Identifier
- St000864: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>2
[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]=>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]=>2
[3,2,4,1]=>2
[3,4,1,2]=>1
[3,4,2,1]=>2
[4,1,2,3]=>1
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>2
[4,3,1,2]=>2
[4,3,2,1]=>3
[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]=>1
[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]=>1
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>1
[1,4,3,5,2]=>1
[1,4,5,2,3]=>0
[1,4,5,3,2]=>1
[1,5,2,3,4]=>0
[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]=>2
[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]=>2
[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]=>2
[2,5,3,1,4]=>1
[2,5,3,4,1]=>1
[2,5,4,1,3]=>2
[2,5,4,3,1]=>2
[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]=>2
[3,2,1,4,5]=>2
[3,2,1,5,4]=>2
[3,2,4,1,5]=>2
[3,2,4,5,1]=>2
[3,2,5,1,4]=>2
[3,2,5,4,1]=>2
[3,4,1,2,5]=>1
[3,4,1,5,2]=>1
[3,4,2,1,5]=>2
[3,4,2,5,1]=>2
[3,4,5,1,2]=>1
[3,4,5,2,1]=>2
[3,5,1,2,4]=>1
[3,5,1,4,2]=>2
[3,5,2,1,4]=>2
[3,5,2,4,1]=>2
[3,5,4,1,2]=>2
[3,5,4,2,1]=>2
[4,1,2,3,5]=>1
[4,1,2,5,3]=>1
[4,1,3,2,5]=>2
[4,1,3,5,2]=>2
[4,1,5,2,3]=>1
[4,1,5,3,2]=>2
[4,2,1,3,5]=>2
[4,2,1,5,3]=>2
[4,2,3,1,5]=>2
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>2
[4,3,1,2,5]=>2
[4,3,1,5,2]=>2
[4,3,2,1,5]=>3
[4,3,2,5,1]=>3
[4,3,5,1,2]=>2
[4,3,5,2,1]=>3
[4,5,1,2,3]=>1
[4,5,1,3,2]=>2
[4,5,2,1,3]=>2
[4,5,2,3,1]=>2
[4,5,3,1,2]=>2
[4,5,3,2,1]=>3
[5,1,2,3,4]=>1
[5,1,2,4,3]=>2
[5,1,3,2,4]=>2
[5,1,3,4,2]=>2
[5,1,4,2,3]=>2
[5,1,4,3,2]=>3
[5,2,1,3,4]=>2
[5,2,1,4,3]=>3
[5,2,3,1,4]=>2
[5,2,3,4,1]=>2
[5,2,4,1,3]=>3
[5,2,4,3,1]=>3
[5,3,1,2,4]=>2
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>3
[5,3,4,1,2]=>3
[5,3,4,2,1]=>3
[5,4,1,2,3]=>2
[5,4,1,3,2]=>3
[5,4,2,1,3]=>3
[5,4,2,3,1]=>3
[5,4,3,1,2]=>3
[5,4,3,2,1]=>4
[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]=>1
[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]=>1
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>1
[1,2,5,4,6,3]=>1
[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]=>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]=>2
[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]=>1
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>1
[1,3,5,4,6,2]=>1
[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]=>1
[1,3,6,4,5,2]=>1
[1,3,6,5,2,4]=>1
[1,3,6,5,4,2]=>2
[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]=>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]=>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]=>1
[1,4,6,5,3,2]=>2
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>0
[1,5,2,4,3,6]=>1
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>0
[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]=>2
[1,5,4,3,6,2]=>2
[1,5,4,6,2,3]=>1
[1,5,4,6,3,2]=>2
[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]=>1
[1,5,6,4,2,3]=>1
[1,5,6,4,3,2]=>2
[1,6,2,3,4,5]=>0
[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]=>2
[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]=>2
[1,6,4,2,3,5]=>1
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>2
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>2
[1,6,5,2,3,4]=>1
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>2
[1,6,5,3,4,2]=>2
[1,6,5,4,2,3]=>2
[1,6,5,4,3,2]=>3
[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]=>2
[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]=>2
[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>2
[2,1,5,6,3,4]=>1
[2,1,5,6,4,3]=>2
[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>2
[2,1,6,4,3,5]=>2
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>2
[2,1,6,5,4,3]=>3
[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]=>2
[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]=>2
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>1
[2,3,6,5,1,4]=>2
[2,3,6,5,4,1]=>2
[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]=>2
[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]=>2
[2,4,6,3,1,5]=>1
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>2
[2,4,6,5,3,1]=>2
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>1
[2,5,1,4,3,6]=>2
[2,5,1,4,6,3]=>2
[2,5,1,6,3,4]=>1
[2,5,1,6,4,3]=>2
[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]=>2
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>2
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>2
[2,5,4,6,3,1]=>2
[2,5,6,1,3,4]=>1
[2,5,6,1,4,3]=>2
[2,5,6,3,1,4]=>1
[2,5,6,3,4,1]=>1
[2,5,6,4,1,3]=>2
[2,5,6,4,3,1]=>2
[2,6,1,3,4,5]=>1
[2,6,1,3,5,4]=>2
[2,6,1,4,3,5]=>2
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>1
[2,6,3,1,5,4]=>2
[2,6,3,4,1,5]=>1
[2,6,3,4,5,1]=>1
[2,6,3,5,1,4]=>2
[2,6,3,5,4,1]=>2
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>2
[2,6,4,3,1,5]=>2
[2,6,4,3,5,1]=>2
[2,6,4,5,1,3]=>2
[2,6,4,5,3,1]=>2
[2,6,5,1,3,4]=>2
[2,6,5,1,4,3]=>3
[2,6,5,3,1,4]=>2
[2,6,5,3,4,1]=>2
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>3
[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]=>2
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>1
[3,1,5,4,2,6]=>2
[3,1,5,4,6,2]=>2
[3,1,5,6,2,4]=>1
[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]=>2
[3,1,6,4,5,2]=>2
[3,1,6,5,2,4]=>2
[3,1,6,5,4,2]=>3
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>2
[3,2,1,5,4,6]=>2
[3,2,1,5,6,4]=>2
[3,2,1,6,4,5]=>2
[3,2,1,6,5,4]=>3
[3,2,4,1,5,6]=>2
[3,2,4,1,6,5]=>2
[3,2,4,5,1,6]=>2
[3,2,4,5,6,1]=>2
[3,2,4,6,1,5]=>2
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>2
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>2
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>2
[3,2,5,6,4,1]=>2
[3,2,6,1,4,5]=>2
[3,2,6,1,5,4]=>3
[3,2,6,4,1,5]=>2
[3,2,6,4,5,1]=>2
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>3
[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]=>2
[3,4,2,1,5,6]=>2
[3,4,2,1,6,5]=>2
[3,4,2,5,1,6]=>2
[3,4,2,5,6,1]=>2
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>2
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>1
[3,4,5,2,1,6]=>2
[3,4,5,2,6,1]=>2
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>2
[3,4,6,1,2,5]=>1
[3,4,6,1,5,2]=>2
[3,4,6,2,1,5]=>2
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>2
[3,4,6,5,2,1]=>2
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>1
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>2
[3,5,1,6,2,4]=>1
[3,5,1,6,4,2]=>2
[3,5,2,1,4,6]=>2
[3,5,2,1,6,4]=>2
[3,5,2,4,1,6]=>2
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>2
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>1
[3,5,6,1,4,2]=>2
[3,5,6,2,1,4]=>2
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>2
[3,6,1,2,4,5]=>1
[3,6,1,2,5,4]=>1
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>2
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>2
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>2
[3,6,2,5,1,4]=>3
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>2
[3,6,4,1,5,2]=>2
[3,6,4,2,1,5]=>2
[3,6,4,2,5,1]=>2
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>2
[3,6,5,1,2,4]=>2
[3,6,5,1,4,2]=>3
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>3
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>3
[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]=>2
[4,1,3,2,6,5]=>2
[4,1,3,5,2,6]=>2
[4,1,3,5,6,2]=>2
[4,1,3,6,2,5]=>2
[4,1,3,6,5,2]=>2
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>2
[4,1,5,6,2,3]=>1
[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]=>2
[4,1,6,3,5,2]=>2
[4,1,6,5,2,3]=>2
[4,1,6,5,3,2]=>3
[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>2
[4,2,1,5,3,6]=>2
[4,2,1,5,6,3]=>2
[4,2,1,6,3,5]=>2
[4,2,1,6,5,3]=>3
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>2
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>2
[4,2,3,6,5,1]=>2
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>2
[4,2,5,3,1,6]=>2
[4,2,5,3,6,1]=>2
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>2
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>3
[4,2,6,3,1,5]=>2
[4,2,6,3,5,1]=>2
[4,2,6,5,1,3]=>3
[4,2,6,5,3,1]=>3
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>2
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>2
[4,3,1,6,2,5]=>2
[4,3,1,6,5,2]=>3
[4,3,2,1,5,6]=>3
[4,3,2,1,6,5]=>3
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>3
[4,3,2,6,1,5]=>3
[4,3,2,6,5,1]=>3
[4,3,5,1,2,6]=>2
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>3
[4,3,5,2,6,1]=>3
[4,3,5,6,1,2]=>2
[4,3,5,6,2,1]=>3
[4,3,6,1,2,5]=>2
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>3
[4,3,6,2,5,1]=>3
[4,3,6,5,1,2]=>3
[4,3,6,5,2,1]=>3
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>1
[4,5,1,3,2,6]=>2
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>1
[4,5,1,6,3,2]=>2
[4,5,2,1,3,6]=>2
[4,5,2,1,6,3]=>2
[4,5,2,3,1,6]=>2
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>2
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>3
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>2
[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>1
[4,6,1,2,5,3]=>1
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>2
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>3
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>3
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>3
[4,6,2,5,3,1]=>3
[4,6,3,1,2,5]=>2
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>3
[4,6,3,5,1,2]=>3
[4,6,3,5,2,1]=>3
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>3
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>3
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>1
[5,1,2,4,3,6]=>2
[5,1,2,4,6,3]=>2
[5,1,2,6,3,4]=>1
[5,1,2,6,4,3]=>2
[5,1,3,2,4,6]=>2
[5,1,3,2,6,4]=>2
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>2
[5,1,3,6,2,4]=>2
[5,1,3,6,4,2]=>2
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>3
[5,1,4,6,2,3]=>2
[5,1,4,6,3,2]=>3
[5,1,6,2,3,4]=>1
[5,1,6,2,4,3]=>2
[5,1,6,3,2,4]=>2
[5,1,6,3,4,2]=>2
[5,1,6,4,2,3]=>2
[5,1,6,4,3,2]=>3
[5,2,1,3,4,6]=>2
[5,2,1,3,6,4]=>2
[5,2,1,4,3,6]=>3
[5,2,1,4,6,3]=>3
[5,2,1,6,3,4]=>2
[5,2,1,6,4,3]=>3
[5,2,3,1,4,6]=>2
[5,2,3,1,6,4]=>2
[5,2,3,4,1,6]=>2
[5,2,3,4,6,1]=>2
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>2
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>3
[5,2,4,3,1,6]=>3
[5,2,4,3,6,1]=>3
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>3
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>3
[5,2,6,3,1,4]=>2
[5,2,6,3,4,1]=>2
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>3
[5,3,1,2,4,6]=>2
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>3
[5,3,1,6,2,4]=>2
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>3
[5,3,2,4,1,6]=>3
[5,3,2,4,6,1]=>3
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>3
[5,3,4,1,2,6]=>3
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>3
[5,3,4,2,6,1]=>3
[5,3,4,6,1,2]=>3
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>3
[5,3,6,2,4,1]=>3
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>3
[5,4,1,2,3,6]=>2
[5,4,1,2,6,3]=>2
[5,4,1,3,2,6]=>3
[5,4,1,3,6,2]=>3
[5,4,1,6,2,3]=>2
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>3
[5,4,2,3,6,1]=>3
[5,4,2,6,1,3]=>3
[5,4,2,6,3,1]=>3
[5,4,3,1,2,6]=>3
[5,4,3,1,6,2]=>3
[5,4,3,2,1,6]=>4
[5,4,3,2,6,1]=>4
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>2
[5,4,6,1,3,2]=>3
[5,4,6,2,1,3]=>3
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>3
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>2
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>2
[5,6,1,4,3,2]=>3
[5,6,2,1,3,4]=>2
[5,6,2,1,4,3]=>3
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>2
[5,6,2,4,1,3]=>3
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>2
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>3
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>2
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>3
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>4
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>2
[6,1,2,4,3,5]=>2
[6,1,2,4,5,3]=>2
[6,1,2,5,3,4]=>2
[6,1,2,5,4,3]=>3
[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>2
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>2
[6,1,3,5,2,4]=>2
[6,1,3,5,4,2]=>3
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>2
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>3
[6,1,4,5,2,3]=>2
[6,1,4,5,3,2]=>3
[6,1,5,2,3,4]=>2
[6,1,5,2,4,3]=>3
[6,1,5,3,2,4]=>3
[6,1,5,3,4,2]=>3
[6,1,5,4,2,3]=>3
[6,1,5,4,3,2]=>4
[6,2,1,3,4,5]=>2
[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>3
[6,2,1,4,5,3]=>3
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>2
[6,2,3,4,5,1]=>2
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>3
[6,2,4,1,3,5]=>3
[6,2,4,1,5,3]=>3
[6,2,4,3,1,5]=>3
[6,2,4,3,5,1]=>3
[6,2,4,5,1,3]=>3
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>3
[6,2,5,1,4,3]=>4
[6,2,5,3,1,4]=>3
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>4
[6,3,1,2,4,5]=>2
[6,3,1,2,5,4]=>2
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>3
[6,3,2,4,5,1]=>3
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>3
[6,3,4,1,5,2]=>3
[6,3,4,2,1,5]=>3
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>3
[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>3
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>4
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>4
[6,4,1,2,3,5]=>2
[6,4,1,2,5,3]=>2
[6,4,1,3,2,5]=>3
[6,4,1,3,5,2]=>3
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>3
[6,4,2,3,5,1]=>3
[6,4,2,5,1,3]=>4
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>3
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>4
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>4
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>3
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>4
[6,4,5,2,3,1]=>4
[6,4,5,3,1,2]=>4
[6,4,5,3,2,1]=>4
[6,5,1,2,3,4]=>2
[6,5,1,2,4,3]=>3
[6,5,1,3,2,4]=>3
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>3
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>3
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>4
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>4
[6,5,3,2,4,1]=>4
[6,5,3,4,1,2]=>4
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>4
[6,5,4,2,1,3]=>4
[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>4
[6,5,4,3,2,1]=>5
[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]=>1
[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]=>1
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,3,6,5,4,7]=>1
[1,2,3,6,5,7,4]=>1
[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]=>1
[1,2,3,7,5,4,6]=>1
[1,2,3,7,5,6,4]=>1
[1,2,3,7,6,4,5]=>1
[1,2,3,7,6,5,4]=>2
[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]=>1
[1,2,4,6,3,5,7]=>0
[1,2,4,6,3,7,5]=>0
[1,2,4,6,5,3,7]=>1
[1,2,4,6,5,7,3]=>1
[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]=>1
[1,2,4,7,5,6,3]=>1
[1,2,4,7,6,3,5]=>1
[1,2,4,7,6,5,3]=>2
[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]=>1
[1,2,5,4,3,7,6]=>1
[1,2,5,4,6,3,7]=>1
[1,2,5,4,6,7,3]=>1
[1,2,5,4,7,3,6]=>1
[1,2,5,4,7,6,3]=>1
[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]=>1
[1,2,5,7,6,4,3]=>2
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>0
[1,2,6,3,5,4,7]=>1
[1,2,6,3,5,7,4]=>1
[1,2,6,3,7,4,5]=>0
[1,2,6,3,7,5,4]=>1
[1,2,6,4,3,5,7]=>1
[1,2,6,4,3,7,5]=>1
[1,2,6,4,5,3,7]=>1
[1,2,6,4,5,7,3]=>1
[1,2,6,4,7,3,5]=>1
[1,2,6,4,7,5,3]=>1
[1,2,6,5,3,4,7]=>1
[1,2,6,5,3,7,4]=>1
[1,2,6,5,4,3,7]=>2
[1,2,6,5,4,7,3]=>2
[1,2,6,5,7,3,4]=>1
[1,2,6,5,7,4,3]=>2
[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]=>1
[1,2,6,7,5,3,4]=>1
[1,2,6,7,5,4,3]=>2
[1,2,7,3,4,5,6]=>0
[1,2,7,3,4,6,5]=>1
[1,2,7,3,5,4,6]=>1
[1,2,7,3,5,6,4]=>1
[1,2,7,3,6,4,5]=>1
[1,2,7,3,6,5,4]=>2
[1,2,7,4,3,5,6]=>1
[1,2,7,4,3,6,5]=>1
[1,2,7,4,5,3,6]=>1
[1,2,7,4,5,6,3]=>1
[1,2,7,4,6,3,5]=>1
[1,2,7,4,6,5,3]=>2
[1,2,7,5,3,4,6]=>1
[1,2,7,5,3,6,4]=>1
[1,2,7,5,4,3,6]=>2
[1,2,7,5,4,6,3]=>2
[1,2,7,5,6,3,4]=>1
[1,2,7,5,6,4,3]=>2
[1,2,7,6,3,4,5]=>1
[1,2,7,6,3,5,4]=>2
[1,2,7,6,4,3,5]=>2
[1,2,7,6,4,5,3]=>2
[1,2,7,6,5,3,4]=>2
[1,2,7,6,5,4,3]=>3
[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]=>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]=>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]=>1
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>0
[1,3,4,6,5,2,7]=>1
[1,3,4,6,5,7,2]=>1
[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]=>1
[1,3,4,7,5,6,2]=>1
[1,3,4,7,6,2,5]=>1
[1,3,4,7,6,5,2]=>2
[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]=>1
[1,3,5,4,2,7,6]=>1
[1,3,5,4,6,2,7]=>1
[1,3,5,4,6,7,2]=>1
[1,3,5,4,7,2,6]=>1
[1,3,5,4,7,6,2]=>1
[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]=>1
[1,3,5,7,6,4,2]=>2
[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]=>0
[1,3,6,4,2,5,7]=>1
[1,3,6,4,2,7,5]=>1
[1,3,6,4,5,2,7]=>1
[1,3,6,4,5,7,2]=>1
[1,3,6,4,7,2,5]=>1
[1,3,6,4,7,5,2]=>1
[1,3,6,5,2,4,7]=>1
[1,3,6,5,2,7,4]=>1
[1,3,6,5,4,2,7]=>2
[1,3,6,5,4,7,2]=>2
[1,3,6,5,7,2,4]=>1
[1,3,6,5,7,4,2]=>2
[1,3,6,7,2,4,5]=>0
[1,3,6,7,2,5,4]=>0
[1,3,6,7,4,2,5]=>1
[1,3,6,7,4,5,2]=>1
[1,3,6,7,5,2,4]=>1
[1,3,6,7,5,4,2]=>2
[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]=>1
[1,3,7,4,2,6,5]=>1
[1,3,7,4,5,2,6]=>1
[1,3,7,4,5,6,2]=>1
[1,3,7,4,6,2,5]=>1
[1,3,7,4,6,5,2]=>2
[1,3,7,5,2,4,6]=>1
[1,3,7,5,2,6,4]=>1
[1,3,7,5,4,2,6]=>2
[1,3,7,5,4,6,2]=>2
[1,3,7,5,6,2,4]=>1
[1,3,7,5,6,4,2]=>2
[1,3,7,6,2,4,5]=>1
[1,3,7,6,2,5,4]=>2
[1,3,7,6,4,2,5]=>2
[1,3,7,6,4,5,2]=>2
[1,3,7,6,5,2,4]=>2
[1,3,7,6,5,4,2]=>3
[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]=>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]=>1
[1,4,3,2,5,6,7]=>1
[1,4,3,2,5,7,6]=>1
[1,4,3,2,6,5,7]=>1
[1,4,3,2,6,7,5]=>1
[1,4,3,2,7,5,6]=>1
[1,4,3,2,7,6,5]=>1
[1,4,3,5,2,6,7]=>1
[1,4,3,5,2,7,6]=>1
[1,4,3,5,6,2,7]=>1
[1,4,3,5,6,7,2]=>1
[1,4,3,5,7,2,6]=>1
[1,4,3,5,7,6,2]=>1
[1,4,3,6,2,5,7]=>1
[1,4,3,6,2,7,5]=>1
[1,4,3,6,5,2,7]=>1
[1,4,3,6,5,7,2]=>1
[1,4,3,6,7,2,5]=>1
[1,4,3,6,7,5,2]=>1
[1,4,3,7,2,5,6]=>1
[1,4,3,7,2,6,5]=>1
[1,4,3,7,5,2,6]=>1
[1,4,3,7,5,6,2]=>1
[1,4,3,7,6,2,5]=>1
[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]=>1
[1,4,5,7,6,3,2]=>2
[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]=>0
[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]=>1
[1,4,6,5,2,3,7]=>1
[1,4,6,5,2,7,3]=>1
[1,4,6,5,3,2,7]=>2
[1,4,6,5,3,7,2]=>2
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Description
The number of circled entries of the shifted recording tableau of a permutation.
The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing.
The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled.
This statistic records the number of circled entries in $Q$.
The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing.
The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled.
This statistic records the number of circled entries in $Q$.
References
[1] Sagan, B. E. Shifted tableaux, Schur $Q$-functions, and a conjecture of R. Stanley MathSciNet:0883894
[2] Worley, D. R. A THEORY OF SHIFTED YOUNG TABLEAUX MathSciNet:2941073
[3] Haiman, M. D. On mixed insertion, symmetry, and shifted Young tableaux MathSciNet:0989194
[2] Worley, D. R. A THEORY OF SHIFTED YOUNG TABLEAUX MathSciNet:2941073
[3] Haiman, M. D. On mixed insertion, symmetry, and shifted Young tableaux MathSciNet:0989194
Code
def statistic(pi):
return GrowthDiagram.rules.ShiftedShapes()(pi).Q_chain().count(3)
Created
Jun 25, 2017 at 20:16 by Martin Rubey
Updated
Feb 09, 2021 at 15:04 by Martin Rubey
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