Identifier
- St000037: 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]=>1
[3,2,1]=>-1
[1,2,3,4]=>1
[1,2,4,3]=>-1
[1,3,2,4]=>-1
[1,3,4,2]=>1
[1,4,2,3]=>1
[1,4,3,2]=>-1
[2,1,3,4]=>-1
[2,1,4,3]=>1
[2,3,1,4]=>1
[2,3,4,1]=>-1
[2,4,1,3]=>-1
[2,4,3,1]=>1
[3,1,2,4]=>1
[3,1,4,2]=>-1
[3,2,1,4]=>-1
[3,2,4,1]=>1
[3,4,1,2]=>1
[3,4,2,1]=>-1
[4,1,2,3]=>-1
[4,1,3,2]=>1
[4,2,1,3]=>1
[4,2,3,1]=>-1
[4,3,1,2]=>-1
[4,3,2,1]=>1
[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]=>1
[1,2,5,4,3]=>-1
[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]=>-1
[1,3,5,4,2]=>1
[1,4,2,3,5]=>1
[1,4,2,5,3]=>-1
[1,4,3,2,5]=>-1
[1,4,3,5,2]=>1
[1,4,5,2,3]=>1
[1,4,5,3,2]=>-1
[1,5,2,3,4]=>-1
[1,5,2,4,3]=>1
[1,5,3,2,4]=>1
[1,5,3,4,2]=>-1
[1,5,4,2,3]=>-1
[1,5,4,3,2]=>1
[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]=>-1
[2,1,5,4,3]=>1
[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]=>1
[2,3,5,4,1]=>-1
[2,4,1,3,5]=>-1
[2,4,1,5,3]=>1
[2,4,3,1,5]=>1
[2,4,3,5,1]=>-1
[2,4,5,1,3]=>-1
[2,4,5,3,1]=>1
[2,5,1,3,4]=>1
[2,5,1,4,3]=>-1
[2,5,3,1,4]=>-1
[2,5,3,4,1]=>1
[2,5,4,1,3]=>1
[2,5,4,3,1]=>-1
[3,1,2,4,5]=>1
[3,1,2,5,4]=>-1
[3,1,4,2,5]=>-1
[3,1,4,5,2]=>1
[3,1,5,2,4]=>1
[3,1,5,4,2]=>-1
[3,2,1,4,5]=>-1
[3,2,1,5,4]=>1
[3,2,4,1,5]=>1
[3,2,4,5,1]=>-1
[3,2,5,1,4]=>-1
[3,2,5,4,1]=>1
[3,4,1,2,5]=>1
[3,4,1,5,2]=>-1
[3,4,2,1,5]=>-1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>1
[3,4,5,2,1]=>-1
[3,5,1,2,4]=>-1
[3,5,1,4,2]=>1
[3,5,2,1,4]=>1
[3,5,2,4,1]=>-1
[3,5,4,1,2]=>-1
[3,5,4,2,1]=>1
[4,1,2,3,5]=>-1
[4,1,2,5,3]=>1
[4,1,3,2,5]=>1
[4,1,3,5,2]=>-1
[4,1,5,2,3]=>-1
[4,1,5,3,2]=>1
[4,2,1,3,5]=>1
[4,2,1,5,3]=>-1
[4,2,3,1,5]=>-1
[4,2,3,5,1]=>1
[4,2,5,1,3]=>1
[4,2,5,3,1]=>-1
[4,3,1,2,5]=>-1
[4,3,1,5,2]=>1
[4,3,2,1,5]=>1
[4,3,2,5,1]=>-1
[4,3,5,1,2]=>-1
[4,3,5,2,1]=>1
[4,5,1,2,3]=>1
[4,5,1,3,2]=>-1
[4,5,2,1,3]=>-1
[4,5,2,3,1]=>1
[4,5,3,1,2]=>1
[4,5,3,2,1]=>-1
[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]=>-1
[5,2,1,4,3]=>1
[5,2,3,1,4]=>1
[5,2,3,4,1]=>-1
[5,2,4,1,3]=>-1
[5,2,4,3,1]=>1
[5,3,1,2,4]=>1
[5,3,1,4,2]=>-1
[5,3,2,1,4]=>-1
[5,3,2,4,1]=>1
[5,3,4,1,2]=>1
[5,3,4,2,1]=>-1
[5,4,1,2,3]=>-1
[5,4,1,3,2]=>1
[5,4,2,1,3]=>1
[5,4,2,3,1]=>-1
[5,4,3,1,2]=>-1
[5,4,3,2,1]=>1
[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]=>1
[1,2,3,6,5,4]=>-1
[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]=>-1
[1,2,4,6,5,3]=>1
[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>-1
[1,2,5,4,3,6]=>-1
[1,2,5,4,6,3]=>1
[1,2,5,6,3,4]=>1
[1,2,5,6,4,3]=>-1
[1,2,6,3,4,5]=>-1
[1,2,6,3,5,4]=>1
[1,2,6,4,3,5]=>1
[1,2,6,4,5,3]=>-1
[1,2,6,5,3,4]=>-1
[1,2,6,5,4,3]=>1
[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]=>-1
[1,3,2,6,5,4]=>1
[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]=>1
[1,3,4,6,5,2]=>-1
[1,3,5,2,4,6]=>-1
[1,3,5,2,6,4]=>1
[1,3,5,4,2,6]=>1
[1,3,5,4,6,2]=>-1
[1,3,5,6,2,4]=>-1
[1,3,5,6,4,2]=>1
[1,3,6,2,4,5]=>1
[1,3,6,2,5,4]=>-1
[1,3,6,4,2,5]=>-1
[1,3,6,4,5,2]=>1
[1,3,6,5,2,4]=>1
[1,3,6,5,4,2]=>-1
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>-1
[1,4,2,5,3,6]=>-1
[1,4,2,5,6,3]=>1
[1,4,2,6,3,5]=>1
[1,4,2,6,5,3]=>-1
[1,4,3,2,5,6]=>-1
[1,4,3,2,6,5]=>1
[1,4,3,5,2,6]=>1
[1,4,3,5,6,2]=>-1
[1,4,3,6,2,5]=>-1
[1,4,3,6,5,2]=>1
[1,4,5,2,3,6]=>1
[1,4,5,2,6,3]=>-1
[1,4,5,3,2,6]=>-1
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>1
[1,4,5,6,3,2]=>-1
[1,4,6,2,3,5]=>-1
[1,4,6,2,5,3]=>1
[1,4,6,3,2,5]=>1
[1,4,6,3,5,2]=>-1
[1,4,6,5,2,3]=>-1
[1,4,6,5,3,2]=>1
[1,5,2,3,4,6]=>-1
[1,5,2,3,6,4]=>1
[1,5,2,4,3,6]=>1
[1,5,2,4,6,3]=>-1
[1,5,2,6,3,4]=>-1
[1,5,2,6,4,3]=>1
[1,5,3,2,4,6]=>1
[1,5,3,2,6,4]=>-1
[1,5,3,4,2,6]=>-1
[1,5,3,4,6,2]=>1
[1,5,3,6,2,4]=>1
[1,5,3,6,4,2]=>-1
[1,5,4,2,3,6]=>-1
[1,5,4,2,6,3]=>1
[1,5,4,3,2,6]=>1
[1,5,4,3,6,2]=>-1
[1,5,4,6,2,3]=>-1
[1,5,4,6,3,2]=>1
[1,5,6,2,3,4]=>1
[1,5,6,2,4,3]=>-1
[1,5,6,3,2,4]=>-1
[1,5,6,3,4,2]=>1
[1,5,6,4,2,3]=>1
[1,5,6,4,3,2]=>-1
[1,6,2,3,4,5]=>1
[1,6,2,3,5,4]=>-1
[1,6,2,4,3,5]=>-1
[1,6,2,4,5,3]=>1
[1,6,2,5,3,4]=>1
[1,6,2,5,4,3]=>-1
[1,6,3,2,4,5]=>-1
[1,6,3,2,5,4]=>1
[1,6,3,4,2,5]=>1
[1,6,3,4,5,2]=>-1
[1,6,3,5,2,4]=>-1
[1,6,3,5,4,2]=>1
[1,6,4,2,3,5]=>1
[1,6,4,2,5,3]=>-1
[1,6,4,3,2,5]=>-1
[1,6,4,3,5,2]=>1
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>-1
[1,6,5,2,3,4]=>-1
[1,6,5,2,4,3]=>1
[1,6,5,3,2,4]=>1
[1,6,5,3,4,2]=>-1
[1,6,5,4,2,3]=>-1
[1,6,5,4,3,2]=>1
[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]=>-1
[2,1,3,6,5,4]=>1
[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]=>1
[2,1,4,6,5,3]=>-1
[2,1,5,3,4,6]=>-1
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>1
[2,1,5,4,6,3]=>-1
[2,1,5,6,3,4]=>-1
[2,1,5,6,4,3]=>1
[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>-1
[2,1,6,4,3,5]=>-1
[2,1,6,4,5,3]=>1
[2,1,6,5,3,4]=>1
[2,1,6,5,4,3]=>-1
[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]=>1
[2,3,1,6,5,4]=>-1
[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]=>-1
[2,3,4,6,5,1]=>1
[2,3,5,1,4,6]=>1
[2,3,5,1,6,4]=>-1
[2,3,5,4,1,6]=>-1
[2,3,5,4,6,1]=>1
[2,3,5,6,1,4]=>1
[2,3,5,6,4,1]=>-1
[2,3,6,1,4,5]=>-1
[2,3,6,1,5,4]=>1
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>-1
[2,3,6,5,1,4]=>-1
[2,3,6,5,4,1]=>1
[2,4,1,3,5,6]=>-1
[2,4,1,3,6,5]=>1
[2,4,1,5,3,6]=>1
[2,4,1,5,6,3]=>-1
[2,4,1,6,3,5]=>-1
[2,4,1,6,5,3]=>1
[2,4,3,1,5,6]=>1
[2,4,3,1,6,5]=>-1
[2,4,3,5,1,6]=>-1
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>1
[2,4,3,6,5,1]=>-1
[2,4,5,1,3,6]=>-1
[2,4,5,1,6,3]=>1
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>-1
[2,4,5,6,1,3]=>-1
[2,4,5,6,3,1]=>1
[2,4,6,1,3,5]=>1
[2,4,6,1,5,3]=>-1
[2,4,6,3,1,5]=>-1
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>1
[2,4,6,5,3,1]=>-1
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>-1
[2,5,1,4,3,6]=>-1
[2,5,1,4,6,3]=>1
[2,5,1,6,3,4]=>1
[2,5,1,6,4,3]=>-1
[2,5,3,1,4,6]=>-1
[2,5,3,1,6,4]=>1
[2,5,3,4,1,6]=>1
[2,5,3,4,6,1]=>-1
[2,5,3,6,1,4]=>-1
[2,5,3,6,4,1]=>1
[2,5,4,1,3,6]=>1
[2,5,4,1,6,3]=>-1
[2,5,4,3,1,6]=>-1
[2,5,4,3,6,1]=>1
[2,5,4,6,1,3]=>1
[2,5,4,6,3,1]=>-1
[2,5,6,1,3,4]=>-1
[2,5,6,1,4,3]=>1
[2,5,6,3,1,4]=>1
[2,5,6,3,4,1]=>-1
[2,5,6,4,1,3]=>-1
[2,5,6,4,3,1]=>1
[2,6,1,3,4,5]=>-1
[2,6,1,3,5,4]=>1
[2,6,1,4,3,5]=>1
[2,6,1,4,5,3]=>-1
[2,6,1,5,3,4]=>-1
[2,6,1,5,4,3]=>1
[2,6,3,1,4,5]=>1
[2,6,3,1,5,4]=>-1
[2,6,3,4,1,5]=>-1
[2,6,3,4,5,1]=>1
[2,6,3,5,1,4]=>1
[2,6,3,5,4,1]=>-1
[2,6,4,1,3,5]=>-1
[2,6,4,1,5,3]=>1
[2,6,4,3,1,5]=>1
[2,6,4,3,5,1]=>-1
[2,6,4,5,1,3]=>-1
[2,6,4,5,3,1]=>1
[2,6,5,1,3,4]=>1
[2,6,5,1,4,3]=>-1
[2,6,5,3,1,4]=>-1
[2,6,5,3,4,1]=>1
[2,6,5,4,1,3]=>1
[2,6,5,4,3,1]=>-1
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>-1
[3,1,2,5,4,6]=>-1
[3,1,2,5,6,4]=>1
[3,1,2,6,4,5]=>1
[3,1,2,6,5,4]=>-1
[3,1,4,2,5,6]=>-1
[3,1,4,2,6,5]=>1
[3,1,4,5,2,6]=>1
[3,1,4,5,6,2]=>-1
[3,1,4,6,2,5]=>-1
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>-1
[3,1,5,4,2,6]=>-1
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>1
[3,1,5,6,4,2]=>-1
[3,1,6,2,4,5]=>-1
[3,1,6,2,5,4]=>1
[3,1,6,4,2,5]=>1
[3,1,6,4,5,2]=>-1
[3,1,6,5,2,4]=>-1
[3,1,6,5,4,2]=>1
[3,2,1,4,5,6]=>-1
[3,2,1,4,6,5]=>1
[3,2,1,5,4,6]=>1
[3,2,1,5,6,4]=>-1
[3,2,1,6,4,5]=>-1
[3,2,1,6,5,4]=>1
[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]=>-1
[3,2,5,1,4,6]=>-1
[3,2,5,1,6,4]=>1
[3,2,5,4,1,6]=>1
[3,2,5,4,6,1]=>-1
[3,2,5,6,1,4]=>-1
[3,2,5,6,4,1]=>1
[3,2,6,1,4,5]=>1
[3,2,6,1,5,4]=>-1
[3,2,6,4,1,5]=>-1
[3,2,6,4,5,1]=>1
[3,2,6,5,1,4]=>1
[3,2,6,5,4,1]=>-1
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>-1
[3,4,1,5,2,6]=>-1
[3,4,1,5,6,2]=>1
[3,4,1,6,2,5]=>1
[3,4,1,6,5,2]=>-1
[3,4,2,1,5,6]=>-1
[3,4,2,1,6,5]=>1
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>-1
[3,4,2,6,1,5]=>-1
[3,4,2,6,5,1]=>1
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>-1
[3,4,5,2,1,6]=>-1
[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>-1
[3,4,6,1,2,5]=>-1
[3,4,6,1,5,2]=>1
[3,4,6,2,1,5]=>1
[3,4,6,2,5,1]=>-1
[3,4,6,5,1,2]=>-1
[3,4,6,5,2,1]=>1
[3,5,1,2,4,6]=>-1
[3,5,1,2,6,4]=>1
[3,5,1,4,2,6]=>1
[3,5,1,4,6,2]=>-1
[3,5,1,6,2,4]=>-1
[3,5,1,6,4,2]=>1
[3,5,2,1,4,6]=>1
[3,5,2,1,6,4]=>-1
[3,5,2,4,1,6]=>-1
[3,5,2,4,6,1]=>1
[3,5,2,6,1,4]=>1
[3,5,2,6,4,1]=>-1
[3,5,4,1,2,6]=>-1
[3,5,4,1,6,2]=>1
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>-1
[3,5,4,6,1,2]=>-1
[3,5,4,6,2,1]=>1
[3,5,6,1,2,4]=>1
[3,5,6,1,4,2]=>-1
[3,5,6,2,1,4]=>-1
[3,5,6,2,4,1]=>1
[3,5,6,4,1,2]=>1
[3,5,6,4,2,1]=>-1
[3,6,1,2,4,5]=>1
[3,6,1,2,5,4]=>-1
[3,6,1,4,2,5]=>-1
[3,6,1,4,5,2]=>1
[3,6,1,5,2,4]=>1
[3,6,1,5,4,2]=>-1
[3,6,2,1,4,5]=>-1
[3,6,2,1,5,4]=>1
[3,6,2,4,1,5]=>1
[3,6,2,4,5,1]=>-1
[3,6,2,5,1,4]=>-1
[3,6,2,5,4,1]=>1
[3,6,4,1,2,5]=>1
[3,6,4,1,5,2]=>-1
[3,6,4,2,1,5]=>-1
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>1
[3,6,4,5,2,1]=>-1
[3,6,5,1,2,4]=>-1
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>1
[3,6,5,2,4,1]=>-1
[3,6,5,4,1,2]=>-1
[3,6,5,4,2,1]=>1
[4,1,2,3,5,6]=>-1
[4,1,2,3,6,5]=>1
[4,1,2,5,3,6]=>1
[4,1,2,5,6,3]=>-1
[4,1,2,6,3,5]=>-1
[4,1,2,6,5,3]=>1
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>-1
[4,1,3,5,2,6]=>-1
[4,1,3,5,6,2]=>1
[4,1,3,6,2,5]=>1
[4,1,3,6,5,2]=>-1
[4,1,5,2,3,6]=>-1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>-1
[4,1,5,6,2,3]=>-1
[4,1,5,6,3,2]=>1
[4,1,6,2,3,5]=>1
[4,1,6,2,5,3]=>-1
[4,1,6,3,2,5]=>-1
[4,1,6,3,5,2]=>1
[4,1,6,5,2,3]=>1
[4,1,6,5,3,2]=>-1
[4,2,1,3,5,6]=>1
[4,2,1,3,6,5]=>-1
[4,2,1,5,3,6]=>-1
[4,2,1,5,6,3]=>1
[4,2,1,6,3,5]=>1
[4,2,1,6,5,3]=>-1
[4,2,3,1,5,6]=>-1
[4,2,3,1,6,5]=>1
[4,2,3,5,1,6]=>1
[4,2,3,5,6,1]=>-1
[4,2,3,6,1,5]=>-1
[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]=>-1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>1
[4,2,5,6,3,1]=>-1
[4,2,6,1,3,5]=>-1
[4,2,6,1,5,3]=>1
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>-1
[4,2,6,5,1,3]=>-1
[4,2,6,5,3,1]=>1
[4,3,1,2,5,6]=>-1
[4,3,1,2,6,5]=>1
[4,3,1,5,2,6]=>1
[4,3,1,5,6,2]=>-1
[4,3,1,6,2,5]=>-1
[4,3,1,6,5,2]=>1
[4,3,2,1,5,6]=>1
[4,3,2,1,6,5]=>-1
[4,3,2,5,1,6]=>-1
[4,3,2,5,6,1]=>1
[4,3,2,6,1,5]=>1
[4,3,2,6,5,1]=>-1
[4,3,5,1,2,6]=>-1
[4,3,5,1,6,2]=>1
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>-1
[4,3,5,6,1,2]=>-1
[4,3,5,6,2,1]=>1
[4,3,6,1,2,5]=>1
[4,3,6,1,5,2]=>-1
[4,3,6,2,1,5]=>-1
[4,3,6,2,5,1]=>1
[4,3,6,5,1,2]=>1
[4,3,6,5,2,1]=>-1
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>-1
[4,5,1,3,2,6]=>-1
[4,5,1,3,6,2]=>1
[4,5,1,6,2,3]=>1
[4,5,1,6,3,2]=>-1
[4,5,2,1,3,6]=>-1
[4,5,2,1,6,3]=>1
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>-1
[4,5,2,6,1,3]=>-1
[4,5,2,6,3,1]=>1
[4,5,3,1,2,6]=>1
[4,5,3,1,6,2]=>-1
[4,5,3,2,1,6]=>-1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>-1
[4,5,6,1,2,3]=>-1
[4,5,6,1,3,2]=>1
[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>-1
[4,5,6,3,1,2]=>-1
[4,5,6,3,2,1]=>1
[4,6,1,2,3,5]=>-1
[4,6,1,2,5,3]=>1
[4,6,1,3,2,5]=>1
[4,6,1,3,5,2]=>-1
[4,6,1,5,2,3]=>-1
[4,6,1,5,3,2]=>1
[4,6,2,1,3,5]=>1
[4,6,2,1,5,3]=>-1
[4,6,2,3,1,5]=>-1
[4,6,2,3,5,1]=>1
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>-1
[4,6,3,1,2,5]=>-1
[4,6,3,1,5,2]=>1
[4,6,3,2,1,5]=>1
[4,6,3,2,5,1]=>-1
[4,6,3,5,1,2]=>-1
[4,6,3,5,2,1]=>1
[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>-1
[4,6,5,2,1,3]=>-1
[4,6,5,2,3,1]=>1
[4,6,5,3,1,2]=>1
[4,6,5,3,2,1]=>-1
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>-1
[5,1,2,4,3,6]=>-1
[5,1,2,4,6,3]=>1
[5,1,2,6,3,4]=>1
[5,1,2,6,4,3]=>-1
[5,1,3,2,4,6]=>-1
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>1
[5,1,3,4,6,2]=>-1
[5,1,3,6,2,4]=>-1
[5,1,3,6,4,2]=>1
[5,1,4,2,3,6]=>1
[5,1,4,2,6,3]=>-1
[5,1,4,3,2,6]=>-1
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>1
[5,1,4,6,3,2]=>-1
[5,1,6,2,3,4]=>-1
[5,1,6,2,4,3]=>1
[5,1,6,3,2,4]=>1
[5,1,6,3,4,2]=>-1
[5,1,6,4,2,3]=>-1
[5,1,6,4,3,2]=>1
[5,2,1,3,4,6]=>-1
[5,2,1,3,6,4]=>1
[5,2,1,4,3,6]=>1
[5,2,1,4,6,3]=>-1
[5,2,1,6,3,4]=>-1
[5,2,1,6,4,3]=>1
[5,2,3,1,4,6]=>1
[5,2,3,1,6,4]=>-1
[5,2,3,4,1,6]=>-1
[5,2,3,4,6,1]=>1
[5,2,3,6,1,4]=>1
[5,2,3,6,4,1]=>-1
[5,2,4,1,3,6]=>-1
[5,2,4,1,6,3]=>1
[5,2,4,3,1,6]=>1
[5,2,4,3,6,1]=>-1
[5,2,4,6,1,3]=>-1
[5,2,4,6,3,1]=>1
[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]=>1
[5,2,6,4,1,3]=>1
[5,2,6,4,3,1]=>-1
[5,3,1,2,4,6]=>1
[5,3,1,2,6,4]=>-1
[5,3,1,4,2,6]=>-1
[5,3,1,4,6,2]=>1
[5,3,1,6,2,4]=>1
[5,3,1,6,4,2]=>-1
[5,3,2,1,4,6]=>-1
[5,3,2,1,6,4]=>1
[5,3,2,4,1,6]=>1
[5,3,2,4,6,1]=>-1
[5,3,2,6,1,4]=>-1
[5,3,2,6,4,1]=>1
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>-1
[5,3,4,2,1,6]=>-1
[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>1
[5,3,4,6,2,1]=>-1
[5,3,6,1,2,4]=>-1
[5,3,6,1,4,2]=>1
[5,3,6,2,1,4]=>1
[5,3,6,2,4,1]=>-1
[5,3,6,4,1,2]=>-1
[5,3,6,4,2,1]=>1
[5,4,1,2,3,6]=>-1
[5,4,1,2,6,3]=>1
[5,4,1,3,2,6]=>1
[5,4,1,3,6,2]=>-1
[5,4,1,6,2,3]=>-1
[5,4,1,6,3,2]=>1
[5,4,2,1,3,6]=>1
[5,4,2,1,6,3]=>-1
[5,4,2,3,1,6]=>-1
[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>1
[5,4,2,6,3,1]=>-1
[5,4,3,1,2,6]=>-1
[5,4,3,1,6,2]=>1
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>-1
[5,4,3,6,1,2]=>-1
[5,4,3,6,2,1]=>1
[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>-1
[5,4,6,2,1,3]=>-1
[5,4,6,2,3,1]=>1
[5,4,6,3,1,2]=>1
[5,4,6,3,2,1]=>-1
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>-1
[5,6,1,3,2,4]=>-1
[5,6,1,3,4,2]=>1
[5,6,1,4,2,3]=>1
[5,6,1,4,3,2]=>-1
[5,6,2,1,3,4]=>-1
[5,6,2,1,4,3]=>1
[5,6,2,3,1,4]=>1
[5,6,2,3,4,1]=>-1
[5,6,2,4,1,3]=>-1
[5,6,2,4,3,1]=>1
[5,6,3,1,2,4]=>1
[5,6,3,1,4,2]=>-1
[5,6,3,2,1,4]=>-1
[5,6,3,2,4,1]=>1
[5,6,3,4,1,2]=>1
[5,6,3,4,2,1]=>-1
[5,6,4,1,2,3]=>-1
[5,6,4,1,3,2]=>1
[5,6,4,2,1,3]=>1
[5,6,4,2,3,1]=>-1
[5,6,4,3,1,2]=>-1
[5,6,4,3,2,1]=>1
[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]=>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]=>-1
[6,2,3,1,4,5]=>-1
[6,2,3,1,5,4]=>1
[6,2,3,4,1,5]=>1
[6,2,3,4,5,1]=>-1
[6,2,3,5,1,4]=>-1
[6,2,3,5,4,1]=>1
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>-1
[6,2,4,3,1,5]=>-1
[6,2,4,3,5,1]=>1
[6,2,4,5,1,3]=>1
[6,2,4,5,3,1]=>-1
[6,2,5,1,3,4]=>-1
[6,2,5,1,4,3]=>1
[6,2,5,3,1,4]=>1
[6,2,5,3,4,1]=>-1
[6,2,5,4,1,3]=>-1
[6,2,5,4,3,1]=>1
[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]=>1
[6,3,2,1,4,5]=>1
[6,3,2,1,5,4]=>-1
[6,3,2,4,1,5]=>-1
[6,3,2,4,5,1]=>1
[6,3,2,5,1,4]=>1
[6,3,2,5,4,1]=>-1
[6,3,4,1,2,5]=>-1
[6,3,4,1,5,2]=>1
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>-1
[6,3,4,5,1,2]=>-1
[6,3,4,5,2,1]=>1
[6,3,5,1,2,4]=>1
[6,3,5,1,4,2]=>-1
[6,3,5,2,1,4]=>-1
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>1
[6,3,5,4,2,1]=>-1
[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]=>-1
[6,4,2,1,3,5]=>-1
[6,4,2,1,5,3]=>1
[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>-1
[6,4,2,5,1,3]=>-1
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>-1
[6,4,3,2,1,5]=>-1
[6,4,3,2,5,1]=>1
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>-1
[6,4,5,1,2,3]=>-1
[6,4,5,1,3,2]=>1
[6,4,5,2,1,3]=>1
[6,4,5,2,3,1]=>-1
[6,4,5,3,1,2]=>-1
[6,4,5,3,2,1]=>1
[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]=>1
[6,5,2,1,3,4]=>1
[6,5,2,1,4,3]=>-1
[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]=>-1
[6,5,3,1,2,4]=>-1
[6,5,3,1,4,2]=>1
[6,5,3,2,1,4]=>1
[6,5,3,2,4,1]=>-1
[6,5,3,4,1,2]=>-1
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>1
[6,5,4,1,3,2]=>-1
[6,5,4,2,1,3]=>-1
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>-1
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Description
The sign of a permutation.
References
[1] Section 1.3 Stanley, R. P. Enumerative combinatorics. Volume 1 MathSciNet:2868112
Code
def statistic(x): return x.sign()
Created
Feb 14, 2013 at 04:32 by Sara Billey
Updated
May 27, 2022 at 09:39 by Martin Rubey
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