Identifier
- St001906: 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]=>0
[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]=>0
[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]=>0
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>1
[3,4,2,1]=>0
[4,1,2,3]=>0
[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]=>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]=>0
[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]=>0
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>1
[1,4,5,3,2]=>0
[1,5,2,3,4]=>0
[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]=>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]=>0
[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]=>0
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>1
[2,4,5,3,1]=>0
[2,5,1,3,4]=>0
[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]=>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]=>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]=>1
[3,4,1,5,2]=>1
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[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]=>0
[3,5,2,4,1]=>0
[3,5,4,1,2]=>1
[3,5,4,2,1]=>0
[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]=>1
[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]=>1
[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]=>1
[4,3,5,2,1]=>0
[4,5,1,2,3]=>1
[4,5,1,3,2]=>1
[4,5,2,1,3]=>1
[4,5,2,3,1]=>0
[4,5,3,1,2]=>1
[4,5,3,2,1]=>0
[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]=>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]=>1
[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]=>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]=>0
[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]=>0
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>0
[1,2,5,6,3,4]=>1
[1,2,5,6,4,3]=>0
[1,2,6,3,4,5]=>0
[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]=>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]=>0
[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]=>0
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>0
[1,3,5,4,6,2]=>0
[1,3,5,6,2,4]=>1
[1,3,5,6,4,2]=>0
[1,3,6,2,4,5]=>0
[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]=>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]=>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]=>1
[1,4,5,2,6,3]=>1
[1,4,5,3,2,6]=>0
[1,4,5,3,6,2]=>0
[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]=>0
[1,4,6,3,5,2]=>0
[1,4,6,5,2,3]=>1
[1,4,6,5,3,2]=>0
[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]=>1
[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]=>1
[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]=>1
[1,5,4,6,3,2]=>0
[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]=>0
[1,5,6,4,2,3]=>1
[1,5,6,4,3,2]=>0
[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]=>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]=>1
[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]=>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]=>0
[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]=>0
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>0
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>0
[2,1,5,6,3,4]=>1
[2,1,5,6,4,3]=>0
[2,1,6,3,4,5]=>0
[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]=>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]=>0
[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]=>0
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>0
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>1
[2,3,5,6,4,1]=>0
[2,3,6,1,4,5]=>0
[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]=>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]=>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]=>1
[2,4,5,1,6,3]=>1
[2,4,5,3,1,6]=>0
[2,4,5,3,6,1]=>0
[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]=>0
[2,4,6,3,5,1]=>0
[2,4,6,5,1,3]=>1
[2,4,6,5,3,1]=>0
[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]=>1
[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]=>1
[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]=>1
[2,5,4,6,3,1]=>0
[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]=>0
[2,5,6,4,1,3]=>1
[2,5,6,4,3,1]=>0
[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]=>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]=>1
[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]=>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]=>0
[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]=>0
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>0
[3,1,5,4,6,2]=>0
[3,1,5,6,2,4]=>1
[3,1,5,6,4,2]=>0
[3,1,6,2,4,5]=>0
[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]=>1
[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]=>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]=>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]=>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]=>2
[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]=>2
[3,5,1,6,4,2]=>1
[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]=>1
[3,5,2,6,4,1]=>0
[3,5,4,1,2,6]=>1
[3,5,4,1,6,2]=>1
[3,5,4,2,1,6]=>0
[3,5,4,2,6,1]=>0
[3,5,4,6,1,2]=>1
[3,5,4,6,2,1]=>1
[3,5,6,1,2,4]=>2
[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]=>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]=>1
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>0
[3,6,4,2,5,1]=>0
[3,6,4,5,1,2]=>1
[3,6,4,5,2,1]=>0
[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]=>0
[3,6,5,4,1,2]=>1
[3,6,5,4,2,1]=>0
[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]=>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]=>1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>0
[4,1,5,3,6,2]=>0
[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]=>0
[4,1,6,3,5,2]=>0
[4,1,6,5,2,3]=>1
[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]=>1
[4,2,5,1,6,3]=>1
[4,2,5,3,1,6]=>0
[4,2,5,3,6,1]=>0
[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]=>0
[4,2,6,3,5,1]=>0
[4,2,6,5,1,3]=>1
[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]=>1
[4,3,5,1,6,2]=>1
[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>0
[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]=>0
[4,3,6,2,5,1]=>0
[4,3,6,5,1,2]=>1
[4,3,6,5,2,1]=>0
[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]=>2
[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]=>0
[4,5,2,3,6,1]=>0
[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]=>0
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>1
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>2
[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]=>0
[4,6,2,3,5,1]=>0
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>0
[4,6,3,1,2,5]=>1
[4,6,3,1,5,2]=>1
[4,6,3,2,1,5]=>0
[4,6,3,2,5,1]=>0
[4,6,3,5,1,2]=>1
[4,6,3,5,2,1]=>0
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>2
[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]=>0
[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]=>1
[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]=>1
[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]=>1
[5,1,4,6,3,2]=>0
[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]=>0
[5,1,6,4,2,3]=>1
[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]=>1
[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]=>1
[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]=>1
[5,2,4,6,3,1]=>0
[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]=>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]=>1
[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]=>1
[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]=>1
[5,3,4,6,2,1]=>0
[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]=>0
[5,3,6,4,1,2]=>1
[5,3,6,4,2,1]=>0
[5,4,1,2,3,6]=>1
[5,4,1,2,6,3]=>1
[5,4,1,3,2,6]=>0
[5,4,1,3,6,2]=>0
[5,4,1,6,2,3]=>1
[5,4,1,6,3,2]=>1
[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]=>1
[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]=>1
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>2
[5,4,6,1,3,2]=>1
[5,4,6,2,1,3]=>2
[5,4,6,2,3,1]=>1
[5,4,6,3,1,2]=>1
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>2
[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]=>0
[5,6,2,4,1,3]=>1
[5,6,2,4,3,1]=>0
[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]=>0
[5,6,3,4,1,2]=>1
[5,6,3,4,2,1]=>0
[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]=>0
[5,6,4,3,1,2]=>1
[5,6,4,3,2,1]=>0
[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]=>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]=>1
[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]=>1
[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]=>1
[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]=>1
[6,4,1,2,5,3]=>1
[6,4,1,3,2,5]=>0
[6,4,1,3,5,2]=>0
[6,4,1,5,2,3]=>1
[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]=>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]=>0
[6,4,5,3,2,1]=>0
[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]=>0
[6,5,1,4,2,3]=>1
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>1
[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]=>1
[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]=>1
[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]=>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]=>0
[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]=>0
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,3,6,5,4,7]=>0
[1,2,3,6,5,7,4]=>0
[1,2,3,6,7,4,5]=>1
[1,2,3,6,7,5,4]=>0
[1,2,3,7,4,5,6]=>0
[1,2,3,7,4,6,5]=>0
[1,2,3,7,5,4,6]=>0
[1,2,3,7,5,6,4]=>0
[1,2,3,7,6,4,5]=>0
[1,2,3,7,6,5,4]=>0
[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]=>0
[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]=>0
[1,2,4,6,3,5,7]=>0
[1,2,4,6,3,7,5]=>0
[1,2,4,6,5,3,7]=>0
[1,2,4,6,5,7,3]=>0
[1,2,4,6,7,3,5]=>1
[1,2,4,6,7,5,3]=>0
[1,2,4,7,3,5,6]=>0
[1,2,4,7,3,6,5]=>0
[1,2,4,7,5,3,6]=>0
[1,2,4,7,5,6,3]=>0
[1,2,4,7,6,3,5]=>0
[1,2,4,7,6,5,3]=>0
[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]=>0
[1,2,5,4,3,6,7]=>0
[1,2,5,4,3,7,6]=>0
[1,2,5,4,6,3,7]=>0
[1,2,5,4,6,7,3]=>0
[1,2,5,4,7,3,6]=>0
[1,2,5,4,7,6,3]=>0
[1,2,5,6,3,4,7]=>1
[1,2,5,6,3,7,4]=>1
[1,2,5,6,4,3,7]=>0
[1,2,5,6,4,7,3]=>0
[1,2,5,6,7,3,4]=>1
[1,2,5,6,7,4,3]=>1
[1,2,5,7,3,4,6]=>1
[1,2,5,7,3,6,4]=>1
[1,2,5,7,4,3,6]=>0
[1,2,5,7,4,6,3]=>0
[1,2,5,7,6,3,4]=>1
[1,2,5,7,6,4,3]=>0
[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]=>1
[1,2,6,3,7,5,4]=>0
[1,2,6,4,3,5,7]=>0
[1,2,6,4,3,7,5]=>0
[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]=>0
[1,2,6,5,3,4,7]=>0
[1,2,6,5,3,7,4]=>0
[1,2,6,5,4,3,7]=>0
[1,2,6,5,4,7,3]=>0
[1,2,6,5,7,3,4]=>1
[1,2,6,5,7,4,3]=>0
[1,2,6,7,3,4,5]=>1
[1,2,6,7,3,5,4]=>1
[1,2,6,7,4,3,5]=>1
[1,2,6,7,4,5,3]=>0
[1,2,6,7,5,3,4]=>1
[1,2,6,7,5,4,3]=>0
[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]=>0
[1,2,7,4,3,5,6]=>0
[1,2,7,4,3,6,5]=>0
[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]=>0
[1,2,7,5,3,4,6]=>0
[1,2,7,5,3,6,4]=>0
[1,2,7,5,4,3,6]=>0
[1,2,7,5,4,6,3]=>0
[1,2,7,5,6,3,4]=>0
[1,2,7,5,6,4,3]=>0
[1,2,7,6,3,4,5]=>1
[1,2,7,6,3,5,4]=>0
[1,2,7,6,4,3,5]=>0
[1,2,7,6,4,5,3]=>0
[1,2,7,6,5,3,4]=>0
[1,2,7,6,5,4,3]=>0
[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]=>0
[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]=>0
[1,3,2,6,4,5,7]=>0
[1,3,2,6,4,7,5]=>0
[1,3,2,6,5,4,7]=>0
[1,3,2,6,5,7,4]=>0
[1,3,2,6,7,4,5]=>1
[1,3,2,6,7,5,4]=>0
[1,3,2,7,4,5,6]=>0
[1,3,2,7,4,6,5]=>0
[1,3,2,7,5,4,6]=>0
[1,3,2,7,5,6,4]=>0
[1,3,2,7,6,4,5]=>0
[1,3,2,7,6,5,4]=>0
[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]=>0
[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]=>0
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>0
[1,3,4,6,5,2,7]=>0
[1,3,4,6,5,7,2]=>0
[1,3,4,6,7,2,5]=>1
[1,3,4,6,7,5,2]=>0
[1,3,4,7,2,5,6]=>0
[1,3,4,7,2,6,5]=>0
[1,3,4,7,5,2,6]=>0
[1,3,4,7,5,6,2]=>0
[1,3,4,7,6,2,5]=>0
[1,3,4,7,6,5,2]=>0
[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]=>0
[1,3,5,4,2,6,7]=>0
[1,3,5,4,2,7,6]=>0
[1,3,5,4,6,2,7]=>0
[1,3,5,4,6,7,2]=>0
[1,3,5,4,7,2,6]=>0
[1,3,5,4,7,6,2]=>0
[1,3,5,6,2,4,7]=>1
[1,3,5,6,2,7,4]=>1
[1,3,5,6,4,2,7]=>0
[1,3,5,6,4,7,2]=>0
[1,3,5,6,7,2,4]=>1
[1,3,5,6,7,4,2]=>1
[1,3,5,7,2,4,6]=>1
[1,3,5,7,2,6,4]=>1
[1,3,5,7,4,2,6]=>0
[1,3,5,7,4,6,2]=>0
[1,3,5,7,6,2,4]=>1
[1,3,5,7,6,4,2]=>0
[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]=>1
[1,3,6,2,7,5,4]=>0
[1,3,6,4,2,5,7]=>0
[1,3,6,4,2,7,5]=>0
[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]=>0
[1,3,6,5,2,4,7]=>0
[1,3,6,5,2,7,4]=>0
[1,3,6,5,4,2,7]=>0
[1,3,6,5,4,7,2]=>0
[1,3,6,5,7,2,4]=>1
[1,3,6,5,7,4,2]=>0
[1,3,6,7,2,4,5]=>1
[1,3,6,7,2,5,4]=>1
[1,3,6,7,4,2,5]=>1
[1,3,6,7,4,5,2]=>0
[1,3,6,7,5,2,4]=>1
[1,3,6,7,5,4,2]=>0
[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]=>0
[1,3,7,4,2,5,6]=>0
[1,3,7,4,2,6,5]=>0
[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]=>0
[1,3,7,5,2,4,6]=>0
[1,3,7,5,2,6,4]=>0
[1,3,7,5,4,2,6]=>0
[1,3,7,5,4,6,2]=>0
[1,3,7,5,6,2,4]=>0
[1,3,7,5,6,4,2]=>0
[1,3,7,6,2,4,5]=>1
[1,3,7,6,2,5,4]=>0
[1,3,7,6,4,2,5]=>0
[1,3,7,6,4,5,2]=>0
[1,3,7,6,5,2,4]=>0
[1,3,7,6,5,4,2]=>0
[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]=>0
[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]=>0
[1,4,2,6,3,5,7]=>0
[1,4,2,6,3,7,5]=>0
[1,4,2,6,5,3,7]=>0
[1,4,2,6,5,7,3]=>0
[1,4,2,6,7,3,5]=>1
[1,4,2,6,7,5,3]=>0
[1,4,2,7,3,5,6]=>0
[1,4,2,7,3,6,5]=>0
[1,4,2,7,5,3,6]=>0
[1,4,2,7,5,6,3]=>0
[1,4,2,7,6,3,5]=>0
[1,4,2,7,6,5,3]=>0
[1,4,3,2,5,6,7]=>0
[1,4,3,2,5,7,6]=>0
[1,4,3,2,6,5,7]=>0
[1,4,3,2,6,7,5]=>0
[1,4,3,2,7,5,6]=>0
[1,4,3,2,7,6,5]=>0
[1,4,3,5,2,6,7]=>0
[1,4,3,5,2,7,6]=>0
[1,4,3,5,6,2,7]=>0
[1,4,3,5,6,7,2]=>0
[1,4,3,5,7,2,6]=>0
[1,4,3,5,7,6,2]=>0
[1,4,3,6,2,5,7]=>0
[1,4,3,6,2,7,5]=>0
[1,4,3,6,5,2,7]=>0
[1,4,3,6,5,7,2]=>0
[1,4,3,6,7,2,5]=>1
[1,4,3,6,7,5,2]=>0
[1,4,3,7,2,5,6]=>0
[1,4,3,7,2,6,5]=>0
[1,4,3,7,5,2,6]=>0
[1,4,3,7,5,6,2]=>0
[1,4,3,7,6,2,5]=>0
[1,4,3,7,6,5,2]=>0
[1,4,5,2,3,6,7]=>1
[1,4,5,2,3,7,6]=>1
[1,4,5,2,6,3,7]=>1
[1,4,5,2,6,7,3]=>1
[1,4,5,2,7,3,6]=>1
[1,4,5,2,7,6,3]=>1
[1,4,5,3,2,6,7]=>0
[1,4,5,3,2,7,6]=>0
[1,4,5,3,6,2,7]=>0
[1,4,5,3,6,7,2]=>0
[1,4,5,3,7,2,6]=>0
[1,4,5,3,7,6,2]=>0
[1,4,5,6,2,3,7]=>1
[1,4,5,6,2,7,3]=>1
[1,4,5,6,3,2,7]=>1
[1,4,5,6,3,7,2]=>1
[1,4,5,6,7,2,3]=>2
[1,4,5,6,7,3,2]=>1
[1,4,5,7,2,3,6]=>1
[1,4,5,7,2,6,3]=>1
[1,4,5,7,3,2,6]=>1
[1,4,5,7,3,6,2]=>1
[1,4,5,7,6,2,3]=>1
[1,4,5,7,6,3,2]=>1
[1,4,6,2,3,5,7]=>1
[1,4,6,2,3,7,5]=>1
[1,4,6,2,5,3,7]=>1
[1,4,6,2,5,7,3]=>1
[1,4,6,2,7,3,5]=>2
[1,4,6,2,7,5,3]=>1
[1,4,6,3,2,5,7]=>0
[1,4,6,3,2,7,5]=>0
[1,4,6,3,5,2,7]=>0
[1,4,6,3,5,7,2]=>0
[1,4,6,3,7,2,5]=>1
[1,4,6,3,7,5,2]=>0
[1,4,6,5,2,3,7]=>1
[1,4,6,5,2,7,3]=>1
[1,4,6,5,3,2,7]=>0
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Description
Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation.
Let $\pi$ be a permutation. Its total displacement St000830The total displacement of a permutation. is $D(\pi) = \sum_i |\pi(i) - i|$, and its absolute length St000216The absolute length of a permutation. is the minimal number $T(\pi)$ of transpositions whose product is $\pi$. Finally, let $I(\pi)$ be the number of inversions St000018The number of inversions of a permutation. of $\pi$.
This statistic equals $\left(D(\pi)-T(\pi)-I(\pi)\right)/2$.
Diaconis and Graham [1] proved that this statistic is always nonnegative.
Let $\pi$ be a permutation. Its total displacement St000830The total displacement of a permutation. is $D(\pi) = \sum_i |\pi(i) - i|$, and its absolute length St000216The absolute length of a permutation. is the minimal number $T(\pi)$ of transpositions whose product is $\pi$. Finally, let $I(\pi)$ be the number of inversions St000018The number of inversions of a permutation. of $\pi$.
This statistic equals $\left(D(\pi)-T(\pi)-I(\pi)\right)/2$.
Diaconis and Graham [1] proved that this statistic is always nonnegative.
References
[1] Diaconis, P., Graham, R. L. Spearman's footrule as a measure of disarray MathSciNet:0652736
[2] (bad identifier) MathOverflow:449361
[2] (bad identifier) MathOverflow:449361
Code
def statistic(pi):
return (sum(abs(e - i) for i, e in enumerate(pi, 1)) - pi.number_of_inversions() - pi.absolute_length())/2
Created
Jun 22, 2023 at 22:48 by Martin Rubey
Updated
Jun 22, 2023 at 22:48 by Martin Rubey
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