Identifier
- St000516: Permutations ⟶ ℤ
Values
=>
[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]=>1
[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]=>1
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>0
[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]=>1
[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]=>1
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>0
[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]=>1
[2,1,4,3,5]=>1
[2,1,4,5,3]=>2
[2,1,5,3,4]=>1
[2,1,5,4,3]=>1
[2,3,1,4,5]=>0
[2,3,1,5,4]=>1
[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]=>1
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>0
[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]=>2
[3,1,4,2,5]=>1
[3,1,4,5,2]=>2
[3,1,5,2,4]=>1
[3,1,5,4,2]=>1
[3,2,1,4,5]=>0
[3,2,1,5,4]=>1
[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]=>1
[3,4,2,1,5]=>0
[3,4,2,5,1]=>1
[3,4,5,1,2]=>0
[3,4,5,2,1]=>0
[3,5,1,2,4]=>0
[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]=>0
[4,1,2,5,3]=>2
[4,1,3,2,5]=>0
[4,1,3,5,2]=>1
[4,1,5,2,3]=>1
[4,1,5,3,2]=>1
[4,2,1,3,5]=>0
[4,2,1,5,3]=>1
[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]=>1
[4,3,2,1,5]=>0
[4,3,2,5,1]=>1
[4,3,5,1,2]=>0
[4,3,5,2,1]=>0
[4,5,1,2,3]=>0
[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]=>0
[5,1,2,4,3]=>0
[5,1,3,2,4]=>0
[5,1,3,4,2]=>0
[5,1,4,2,3]=>1
[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]=>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]=>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]=>1
[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]=>1
[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]=>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]=>1
[1,3,2,5,4,6]=>1
[1,3,2,5,6,4]=>2
[1,3,2,6,4,5]=>1
[1,3,2,6,5,4]=>1
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>1
[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]=>1
[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]=>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]=>2
[1,4,2,5,3,6]=>1
[1,4,2,5,6,3]=>2
[1,4,2,6,3,5]=>1
[1,4,2,6,5,3]=>1
[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>1
[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]=>1
[1,4,5,3,2,6]=>0
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>0
[1,4,5,6,3,2]=>0
[1,4,6,2,3,5]=>0
[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]=>0
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>0
[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]=>0
[1,5,3,2,6,4]=>1
[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]=>1
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>1
[1,5,4,6,2,3]=>0
[1,5,4,6,3,2]=>0
[1,5,6,2,3,4]=>0
[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]=>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]=>1
[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]=>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]=>0
[2,1,3,4,6,5]=>1
[2,1,3,5,4,6]=>1
[2,1,3,5,6,4]=>2
[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]=>3
[2,1,4,5,3,6]=>2
[2,1,4,5,6,3]=>3
[2,1,4,6,3,5]=>2
[2,1,4,6,5,3]=>2
[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>3
[2,1,5,4,3,6]=>1
[2,1,5,4,6,3]=>2
[2,1,5,6,3,4]=>2
[2,1,5,6,4,3]=>2
[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]=>2
[2,1,6,5,4,3]=>2
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>1
[2,3,1,5,4,6]=>1
[2,3,1,5,6,4]=>2
[2,3,1,6,4,5]=>1
[2,3,1,6,5,4]=>1
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>1
[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]=>1
[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]=>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]=>2
[2,4,1,5,3,6]=>1
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>1
[2,4,1,6,5,3]=>1
[2,4,3,1,5,6]=>0
[2,4,3,1,6,5]=>1
[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]=>1
[2,4,5,3,1,6]=>0
[2,4,5,3,6,1]=>1
[2,4,5,6,1,3]=>0
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>0
[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]=>0
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>0
[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]=>0
[2,5,3,1,6,4]=>1
[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]=>1
[2,5,4,3,1,6]=>0
[2,5,4,3,6,1]=>1
[2,5,4,6,1,3]=>0
[2,5,4,6,3,1]=>0
[2,5,6,1,3,4]=>0
[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]=>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]=>1
[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]=>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]=>0
[3,1,2,4,6,5]=>2
[3,1,2,5,4,6]=>2
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>2
[3,1,2,6,5,4]=>2
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>3
[3,1,4,5,2,6]=>2
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>2
[3,1,4,6,5,2]=>2
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>3
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>2
[3,1,5,6,2,4]=>2
[3,1,5,6,4,2]=>2
[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]=>2
[3,1,6,5,4,2]=>2
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>1
[3,2,1,5,4,6]=>1
[3,2,1,5,6,4]=>2
[3,2,1,6,4,5]=>1
[3,2,1,6,5,4]=>1
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>1
[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]=>1
[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]=>0
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>2
[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]=>2
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>2
[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]=>1
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>0
[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]=>0
[3,5,1,2,6,4]=>2
[3,5,1,4,2,6]=>0
[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]=>0
[3,5,2,1,6,4]=>2
[3,5,2,4,1,6]=>0
[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]=>0
[3,5,4,1,6,2]=>1
[3,5,4,2,1,6]=>0
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>0
[3,5,4,6,2,1]=>0
[3,5,6,1,2,4]=>0
[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]=>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]=>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]=>1
[3,6,2,5,4,1]=>1
[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]=>0
[4,1,2,3,6,5]=>3
[4,1,2,5,3,6]=>2
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>2
[4,1,2,6,5,3]=>2
[4,1,3,2,5,6]=>0
[4,1,3,2,6,5]=>2
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>2
[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]=>3
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>3
[4,1,5,6,2,3]=>2
[4,1,5,6,3,2]=>2
[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]=>2
[4,1,6,5,3,2]=>2
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>2
[4,2,1,5,3,6]=>1
[4,2,1,5,6,3]=>2
[4,2,1,6,3,5]=>1
[4,2,1,6,5,3]=>1
[4,2,3,1,5,6]=>0
[4,2,3,1,6,5]=>1
[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]=>1
[4,2,5,3,1,6]=>0
[4,2,5,3,6,1]=>1
[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]=>2
[4,3,1,5,2,6]=>1
[4,3,1,5,6,2]=>2
[4,3,1,6,2,5]=>1
[4,3,1,6,5,2]=>1
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>2
[4,3,2,5,1,6]=>1
[4,3,2,5,6,1]=>2
[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]=>1
[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>1
[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]=>0
[4,5,1,2,6,3]=>2
[4,5,1,3,2,6]=>0
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>1
[4,5,1,6,3,2]=>1
[4,5,2,1,3,6]=>0
[4,5,2,1,6,3]=>2
[4,5,2,3,1,6]=>0
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>1
[4,5,2,6,3,1]=>1
[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>1
[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>0
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>0
[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]=>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]=>1
[4,6,1,5,3,2]=>1
[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]=>1
[4,6,2,5,3,1]=>1
[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]=>0
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>2
[5,1,2,6,3,4]=>2
[5,1,2,6,4,3]=>2
[5,1,3,2,4,6]=>0
[5,1,3,2,6,4]=>2
[5,1,3,4,2,6]=>0
[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]=>3
[5,1,4,3,2,6]=>1
[5,1,4,3,6,2]=>3
[5,1,4,6,2,3]=>2
[5,1,4,6,3,2]=>2
[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]=>0
[5,2,1,3,6,4]=>2
[5,2,1,4,3,6]=>0
[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]=>0
[5,2,3,1,6,4]=>1
[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]=>1
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>1
[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]=>2
[5,3,1,4,2,6]=>0
[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]=>0
[5,3,2,1,6,4]=>2
[5,3,2,4,1,6]=>0
[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]=>0
[5,3,4,1,6,2]=>1
[5,3,4,2,1,6]=>0
[5,3,4,2,6,1]=>1
[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]=>2
[5,4,1,3,2,6]=>0
[5,4,1,3,6,2]=>2
[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]=>2
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>2
[5,4,2,6,1,3]=>1
[5,4,2,6,3,1]=>1
[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>1
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>1
[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]=>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]=>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]=>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]=>2
[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]=>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]=>2
[6,1,4,5,3,2]=>2
[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]=>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]=>1
[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]=>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]=>1
[6,3,1,5,4,2]=>1
[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]=>1
[6,3,2,5,4,1]=>1
[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]=>1
[6,4,1,5,3,2]=>1
[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]=>1
[6,4,2,5,3,1]=>1
[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]=>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]=>1
[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]=>1
[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]=>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]=>1
[1,2,4,3,6,5,7]=>1
[1,2,4,3,6,7,5]=>2
[1,2,4,3,7,5,6]=>1
[1,2,4,3,7,6,5]=>1
[1,2,4,5,3,6,7]=>0
[1,2,4,5,3,7,6]=>1
[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]=>1
[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]=>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]=>2
[1,2,5,3,6,4,7]=>1
[1,2,5,3,6,7,4]=>2
[1,2,5,3,7,4,6]=>1
[1,2,5,3,7,6,4]=>1
[1,2,5,4,3,6,7]=>0
[1,2,5,4,3,7,6]=>1
[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]=>1
[1,2,5,6,4,3,7]=>0
[1,2,5,6,4,7,3]=>1
[1,2,5,6,7,3,4]=>0
[1,2,5,6,7,4,3]=>0
[1,2,5,7,3,4,6]=>0
[1,2,5,7,3,6,4]=>0
[1,2,5,7,4,3,6]=>0
[1,2,5,7,4,6,3]=>0
[1,2,5,7,6,3,4]=>0
[1,2,5,7,6,4,3]=>0
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>2
[1,2,6,3,5,4,7]=>0
[1,2,6,3,5,7,4]=>1
[1,2,6,3,7,4,5]=>1
[1,2,6,3,7,5,4]=>1
[1,2,6,4,3,5,7]=>0
[1,2,6,4,3,7,5]=>1
[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]=>0
[1,2,6,5,3,4,7]=>0
[1,2,6,5,3,7,4]=>1
[1,2,6,5,4,3,7]=>0
[1,2,6,5,4,7,3]=>1
[1,2,6,5,7,3,4]=>0
[1,2,6,5,7,4,3]=>0
[1,2,6,7,3,4,5]=>0
[1,2,6,7,3,5,4]=>0
[1,2,6,7,4,3,5]=>0
[1,2,6,7,4,5,3]=>0
[1,2,6,7,5,3,4]=>0
[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]=>1
[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]=>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]=>0
[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]=>1
[1,3,2,4,6,5,7]=>1
[1,3,2,4,6,7,5]=>2
[1,3,2,4,7,5,6]=>1
[1,3,2,4,7,6,5]=>1
[1,3,2,5,4,6,7]=>1
[1,3,2,5,4,7,6]=>3
[1,3,2,5,6,4,7]=>2
[1,3,2,5,6,7,4]=>3
[1,3,2,5,7,4,6]=>2
[1,3,2,5,7,6,4]=>2
[1,3,2,6,4,5,7]=>1
[1,3,2,6,4,7,5]=>3
[1,3,2,6,5,4,7]=>1
[1,3,2,6,5,7,4]=>2
[1,3,2,6,7,4,5]=>2
[1,3,2,6,7,5,4]=>2
[1,3,2,7,4,5,6]=>1
[1,3,2,7,4,6,5]=>1
[1,3,2,7,5,4,6]=>1
[1,3,2,7,5,6,4]=>1
[1,3,2,7,6,4,5]=>2
[1,3,2,7,6,5,4]=>2
[1,3,4,2,5,6,7]=>0
[1,3,4,2,5,7,6]=>1
[1,3,4,2,6,5,7]=>1
[1,3,4,2,6,7,5]=>2
[1,3,4,2,7,5,6]=>1
[1,3,4,2,7,6,5]=>1
[1,3,4,5,2,6,7]=>0
[1,3,4,5,2,7,6]=>1
[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]=>1
[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]=>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]=>2
[1,3,5,2,6,4,7]=>1
[1,3,5,2,6,7,4]=>2
[1,3,5,2,7,4,6]=>1
[1,3,5,2,7,6,4]=>1
[1,3,5,4,2,6,7]=>0
[1,3,5,4,2,7,6]=>1
[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]=>1
[1,3,5,6,4,2,7]=>0
[1,3,5,6,4,7,2]=>1
[1,3,5,6,7,2,4]=>0
[1,3,5,6,7,4,2]=>0
[1,3,5,7,2,4,6]=>0
[1,3,5,7,2,6,4]=>0
[1,3,5,7,4,2,6]=>0
[1,3,5,7,4,6,2]=>0
[1,3,5,7,6,2,4]=>0
[1,3,5,7,6,4,2]=>0
[1,3,6,2,4,5,7]=>0
[1,3,6,2,4,7,5]=>2
[1,3,6,2,5,4,7]=>0
[1,3,6,2,5,7,4]=>1
[1,3,6,2,7,4,5]=>1
[1,3,6,2,7,5,4]=>1
[1,3,6,4,2,5,7]=>0
[1,3,6,4,2,7,5]=>1
[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]=>0
[1,3,6,5,2,4,7]=>0
[1,3,6,5,2,7,4]=>1
[1,3,6,5,4,2,7]=>0
[1,3,6,5,4,7,2]=>1
[1,3,6,5,7,2,4]=>0
[1,3,6,5,7,4,2]=>0
[1,3,6,7,2,4,5]=>0
[1,3,6,7,2,5,4]=>0
[1,3,6,7,4,2,5]=>0
[1,3,6,7,4,5,2]=>0
[1,3,6,7,5,2,4]=>0
[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]=>1
[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]=>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]=>0
[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]=>2
[1,4,2,3,6,5,7]=>2
[1,4,2,3,6,7,5]=>4
[1,4,2,3,7,5,6]=>2
[1,4,2,3,7,6,5]=>2
[1,4,2,5,3,6,7]=>1
[1,4,2,5,3,7,6]=>3
[1,4,2,5,6,3,7]=>2
[1,4,2,5,6,7,3]=>3
[1,4,2,5,7,3,6]=>2
[1,4,2,5,7,6,3]=>2
[1,4,2,6,3,5,7]=>1
[1,4,2,6,3,7,5]=>3
[1,4,2,6,5,3,7]=>1
[1,4,2,6,5,7,3]=>2
[1,4,2,6,7,3,5]=>2
[1,4,2,6,7,5,3]=>2
[1,4,2,7,3,5,6]=>1
[1,4,2,7,3,6,5]=>1
[1,4,2,7,5,3,6]=>1
[1,4,2,7,5,6,3]=>1
[1,4,2,7,6,3,5]=>2
[1,4,2,7,6,5,3]=>2
[1,4,3,2,5,6,7]=>0
[1,4,3,2,5,7,6]=>1
[1,4,3,2,6,5,7]=>1
[1,4,3,2,6,7,5]=>2
[1,4,3,2,7,5,6]=>1
[1,4,3,2,7,6,5]=>1
[1,4,3,5,2,6,7]=>0
[1,4,3,5,2,7,6]=>1
[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]=>1
[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]=>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]=>0
[1,4,5,2,3,7,6]=>2
[1,4,5,2,6,3,7]=>1
[1,4,5,2,6,7,3]=>2
[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]=>2
[1,4,5,3,6,2,7]=>1
[1,4,5,3,6,7,2]=>2
[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]=>1
[1,4,5,6,3,2,7]=>0
[1,4,5,6,3,7,2]=>1
[1,4,5,6,7,2,3]=>0
[1,4,5,6,7,3,2]=>0
[1,4,5,7,2,3,6]=>0
[1,4,5,7,2,6,3]=>0
[1,4,5,7,3,2,6]=>0
[1,4,5,7,3,6,2]=>0
[1,4,5,7,6,2,3]=>0
[1,4,5,7,6,3,2]=>0
[1,4,6,2,3,5,7]=>0
[1,4,6,2,3,7,5]=>2
[1,4,6,2,5,3,7]=>0
[1,4,6,2,5,7,3]=>1
[1,4,6,2,7,3,5]=>1
[1,4,6,2,7,5,3]=>1
[1,4,6,3,2,5,7]=>0
[1,4,6,3,2,7,5]=>2
[1,4,6,3,5,2,7]=>0
[1,4,6,3,5,7,2]=>1
[1,4,6,3,7,2,5]=>1
[1,4,6,3,7,5,2]=>1
[1,4,6,5,2,3,7]=>0
[1,4,6,5,2,7,3]=>1
[1,4,6,5,3,2,7]=>0
[1,4,6,5,3,7,2]=>1
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Description
The number of stretching pairs of a permutation.
This is the number of pairs $(i,j)$ with $\pi(i) < i < j < \pi(j)$.
This is the number of pairs $(i,j)$ with $\pi(i) < i < j < \pi(j)$.
References
[1] Triangle read by rows: T(n,k) is the number of stretching pairs in all permutations in S_n,k (=set of permutations in S_n with k cycles) (n>=3; 1<=k<=n-2). OEIS:A216118
[2] Ferraz de Andrade, R., Lundberg, E., Nagle, B. Asymptotics of the Extremal Excedance Set Statistic arXiv:1403.0691
[2] Ferraz de Andrade, R., Lundberg, E., Nagle, B. Asymptotics of the Extremal Excedance Set Statistic arXiv:1403.0691
Code
def statistic(pi):
return len([(i,j) for i in range(1, len(pi)) for j in range(i+1, len(pi)+1)
if pi(i) < i < j < pi(j)])
Created
May 30, 2016 at 06:15 by Martin Rubey
Updated
May 30, 2016 at 06:15 by Martin Rubey
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