Identifier
- St000375: 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]=>0
[3,4,2,1]=>1
[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]=>1
[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]=>0
[1,4,5,3,2]=>1
[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]=>1
[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]=>0
[2,4,5,3,1]=>1
[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]=>1
[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]=>0
[3,4,1,5,2]=>0
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>0
[3,4,5,2,1]=>1
[3,5,1,2,4]=>0
[3,5,1,4,2]=>0
[3,5,2,1,4]=>1
[3,5,2,4,1]=>1
[3,5,4,1,2]=>0
[3,5,4,2,1]=>1
[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]=>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]=>1
[4,3,1,2,5]=>0
[4,3,1,5,2]=>0
[4,3,2,1,5]=>1
[4,3,2,5,1]=>1
[4,3,5,1,2]=>0
[4,3,5,2,1]=>1
[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]=>0
[4,5,3,2,1]=>1
[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]=>1
[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]=>1
[5,3,1,2,4]=>0
[5,3,1,4,2]=>0
[5,3,2,1,4]=>1
[5,3,2,4,1]=>1
[5,3,4,1,2]=>0
[5,3,4,2,1]=>1
[5,4,1,2,3]=>0
[5,4,1,3,2]=>1
[5,4,2,1,3]=>1
[5,4,2,3,1]=>2
[5,4,3,1,2]=>0
[5,4,3,2,1]=>1
[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]=>0
[1,2,5,6,4,3]=>1
[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]=>1
[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]=>0
[1,3,5,6,4,2]=>1
[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]=>1
[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]=>0
[1,4,5,2,6,3]=>0
[1,4,5,3,2,6]=>1
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>0
[1,4,5,6,3,2]=>1
[1,4,6,2,3,5]=>0
[1,4,6,2,5,3]=>0
[1,4,6,3,2,5]=>1
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>0
[1,4,6,5,3,2]=>1
[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]=>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]=>1
[1,5,4,2,3,6]=>0
[1,5,4,2,6,3]=>0
[1,5,4,3,2,6]=>1
[1,5,4,3,6,2]=>1
[1,5,4,6,2,3]=>0
[1,5,4,6,3,2]=>1
[1,5,6,2,3,4]=>0
[1,5,6,2,4,3]=>1
[1,5,6,3,2,4]=>1
[1,5,6,3,4,2]=>2
[1,5,6,4,2,3]=>0
[1,5,6,4,3,2]=>1
[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]=>1
[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]=>1
[1,6,4,2,3,5]=>0
[1,6,4,2,5,3]=>0
[1,6,4,3,2,5]=>1
[1,6,4,3,5,2]=>1
[1,6,4,5,2,3]=>0
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>0
[1,6,5,2,4,3]=>1
[1,6,5,3,2,4]=>1
[1,6,5,3,4,2]=>2
[1,6,5,4,2,3]=>0
[1,6,5,4,3,2]=>1
[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]=>0
[2,1,5,6,4,3]=>1
[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]=>1
[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]=>0
[2,3,5,6,4,1]=>1
[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]=>1
[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]=>0
[2,4,5,1,6,3]=>0
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>1
[2,4,5,6,1,3]=>0
[2,4,5,6,3,1]=>1
[2,4,6,1,3,5]=>0
[2,4,6,1,5,3]=>0
[2,4,6,3,1,5]=>1
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>0
[2,4,6,5,3,1]=>1
[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]=>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]=>1
[2,5,4,1,3,6]=>0
[2,5,4,1,6,3]=>0
[2,5,4,3,1,6]=>1
[2,5,4,3,6,1]=>1
[2,5,4,6,1,3]=>0
[2,5,4,6,3,1]=>1
[2,5,6,1,3,4]=>0
[2,5,6,1,4,3]=>1
[2,5,6,3,1,4]=>1
[2,5,6,3,4,1]=>2
[2,5,6,4,1,3]=>0
[2,5,6,4,3,1]=>1
[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]=>1
[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]=>1
[2,6,4,1,3,5]=>0
[2,6,4,1,5,3]=>0
[2,6,4,3,1,5]=>1
[2,6,4,3,5,1]=>1
[2,6,4,5,1,3]=>0
[2,6,4,5,3,1]=>1
[2,6,5,1,3,4]=>0
[2,6,5,1,4,3]=>1
[2,6,5,3,1,4]=>1
[2,6,5,3,4,1]=>2
[2,6,5,4,1,3]=>0
[2,6,5,4,3,1]=>1
[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]=>0
[3,1,5,6,4,2]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>0
[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]=>0
[3,4,5,1,6,2]=>0
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>0
[3,4,6,1,5,2]=>0
[3,4,6,2,1,5]=>1
[3,4,6,2,5,1]=>1
[3,4,6,5,1,2]=>0
[3,4,6,5,2,1]=>1
[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]=>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]=>2
[3,5,4,1,2,6]=>0
[3,5,4,1,6,2]=>0
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>0
[3,5,4,6,2,1]=>1
[3,5,6,1,2,4]=>0
[3,5,6,1,4,2]=>1
[3,5,6,2,1,4]=>1
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>0
[3,5,6,4,2,1]=>1
[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]=>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]=>2
[3,6,4,1,2,5]=>0
[3,6,4,1,5,2]=>0
[3,6,4,2,1,5]=>1
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>0
[3,6,4,5,2,1]=>1
[3,6,5,1,2,4]=>0
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>1
[3,6,5,2,4,1]=>2
[3,6,5,4,1,2]=>0
[3,6,5,4,2,1]=>1
[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]=>0
[4,1,5,2,6,3]=>0
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>1
[4,1,5,6,2,3]=>0
[4,1,5,6,3,2]=>1
[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]=>1
[4,1,6,5,2,3]=>0
[4,1,6,5,3,2]=>1
[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]=>1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>0
[4,2,5,6,3,1]=>1
[4,2,6,1,3,5]=>0
[4,2,6,1,5,3]=>0
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>0
[4,2,6,5,3,1]=>1
[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]=>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]=>0
[4,3,5,1,6,2]=>0
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>1
[4,3,5,6,1,2]=>0
[4,3,5,6,2,1]=>1
[4,3,6,1,2,5]=>0
[4,3,6,1,5,2]=>0
[4,3,6,2,1,5]=>1
[4,3,6,2,5,1]=>1
[4,3,6,5,1,2]=>0
[4,3,6,5,2,1]=>1
[4,5,1,2,3,6]=>0
[4,5,1,2,6,3]=>0
[4,5,1,3,2,6]=>1
[4,5,1,3,6,2]=>1
[4,5,1,6,2,3]=>0
[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]=>2
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>1
[4,5,2,6,3,1]=>2
[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>0
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>0
[4,5,3,6,2,1]=>1
[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]=>1
[4,5,6,3,2,1]=>2
[4,6,1,2,3,5]=>0
[4,6,1,2,5,3]=>0
[4,6,1,3,2,5]=>1
[4,6,1,3,5,2]=>1
[4,6,1,5,2,3]=>0
[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]=>2
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>2
[4,6,3,1,2,5]=>0
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>1
[4,6,3,2,5,1]=>1
[4,6,3,5,1,2]=>0
[4,6,3,5,2,1]=>1
[4,6,5,1,2,3]=>0
[4,6,5,1,3,2]=>1
[4,6,5,2,1,3]=>1
[4,6,5,2,3,1]=>2
[4,6,5,3,1,2]=>1
[4,6,5,3,2,1]=>2
[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]=>1
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>0
[5,1,4,6,3,2]=>1
[5,1,6,2,3,4]=>0
[5,1,6,2,4,3]=>1
[5,1,6,3,2,4]=>1
[5,1,6,3,4,2]=>2
[5,1,6,4,2,3]=>0
[5,1,6,4,3,2]=>1
[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]=>1
[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]=>1
[5,2,4,3,6,1]=>1
[5,2,4,6,1,3]=>0
[5,2,4,6,3,1]=>1
[5,2,6,1,3,4]=>0
[5,2,6,1,4,3]=>1
[5,2,6,3,1,4]=>1
[5,2,6,3,4,1]=>2
[5,2,6,4,1,3]=>0
[5,2,6,4,3,1]=>1
[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]=>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]=>2
[5,3,4,1,2,6]=>0
[5,3,4,1,6,2]=>0
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>0
[5,3,4,6,2,1]=>1
[5,3,6,1,2,4]=>0
[5,3,6,1,4,2]=>1
[5,3,6,2,1,4]=>1
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>0
[5,3,6,4,2,1]=>1
[5,4,1,2,3,6]=>0
[5,4,1,2,6,3]=>0
[5,4,1,3,2,6]=>1
[5,4,1,3,6,2]=>1
[5,4,1,6,2,3]=>0
[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]=>2
[5,4,2,3,6,1]=>2
[5,4,2,6,1,3]=>1
[5,4,2,6,3,1]=>2
[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>0
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>1
[5,4,3,6,1,2]=>0
[5,4,3,6,2,1]=>1
[5,4,6,1,2,3]=>0
[5,4,6,1,3,2]=>1
[5,4,6,2,1,3]=>1
[5,4,6,2,3,1]=>2
[5,4,6,3,1,2]=>1
[5,4,6,3,2,1]=>2
[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]=>0
[5,6,1,4,3,2]=>1
[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]=>1
[5,6,2,4,3,1]=>2
[5,6,3,1,2,4]=>0
[5,6,3,1,4,2]=>1
[5,6,3,2,1,4]=>1
[5,6,3,2,4,1]=>2
[5,6,3,4,1,2]=>0
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>0
[5,6,4,1,3,2]=>1
[5,6,4,2,1,3]=>1
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>1
[5,6,4,3,2,1]=>2
[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]=>1
[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]=>1
[6,1,4,2,3,5]=>0
[6,1,4,2,5,3]=>0
[6,1,4,3,2,5]=>1
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>0
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>0
[6,1,5,2,4,3]=>1
[6,1,5,3,2,4]=>1
[6,1,5,3,4,2]=>2
[6,1,5,4,2,3]=>0
[6,1,5,4,3,2]=>1
[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]=>1
[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]=>1
[6,2,4,1,3,5]=>0
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>1
[6,2,4,3,5,1]=>1
[6,2,4,5,1,3]=>0
[6,2,4,5,3,1]=>1
[6,2,5,1,3,4]=>0
[6,2,5,1,4,3]=>1
[6,2,5,3,1,4]=>1
[6,2,5,3,4,1]=>2
[6,2,5,4,1,3]=>0
[6,2,5,4,3,1]=>1
[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]=>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]=>2
[6,3,4,1,2,5]=>0
[6,3,4,1,5,2]=>0
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>1
[6,3,4,5,1,2]=>0
[6,3,4,5,2,1]=>1
[6,3,5,1,2,4]=>0
[6,3,5,1,4,2]=>1
[6,3,5,2,1,4]=>1
[6,3,5,2,4,1]=>2
[6,3,5,4,1,2]=>0
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>1
[6,4,1,3,5,2]=>1
[6,4,1,5,2,3]=>0
[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]=>2
[6,4,2,3,5,1]=>2
[6,4,2,5,1,3]=>1
[6,4,2,5,3,1]=>2
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>1
[6,4,3,5,1,2]=>0
[6,4,3,5,2,1]=>1
[6,4,5,1,2,3]=>0
[6,4,5,1,3,2]=>1
[6,4,5,2,1,3]=>1
[6,4,5,2,3,1]=>2
[6,4,5,3,1,2]=>1
[6,4,5,3,2,1]=>2
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>1
[6,5,1,3,2,4]=>1
[6,5,1,3,4,2]=>2
[6,5,1,4,2,3]=>0
[6,5,1,4,3,2]=>1
[6,5,2,1,3,4]=>1
[6,5,2,1,4,3]=>2
[6,5,2,3,1,4]=>2
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>1
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>1
[6,5,3,2,1,4]=>1
[6,5,3,2,4,1]=>2
[6,5,3,4,1,2]=>0
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>1
[6,5,4,2,1,3]=>1
[6,5,4,2,3,1]=>2
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>2
[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]=>0
[1,2,3,6,7,5,4]=>1
[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]=>1
[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]=>0
[1,2,4,6,7,5,3]=>1
[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]=>1
[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]=>0
[1,2,5,6,3,7,4]=>0
[1,2,5,6,4,3,7]=>1
[1,2,5,6,4,7,3]=>1
[1,2,5,6,7,3,4]=>0
[1,2,5,6,7,4,3]=>1
[1,2,5,7,3,4,6]=>0
[1,2,5,7,3,6,4]=>0
[1,2,5,7,4,3,6]=>1
[1,2,5,7,4,6,3]=>1
[1,2,5,7,6,3,4]=>0
[1,2,5,7,6,4,3]=>1
[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]=>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]=>0
[1,2,6,4,7,5,3]=>1
[1,2,6,5,3,4,7]=>0
[1,2,6,5,3,7,4]=>0
[1,2,6,5,4,3,7]=>1
[1,2,6,5,4,7,3]=>1
[1,2,6,5,7,3,4]=>0
[1,2,6,5,7,4,3]=>1
[1,2,6,7,3,4,5]=>0
[1,2,6,7,3,5,4]=>1
[1,2,6,7,4,3,5]=>1
[1,2,6,7,4,5,3]=>2
[1,2,6,7,5,3,4]=>0
[1,2,6,7,5,4,3]=>1
[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]=>1
[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]=>1
[1,2,7,5,3,4,6]=>0
[1,2,7,5,3,6,4]=>0
[1,2,7,5,4,3,6]=>1
[1,2,7,5,4,6,3]=>1
[1,2,7,5,6,3,4]=>0
[1,2,7,5,6,4,3]=>1
[1,2,7,6,3,4,5]=>0
[1,2,7,6,3,5,4]=>1
[1,2,7,6,4,3,5]=>1
[1,2,7,6,4,5,3]=>2
[1,2,7,6,5,3,4]=>0
[1,2,7,6,5,4,3]=>1
[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]=>0
[1,3,2,6,7,5,4]=>1
[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]=>1
[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]=>0
[1,3,4,6,7,5,2]=>1
[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]=>1
[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]=>0
[1,3,5,6,2,7,4]=>0
[1,3,5,6,4,2,7]=>1
[1,3,5,6,4,7,2]=>1
[1,3,5,6,7,2,4]=>0
[1,3,5,6,7,4,2]=>1
[1,3,5,7,2,4,6]=>0
[1,3,5,7,2,6,4]=>0
[1,3,5,7,4,2,6]=>1
[1,3,5,7,4,6,2]=>1
[1,3,5,7,6,2,4]=>0
[1,3,5,7,6,4,2]=>1
[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]=>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]=>0
[1,3,6,4,7,5,2]=>1
[1,3,6,5,2,4,7]=>0
[1,3,6,5,2,7,4]=>0
[1,3,6,5,4,2,7]=>1
[1,3,6,5,4,7,2]=>1
[1,3,6,5,7,2,4]=>0
[1,3,6,5,7,4,2]=>1
[1,3,6,7,2,4,5]=>0
[1,3,6,7,2,5,4]=>1
[1,3,6,7,4,2,5]=>1
[1,3,6,7,4,5,2]=>2
[1,3,6,7,5,2,4]=>0
[1,3,6,7,5,4,2]=>1
[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]=>1
[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]=>1
[1,3,7,5,2,4,6]=>0
[1,3,7,5,2,6,4]=>0
[1,3,7,5,4,2,6]=>1
[1,3,7,5,4,6,2]=>1
[1,3,7,5,6,2,4]=>0
[1,3,7,5,6,4,2]=>1
[1,3,7,6,2,4,5]=>0
[1,3,7,6,2,5,4]=>1
[1,3,7,6,4,2,5]=>1
[1,3,7,6,4,5,2]=>2
[1,3,7,6,5,2,4]=>0
[1,3,7,6,5,4,2]=>1
[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]=>0
[1,4,2,6,7,5,3]=>1
[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]=>1
[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]=>0
[1,4,3,6,7,5,2]=>1
[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]=>1
[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]=>0
[1,4,5,3,2,6,7]=>1
[1,4,5,3,2,7,6]=>1
[1,4,5,3,6,2,7]=>1
[1,4,5,3,6,7,2]=>1
[1,4,5,3,7,2,6]=>1
[1,4,5,3,7,6,2]=>1
[1,4,5,6,2,3,7]=>0
[1,4,5,6,2,7,3]=>0
[1,4,5,6,3,2,7]=>1
[1,4,5,6,3,7,2]=>1
[1,4,5,6,7,2,3]=>0
[1,4,5,6,7,3,2]=>1
[1,4,5,7,2,3,6]=>0
[1,4,5,7,2,6,3]=>0
[1,4,5,7,3,2,6]=>1
[1,4,5,7,3,6,2]=>1
[1,4,5,7,6,2,3]=>0
[1,4,5,7,6,3,2]=>1
[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]=>1
[1,4,6,3,2,7,5]=>1
[1,4,6,3,5,2,7]=>1
[1,4,6,3,5,7,2]=>1
[1,4,6,3,7,2,5]=>1
[1,4,6,3,7,5,2]=>2
[1,4,6,5,2,3,7]=>0
[1,4,6,5,2,7,3]=>0
[1,4,6,5,3,2,7]=>1
[1,4,6,5,3,7,2]=>1
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Description
The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$.
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j < j$ and there exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also St000213The number of weak exceedances (also weak excedences) of a permutation. and St000119The number of occurrences of the pattern 321 in a permutation..
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j < j$ and there exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also St000213The number of weak exceedances (also weak excedences) of a permutation. and St000119The number of occurrences of the pattern 321 in a permutation..
References
[1] Chen, J. N., Zhou, R. D. P. On the Sign-imbalance of Permutation Tableaux arXiv:1602.00105
Code
def statistic(pi):
patterns = pi.pattern_positions([3,2,1])
return sum( 1 for i in range(len(pi)) if pi[i] not in pi.weak_excedences() and any( i == pattern[1] for pattern in patterns ) )
Created
Feb 02, 2016 at 20:19 by Christian Stump
Updated
May 10, 2019 at 17:29 by Henning Ulfarsson
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