]=>0
[5,3,6,1,4,2]=>0
[5,3,6,2,1,4]=>0
[5,3,6,2,4,1]=>0
[5,3,6,4,1,2]=>0
[5,3,6,4,2,1]=>0
[5,4,1,2,3,6]=>0
[5,4,1,2,6,3]=>0
[5,4,1,3,2,6]=>0
[5,4,1,3,6,2]=>0
[5,4,1,6,2,3]=>0
[5,4,1,6,3,2]=>0
[5,4,2,1,3,6]=>0
[5,4,2,1,6,3]=>0
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>0
[5,4,2,6,1,3]=>0
[5,4,2,6,3,1]=>0
[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>0
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>0
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>0
[5,4,6,1,3,2]=>0
[5,4,6,2,1,3]=>0
[5,4,6,2,3,1]=>0
[5,4,6,3,1,2]=>0
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>24
[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]=>0
[5,6,2,1,3,4]=>0
[5,6,2,1,4,3]=>0
[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]=>0
[5,6,3,1,2,4]=>0
[5,6,3,1,4,2]=>0
[5,6,3,2,1,4]=>0
[5,6,3,2,4,1]=>0
[5,6,3,4,1,2]=>0
[5,6,3,4,2,1]=>0
[5,6,4,1,2,3]=>0
[5,6,4,1,3,2]=>0
[5,6,4,2,1,3]=>0
[5,6,4,2,3,1]=>0
[5,6,4,3,1,2]=>0
[5,6,4,3,2,1]=>0
[6,1,2,3,4,5]=>120
[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]=>0
[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]=>0
[6,1,4,2,3,5]=>0
[6,1,4,2,5,3]=>0
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>0
[6,1,4,5,2,3]=>0
[6,1,4,5,3,2]=>0
[6,1,5,2,3,4]=>0
[6,1,5,2,4,3]=>0
[6,1,5,3,2,4]=>0
[6,1,5,3,4,2]=>0
[6,1,5,4,2,3]=>0
[6,1,5,4,3,2]=>0
[6,2,1,3,4,5]=>0
[6,2,1,3,5,4]=>0
[6,2,1,4,3,5]=>0
[6,2,1,4,5,3]=>0
[6,2,1,5,3,4]=>0
[6,2,1,5,4,3]=>0
[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]=>0
[6,2,4,1,3,5]=>0
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>0
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>0
[6,2,4,5,3,1]=>0
[6,2,5,1,3,4]=>0
[6,2,5,1,4,3]=>0
[6,2,5,3,1,4]=>0
[6,2,5,3,4,1]=>0
[6,2,5,4,1,3]=>0
[6,2,5,4,3,1]=>0
[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>0
[6,3,1,4,2,5]=>0
[6,3,1,4,5,2]=>0
[6,3,1,5,2,4]=>0
[6,3,1,5,4,2]=>0
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>0
[6,3,2,4,1,5]=>0
[6,3,2,4,5,1]=>0
[6,3,2,5,1,4]=>0
[6,3,2,5,4,1]=>0
[6,3,4,1,2,5]=>0
[6,3,4,1,5,2]=>0
[6,3,4,2,1,5]=>0
[6,3,4,2,5,1]=>0
[6,3,4,5,1,2]=>0
[6,3,4,5,2,1]=>0
[6,3,5,1,2,4]=>0
[6,3,5,1,4,2]=>0
[6,3,5,2,1,4]=>0
[6,3,5,2,4,1]=>0
[6,3,5,4,1,2]=>0
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>0
[6,4,1,3,5,2]=>0
[6,4,1,5,2,3]=>0
[6,4,1,5,3,2]=>0
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>0
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>0
[6,4,2,5,3,1]=>0
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>0
[6,4,3,5,2,1]=>0
[6,4,5,1,2,3]=>0
[6,4,5,1,3,2]=>0
[6,4,5,2,1,3]=>0
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>0
[6,4,5,3,2,1]=>0
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>0
[6,5,1,3,2,4]=>0
[6,5,1,3,4,2]=>0
[6,5,1,4,2,3]=>0
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>0
[6,5,2,1,4,3]=>0
[6,5,2,3,1,4]=>0
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>0
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>0
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>0
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>0
[6,5,4,2,1,3]=>0
[6,5,4,2,3,1]=>0
[6,5,4,3,1,2]=>0
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>1
[1,2,3,6,4,7,5]=>2
[1,2,6,3,4,7,5]=>6
[1,3,2,4,5,6,7]=>1
[1,3,7,2,4,5,6]=>24
[1,3,7,6,5,4,2]=>0
[1,4,6,7,2,3,5]=>6
[1,4,6,7,5,3,2]=>0
[1,4,7,2,3,5,6]=>24
[1,4,7,6,5,3,2]=>0
[1,5,2,3,4,7,6]=>6
[1,5,2,7,3,4,6]=>18
[1,5,4,7,6,3,2]=>0
[1,5,6,2,7,3,4]=>6
[1,5,6,4,7,3,2]=>0
[1,5,6,7,2,3,4]=>6
[1,5,6,7,4,3,2]=>0
[1,5,7,2,3,4,6]=>24
[1,5,7,6,4,3,2]=>0
[1,6,2,3,4,7,5]=>24
[1,6,2,3,7,4,5]=>24
[1,6,2,7,3,4,5]=>24
[1,6,5,4,3,7,2]=>0
[1,6,5,4,7,3,2]=>0
[1,6,5,7,4,3,2]=>0
[1,6,7,2,3,4,5]=>24
[1,6,7,5,4,3,2]=>0
[1,7,2,3,4,5,6]=>120
[1,7,3,5,6,4,2]=>0
[1,7,3,6,5,4,2]=>0
[1,7,4,3,6,5,2]=>0
[1,7,4,5,3,6,2]=>0
[1,7,4,5,6,3,2]=>0
[1,7,4,6,5,3,2]=>0
[1,7,5,4,3,6,2]=>0
[1,7,5,4,6,3,2]=>0
[1,7,6,4,5,3,2]=>0
[1,7,6,5,4,3,2]=>0
[2,1,3,4,5,6,7]=>1
[2,1,3,4,7,5,6]=>2
[2,1,3,7,4,5,6]=>6
[2,1,6,3,4,5,7]=>6
[2,1,7,3,4,5,6]=>24
[2,1,7,6,5,4,3]=>0
[2,3,1,4,5,6,7]=>1
[2,3,4,1,5,6,7]=>1
[2,3,4,1,5,7,6]=>1
[2,3,4,5,1,6,7]=>1
[2,3,4,5,1,7,6]=>1
[2,3,4,5,6,1,7]=>1
[2,3,4,5,6,7,1]=>1
[2,3,4,5,7,1,6]=>2
[2,3,4,6,1,7,5]=>2
[2,3,4,6,7,1,5]=>2
[2,3,4,7,1,5,6]=>6
[2,3,5,6,7,1,4]=>2
[2,4,1,3,5,6,7]=>2
[2,5,1,3,4,6,7]=>6
[2,5,7,1,3,4,6]=>24
[2,6,1,3,4,5,7]=>24
[2,6,1,7,3,4,5]=>24
[2,6,5,4,3,1,7]=>0
[2,6,7,1,3,4,5]=>24
[2,7,1,3,4,5,6]=>120
[3,1,2,4,5,6,7]=>2
[3,1,2,4,5,7,6]=>2
[3,2,1,4,5,6,7]=>0
[3,2,4,5,6,7,1]=>0
[3,4,1,2,5,6,7]=>2
[3,4,2,5,6,7,1]=>0
[3,4,5,2,6,7,1]=>0
[3,4,5,6,2,7,1]=>0
[3,4,5,6,7,1,2]=>2
[3,5,6,1,2,4,7]=>6
[3,5,6,4,2,1,7]=>0
[3,6,1,2,4,5,7]=>24
[3,6,5,4,2,1,7]=>0
[4,1,2,3,5,6,7]=>6
[4,1,2,3,5,7,6]=>6
[4,1,6,2,3,5,7]=>18
[4,2,3,5,6,7,1]=>0
[4,2,5,1,3,6,7]=>0
[4,3,2,1,5,6,7]=>0
[4,3,2,5,6,7,1]=>0
[4,3,5,2,6,7,1]=>0
[4,3,6,5,2,1,7]=>0
[4,5,1,6,2,3,7]=>6
[4,5,2,3,6,7,1]=>0
[4,5,3,6,2,1,7]=>0
[4,5,6,1,2,3,7]=>6
[4,5,6,3,2,1,7]=>0
[4,6,1,2,3,5,7]=>24
[4,6,1,2,3,7,5]=>24
[4,6,5,3,2,1,7]=>0
[5,1,2,3,4,6,7]=>24
[5,1,2,3,4,7,6]=>24
[5,1,2,3,6,4,7]=>24
[5,1,2,3,6,7,4]=>24
[5,1,2,3,7,4,6]=>48
[5,1,2,6,3,4,7]=>24
[5,1,6,2,3,4,7]=>24
[5,1,6,2,3,7,4]=>24
[5,2,3,4,6,7,1]=>0
[5,2,6,7,1,3,4]=>0
[5,3,2,4,6,7,1]=>0
[5,3,2,6,1,4,7]=>0
[5,3,6,7,1,2,4]=>0
[5,4,3,2,1,6,7]=>0
[5,4,3,2,1,7,6]=>0
[5,4,3,2,6,1,7]=>0
[5,4,3,6,2,1,7]=>0
[5,4,6,3,2,1,7]=>0
[5,4,6,7,1,2,3]=>0
[5,6,1,2,3,4,7]=>24
[5,6,1,2,3,7,4]=>24
[5,6,3,4,1,2,7]=>0
[5,6,4,3,2,1,7]=>0
[5,6,7,1,2,3,4]=>24
[6,1,2,3,4,5,7]=>120
[6,1,2,3,4,7,5]=>120
[6,1,2,3,7,4,5]=>120
[6,1,2,7,3,4,5]=>120
[6,2,3,4,5,7,1]=>0
[6,2,4,5,3,1,7]=>0
[6,2,5,4,3,1,7]=>0
[6,3,2,5,4,1,7]=>0
[6,3,4,2,5,1,7]=>0
[6,3,4,5,2,1,7]=>0
[6,3,4,7,1,2,5]=>0
[6,3,5,4,2,1,7]=>0
[6,4,3,2,5,1,7]=>0
[6,4,3,2,7,1,5]=>0
[6,4,3,5,2,1,7]=>0
[6,4,5,7,1,2,3]=>0
[6,4,7,2,5,1,3]=>0
[6,4,7,3,5,1,2]=>0
[6,5,3,4,2,1,7]=>0
[6,5,4,3,2,1,7]=>0
[6,5,7,3,4,1,2]=>0
[6,7,1,2,3,4,5]=>120
[6,7,3,4,1,2,5]=>0
[6,7,4,5,1,2,3]=>0
[7,1,2,3,4,5,6]=>720
[7,2,1,3,4,5,6]=>0
[7,2,3,1,4,5,6]=>0
[7,2,3,4,1,5,6]=>0
[7,2,3,4,5,1,6]=>0
[7,3,1,2,4,5,6]=>0
[7,3,2,1,4,5,6]=>0
[7,3,2,4,1,5,6]=>0
[7,3,4,1,2,5,6]=>0
[7,4,1,2,3,5,6]=>0
[7,4,2,1,3,5,6]=>0
[7,4,5,6,1,2,3]=>0
[7,5,1,2,3,4,6]=>0
[7,5,6,1,2,3,4]=>0
[7,5,6,3,4,1,2]=>0
[7,6,1,2,3,4,5]=>0
[7,6,4,5,1,2,3]=>0
[7,6,4,5,3,2,1]=>0
[7,6,5,1,2,3,4]=>0
[7,6,5,3,4,1,2]=>0
[7,6,5,4,1,2,3]=>0
[7,6,5,4,3,1,2]=>0
[7,6,5,4,3,2,1]=>0
[8,7,6,5,4,3,2,1]=>0
[7,6,8,5,4,3,2,1]=>0
[7,8,5,6,4,3,2,1]=>0
[7,8,6,4,5,3,2,1]=>0
[8,6,7,4,5,3,2,1]=>0
[7,6,5,4,8,3,2,1]=>0
[6,5,7,4,8,3,2,1]=>0
[7,8,6,5,3,4,2,1]=>0
[8,6,7,5,3,4,2,1]=>0
[8,7,5,6,3,4,2,1]=>0
[6,7,8,3,4,5,2,1]=>0
[7,8,6,5,4,2,3,1]=>0
[8,6,7,5,4,2,3,1]=>0
[8,7,5,6,4,2,3,1]=>0
[8,7,6,4,5,2,3,1]=>0
[8,6,5,7,3,2,4,1]=>0
[6,7,8,5,2,3,4,1]=>0
[8,5,6,7,2,3,4,1]=>0
[7,8,3,2,4,5,6,1]=>0
[7,6,5,4,3,2,8,1]=>0
[6,5,7,4,3,2,8,1]=>0
[6,5,4,3,7,2,8,1]=>0
[5,4,6,3,7,2,8,1]=>0
[3,4,5,2,6,7,8,1]=>0
[5,2,3,4,6,7,8,1]=>0
[4,3,2,5,6,7,8,1]=>0
[3,4,2,5,6,7,8,1]=>0
[4,2,3,5,6,7,8,1]=>0
[3,2,4,5,6,7,8,1]=>0
[2,3,4,5,6,7,8,1]=>1
[8,7,6,5,4,3,1,2]=>0
[7,8,6,5,4,3,1,2]=>0
[8,6,7,5,4,3,1,2]=>0
[8,7,5,6,4,3,1,2]=>0
[8,7,6,4,5,3,1,2]=>0
[8,7,6,5,3,4,1,2]=>0
[8,7,5,6,3,4,1,2]=>0
[7,8,5,6,3,4,1,2]=>0
[5,6,7,8,3,4,1,2]=>0
[7,8,3,4,5,6,1,2]=>0
[3,4,5,6,7,8,1,2]=>2
[8,7,6,5,4,2,1,3]=>0
[7,6,8,5,4,2,1,3]=>0
[8,7,6,5,4,1,2,3]=>0
[6,7,8,5,4,1,2,3]=>0
[8,5,6,7,4,1,2,3]=>0
[8,7,6,4,5,1,2,3]=>0
[8,6,7,4,5,1,2,3]=>0
[8,7,4,5,6,1,2,3]=>0
[7,8,4,5,6,1,2,3]=>0
[6,7,4,5,8,1,2,3]=>0
[7,6,5,8,3,2,1,4]=>0
[7,5,6,8,2,3,1,4]=>0
[6,7,5,8,3,1,2,4]=>0
[6,5,7,8,2,1,3,4]=>0
[8,7,6,5,1,2,3,4]=>0
[8,7,5,6,1,2,3,4]=>0
[7,8,5,6,1,2,3,4]=>0
[8,5,6,7,1,2,3,4]=>0
[5,6,7,8,1,2,3,4]=>24
[8,7,6,4,3,2,1,5]=>0
[8,7,6,4,2,1,3,5]=>0
[8,7,6,1,2,3,4,5]=>0
[8,6,7,1,2,3,4,5]=>0
[6,7,8,1,2,3,4,5]=>120
[7,8,5,4,2,1,3,6]=>0
[7,8,5,4,1,2,3,6]=>0
[8,7,1,2,3,4,5,6]=>0
[7,8,1,2,3,4,5,6]=>720
[8,6,5,4,3,2,1,7]=>0
[8,6,5,4,3,1,2,7]=>0
[8,5,6,3,4,1,2,7]=>0
[8,6,5,4,2,1,3,7]=>0
[8,6,4,3,2,1,5,7]=>0
[8,6,4,2,1,3,5,7]=>0
[8,2,3,4,1,5,6,7]=>0
[8,4,1,2,3,5,6,7]=>0
[8,3,2,1,4,5,6,7]=>0
[8,2,3,1,4,5,6,7]=>0
[8,3,1,2,4,5,6,7]=>0
[8,2,1,3,4,5,6,7]=>0
[8,1,2,3,4,5,6,7]=>5040
[7,6,5,4,3,2,1,8]=>0
[6,7,5,4,3,2,1,8]=>0
[6,5,7,4,3,2,1,8]=>0
[5,6,7,4,3,2,1,8]=>0
[7,6,4,5,3,2,1,8]=>0
[6,5,4,7,3,2,1,8]=>0
[7,5,6,3,4,2,1,8]=>0
[7,6,4,3,5,2,1,8]=>0
[7,6,3,4,5,2,1,8]=>0
[7,5,4,3,6,2,1,8]=>0
[6,7,5,4,2,3,1,8]=>0
[6,5,7,3,2,4,1,8]=>0
[5,6,7,2,3,4,1,8]=>0
[2,3,4,5,6,7,1,8]=>1
[5,6,7,1,2,3,4,8]=>24
[6,7,1,2,3,4,5,8]=>120
[7,1,2,3,4,5,6,8]=>720
[6,5,4,3,2,1,7,8]=>0
[2,3,4,5,6,1,7,8]=>1
[5,6,3,4,1,2,7,8]=>0
[4,5,6,1,2,3,7,8]=>6
[6,1,2,3,4,5,7,8]=>120
[5,4,3,2,1,6,7,8]=>0
[2,3,4,5,1,6,7,8]=>1
[5,1,2,3,4,6,7,8]=>24
[4,3,2,1,5,6,7,8]=>0
[3,4,1,2,5,6,7,8]=>2
[3,2,1,4,5,6,7,8]=>0
[2,1,3,4,5,6,7,8]=>1
[1,2,3,4,5,6,7,8]=>1
[6,5,8,7,4,3,2,1]=>0
[3,5,8,7,6,4,2,1]=>0
[4,3,6,5,8,7,2,1]=>0
[2,6,8,7,5,4,3,1]=>0
[2,3,5,6,8,7,4,1]=>0
[3,2,6,5,4,8,7,1]=>0
[4,3,6,5,7,2,8,1]=>0
[3,2,6,5,7,4,8,1]=>0
[4,3,5,2,7,6,8,1]=>0
[3,2,5,4,7,6,8,1]=>0
[1,8,7,6,5,4,3,2]=>0
[1,7,8,6,5,4,3,2]=>0
[1,6,8,7,5,4,3,2]=>0
[1,7,6,8,5,4,3,2]=>0
[1,6,7,8,5,4,3,2]=>0
[1,5,8,7,6,4,3,2]=>0
[1,7,6,5,8,4,3,2]=>0
[1,3,5,7,8,6,4,2]=>0
[1,4,3,8,7,6,5,2]=>0
[1,6,5,4,3,8,7,2]=>0
[1,4,3,6,5,8,7,2]=>0
[2,1,8,7,6,5,4,3]=>0
[2,1,6,5,7,4,8,3]=>0
[2,1,5,4,7,6,8,3]=>0
[1,2,6,7,8,5,4,3]=>0
[3,2,1,8,7,6,5,4]=>0
[3,2,1,6,5,8,7,4]=>0
[1,2,3,5,6,7,8,4]=>1
[4,3,2,1,8,7,6,5]=>0
[3,4,2,1,7,8,6,5]=>0
[2,4,3,1,6,8,7,5]=>0
[2,4,3,1,7,6,8,5]=>0
[3,2,4,1,6,8,7,5]=>0
[3,2,4,1,7,6,8,5]=>0
[2,3,4,1,6,7,8,5]=>1
[2,1,4,3,8,7,6,5]=>0
[2,1,4,3,6,8,7,5]=>0
[2,1,4,3,7,6,8,5]=>0
[5,4,3,2,1,8,7,6]=>0
[3,2,5,4,1,8,7,6]=>0
[3,2,1,4,5,8,7,6]=>0
[2,3,1,4,5,7,8,6]=>1
[6,5,4,3,2,1,8,7]=>0
[4,3,5,2,6,1,8,7]=>0
[3,2,5,4,6,1,8,7]=>0
[2,3,4,5,6,1,8,7]=>1
[2,1,6,5,4,3,8,7]=>0
[2,1,4,6,5,3,8,7]=>0
[2,1,5,4,6,3,8,7]=>0
[4,3,2,1,6,5,8,7]=>0
[2,4,3,1,6,5,8,7]=>0
[3,2,4,1,6,5,8,7]=>0
[2,1,4,3,6,5,8,7]=>1
[2,1,3,4,5,6,8,7]=>1
[1,2,3,4,5,6,8,7]=>1
[5,7,6,4,3,2,1,8]=>0
[4,7,6,5,3,2,1,8]=>0
[3,2,7,6,5,4,1,8]=>0
[5,4,3,2,7,6,1,8]=>0
[3,2,5,4,7,6,1,8]=>0
[1,4,3,2,7,6,5,8]=>0
[1,3,4,2,6,7,5,8]=>1
[1,3,2,5,4,7,6,8]=>1
[1,2,3,5,4,7,6,8]=>1
[1,3,2,4,5,7,6,8]=>1
[1,2,3,4,5,7,6,8]=>1
[1,2,4,3,6,5,7,8]=>1
[1,3,2,5,4,6,7,8]=>1
[1,2,3,5,4,6,7,8]=>1
[1,3,2,4,5,6,7,8]=>1
[1,8,4,7,6,5,3,2]=>0
[1,8,5,4,7,6,3,2]=>0
[1,8,7,4,5,6,3,2]=>0
[1,8,7,4,6,5,3,2]=>0
[1,8,6,5,4,7,3,2]=>0
[1,8,7,5,4,6,3,2]=>0
[1,8,7,5,6,4,3,2]=>0
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Description
The cardinality of the preimage of the Simion-Schmidt map.
The Simion-Schmidt bijection transforms a [3,1,2]-avoiding permutation into a [3,2,1]-avoiding permutation. More generally, it can be thought of as a map $S$ that turns any permutation into a [3,2,1]-avoiding permutation. This statistic is the size of $S^{-1}(\pi)$ for each permutation $\pi$.
The map $S$ can also be realized using the quotient of the $0$-Hecke Monoid of the symmetric group by the relation $\pi_i \pi_{i+1} \pi_i = \pi_{i+1} \pi_i$, sending each element of the fiber of the quotient to the unique [3,2,1]-avoiding element in that fiber.
The Simion-Schmidt bijection transforms a [3,1,2]-avoiding permutation into a [3,2,1]-avoiding permutation. More generally, it can be thought of as a map $S$ that turns any permutation into a [3,2,1]-avoiding permutation. This statistic is the size of $S^{-1}(\pi)$ for each permutation $\pi$.
The map $S$ can also be realized using the quotient of the $0$-Hecke Monoid of the symmetric group by the relation $\pi_i \pi_{i+1} \pi_i = \pi_{i+1} \pi_i$, sending each element of the fiber of the quotient to the unique [3,2,1]-avoiding element in that fiber.
References
[1] Bóna, Miklós Combinatorics of permutations MathSciNet:2919720
Code
def statistic(x):
return sum(1 for pi in Permutations(x.size()) if pi.simion_schmidt([3,2,1]) == x)
Created
Jun 18, 2013 at 18:08 by Tom Denton
Updated
Mar 17, 2018 at 16:36 by Martin Rubey
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