Identifier
- St000338: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>2
[2,1]=>0
[1,2,3]=>3
[1,3,2]=>1
[2,1,3]=>0
[2,3,1]=>1
[3,1,2]=>0
[3,2,1]=>1
[1,2,3,4]=>4
[1,2,4,3]=>2
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>1
[1,4,3,2]=>2
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>1
[2,3,4,1]=>2
[2,4,1,3]=>1
[2,4,3,1]=>2
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>1
[3,2,4,1]=>0
[3,4,1,2]=>1
[3,4,2,1]=>2
[4,1,2,3]=>0
[4,1,3,2]=>0
[4,2,1,3]=>1
[4,2,3,1]=>0
[4,3,1,2]=>1
[4,3,2,1]=>0
[1,2,3,4,5]=>5
[1,2,3,5,4]=>3
[1,2,4,3,5]=>2
[1,2,4,5,3]=>3
[1,2,5,3,4]=>2
[1,2,5,4,3]=>3
[1,3,2,4,5]=>1
[1,3,2,5,4]=>1
[1,3,4,2,5]=>2
[1,3,4,5,2]=>3
[1,3,5,2,4]=>2
[1,3,5,4,2]=>3
[1,4,2,3,5]=>1
[1,4,2,5,3]=>1
[1,4,3,2,5]=>2
[1,4,3,5,2]=>1
[1,4,5,2,3]=>2
[1,4,5,3,2]=>3
[1,5,2,3,4]=>1
[1,5,2,4,3]=>1
[1,5,3,2,4]=>2
[1,5,3,4,2]=>1
[1,5,4,2,3]=>2
[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]=>1
[2,3,1,5,4]=>1
[2,3,4,1,5]=>2
[2,3,4,5,1]=>3
[2,3,5,1,4]=>2
[2,3,5,4,1]=>3
[2,4,1,3,5]=>1
[2,4,1,5,3]=>1
[2,4,3,1,5]=>2
[2,4,3,5,1]=>1
[2,4,5,1,3]=>2
[2,4,5,3,1]=>3
[2,5,1,3,4]=>1
[2,5,1,4,3]=>1
[2,5,3,1,4]=>2
[2,5,3,4,1]=>1
[2,5,4,1,3]=>2
[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]=>1
[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]=>1
[3,4,1,5,2]=>1
[3,4,2,1,5]=>2
[3,4,2,5,1]=>1
[3,4,5,1,2]=>2
[3,4,5,2,1]=>3
[3,5,1,2,4]=>1
[3,5,1,4,2]=>1
[3,5,2,1,4]=>2
[3,5,2,4,1]=>1
[3,5,4,1,2]=>2
[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]=>0
[4,2,1,3,5]=>1
[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]=>1
[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]=>1
[4,5,1,3,2]=>1
[4,5,2,1,3]=>2
[4,5,2,3,1]=>1
[4,5,3,1,2]=>2
[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]=>0
[5,2,1,3,4]=>1
[5,2,1,4,3]=>1
[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]=>1
[5,3,1,4,2]=>1
[5,3,2,1,4]=>0
[5,3,2,4,1]=>1
[5,3,4,1,2]=>0
[5,3,4,2,1]=>0
[5,4,1,2,3]=>1
[5,4,1,3,2]=>1
[5,4,2,1,3]=>0
[5,4,2,3,1]=>1
[5,4,3,1,2]=>0
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>6
[1,2,3,4,6,5]=>4
[1,2,3,5,4,6]=>3
[1,2,3,5,6,4]=>4
[1,2,3,6,4,5]=>3
[1,2,3,6,5,4]=>4
[1,2,4,3,5,6]=>2
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>3
[1,2,4,5,6,3]=>4
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>4
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>3
[1,2,5,6,4,3]=>4
[1,2,6,3,4,5]=>2
[1,2,6,3,5,4]=>2
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>2
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>2
[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]=>2
[1,3,4,2,6,5]=>2
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>2
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>4
[1,3,6,2,4,5]=>2
[1,3,6,2,5,4]=>2
[1,3,6,4,2,5]=>3
[1,3,6,4,5,2]=>2
[1,3,6,5,2,4]=>3
[1,3,6,5,4,2]=>2
[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]=>2
[1,4,3,2,6,5]=>2
[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]=>2
[1,4,5,2,6,3]=>2
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>2
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>3
[1,4,6,3,5,2]=>2
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>2
[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]=>2
[1,5,3,2,6,4]=>2
[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]=>2
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>1
[1,5,4,3,6,2]=>2
[1,5,4,6,2,3]=>1
[1,5,4,6,3,2]=>1
[1,5,6,2,3,4]=>2
[1,5,6,2,4,3]=>2
[1,5,6,3,2,4]=>3
[1,5,6,3,4,2]=>2
[1,5,6,4,2,3]=>3
[1,5,6,4,3,2]=>2
[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]=>2
[1,6,3,2,5,4]=>2
[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]=>2
[1,6,4,2,5,3]=>2
[1,6,4,3,2,5]=>1
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>2
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>1
[1,6,5,3,4,2]=>2
[1,6,5,4,2,3]=>1
[1,6,5,4,3,2]=>2
[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]=>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]=>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]=>2
[2,3,4,1,6,5]=>2
[2,3,4,5,1,6]=>3
[2,3,4,5,6,1]=>4
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>4
[2,3,5,1,4,6]=>2
[2,3,5,1,6,4]=>2
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>3
[2,3,5,6,4,1]=>4
[2,3,6,1,4,5]=>2
[2,3,6,1,5,4]=>2
[2,3,6,4,1,5]=>3
[2,3,6,4,5,1]=>2
[2,3,6,5,1,4]=>3
[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]=>1
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>2
[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]=>2
[2,4,5,1,6,3]=>2
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>2
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>2
[2,4,6,1,5,3]=>2
[2,4,6,3,1,5]=>3
[2,4,6,3,5,1]=>2
[2,4,6,5,1,3]=>3
[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]=>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]=>2
[2,5,3,1,6,4]=>2
[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]=>1
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>1
[2,5,4,6,3,1]=>1
[2,5,6,1,3,4]=>2
[2,5,6,1,4,3]=>2
[2,5,6,3,1,4]=>3
[2,5,6,3,4,1]=>2
[2,5,6,4,1,3]=>3
[2,5,6,4,3,1]=>2
[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]=>2
[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]=>1
[2,6,3,5,4,1]=>1
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>2
[2,6,4,3,1,5]=>1
[2,6,4,3,5,1]=>2
[2,6,4,5,1,3]=>1
[2,6,4,5,3,1]=>1
[2,6,5,1,3,4]=>2
[2,6,5,1,4,3]=>2
[2,6,5,3,1,4]=>1
[2,6,5,3,4,1]=>2
[2,6,5,4,1,3]=>1
[2,6,5,4,3,1]=>2
[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]=>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]=>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]=>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]=>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]=>2
[3,4,2,1,6,5]=>2
[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]=>2
[3,4,5,1,6,2]=>2
[3,4,5,2,1,6]=>3
[3,4,5,2,6,1]=>2
[3,4,5,6,1,2]=>3
[3,4,5,6,2,1]=>4
[3,4,6,1,2,5]=>2
[3,4,6,1,5,2]=>2
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>3
[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]=>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]=>2
[3,5,2,1,6,4]=>2
[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]=>2
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>2
[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]=>2
[3,5,6,2,1,4]=>3
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>3
[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]=>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]=>2
[3,6,2,1,5,4]=>2
[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]=>2
[3,6,4,1,5,2]=>2
[3,6,4,2,1,5]=>1
[3,6,4,2,5,1]=>2
[3,6,4,5,1,2]=>1
[3,6,4,5,2,1]=>1
[3,6,5,1,2,4]=>2
[3,6,5,1,4,2]=>2
[3,6,5,2,1,4]=>1
[3,6,5,2,4,1]=>2
[3,6,5,4,1,2]=>1
[3,6,5,4,2,1]=>2
[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]=>0
[4,1,5,3,6,2]=>0
[4,1,5,6,2,3]=>0
[4,1,5,6,3,2]=>0
[4,1,6,2,3,5]=>0
[4,1,6,2,5,3]=>0
[4,1,6,3,2,5]=>0
[4,1,6,3,5,2]=>0
[4,1,6,5,2,3]=>0
[4,1,6,5,3,2]=>0
[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]=>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]=>0
[4,2,5,3,6,1]=>0
[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]=>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]=>0
[4,3,2,1,6,5]=>0
[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]=>0
[4,3,5,2,6,1]=>0
[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]=>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]=>2
[4,5,2,1,6,3]=>2
[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]=>2
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>2
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>1
[4,5,6,1,2,3]=>2
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>3
[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>3
[4,5,6,3,2,1]=>2
[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]=>2
[4,6,2,1,5,3]=>2
[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]=>2
[4,6,3,1,5,2]=>2
[4,6,3,2,1,5]=>1
[4,6,3,2,5,1]=>2
[4,6,3,5,1,2]=>1
[4,6,3,5,2,1]=>1
[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]=>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]=>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]=>0
[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]=>0
[5,1,4,6,3,2]=>0
[5,1,6,2,3,4]=>0
[5,1,6,2,4,3]=>0
[5,1,6,3,2,4]=>0
[5,1,6,3,4,2]=>0
[5,1,6,4,2,3]=>0
[5,1,6,4,3,2]=>0
[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]=>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]=>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]=>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]=>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]=>0
[5,3,2,1,6,4]=>0
[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]=>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]=>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]=>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]=>0
[5,4,2,1,6,3]=>0
[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]=>0
[5,4,3,1,6,2]=>0
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>1
[5,4,3,6,2,1]=>1
[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]=>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]=>2
[5,6,2,1,4,3]=>2
[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]=>2
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>1
[5,6,3,2,4,1]=>2
[5,6,3,4,1,2]=>1
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>2
[5,6,4,1,3,2]=>2
[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]=>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]=>0
[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]=>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]=>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]=>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]=>0
[6,3,2,1,5,4]=>0
[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]=>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]=>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]=>0
[6,4,2,1,5,3]=>0
[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]=>0
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>1
[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]=>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]=>0
[6,5,2,1,4,3]=>0
[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]=>0
[6,5,3,1,4,2]=>0
[6,5,3,2,1,4]=>1
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>0
[6,5,4,2,1,3]=>1
[6,5,4,2,3,1]=>0
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of pixed points of a permutation.
For a permutation $\sigma = p \tau_{1} \tau_{2} \cdots \tau_{k}$ in its hook factorization, [1] defines
$$\textrm{pix} \, \sigma = \textrm{length} (p)$$.
For a permutation $\sigma = p \tau_{1} \tau_{2} \cdots \tau_{k}$ in its hook factorization, [1] defines
$$\textrm{pix} \, \sigma = \textrm{length} (p)$$.
References
[1] Foata, D., Han, G.-N. Fix-Mahonian Calculus III; a Quadruple Distribution arXiv:math/0703454
Code
def hook_factorization(w):
"""
sage: w=[1,2,4,5,6,4,5,6,4,1,3,6,5,5,4,6,1,1,4,5,1,1]
sage: hook_factorization(w)
[[1, 2, 4, 5],
[6, 4, 5, 6],
[4, 1, 3],
[6, 5],
[5, 4],
[6, 1, 1, 4],
[5, 1, 1]]
sage: w=[1,3,4,14,12,2,5,11,15,8,6,7,13,9,10]
sage: hook_factorization(w)
[[1, 3, 4, 14], [12, 2, 5, 11, 15], [8, 6, 7], [13, 9, 10]]
"""
if len(w) == 0:
return []
w1 = w + [max(w)+1]
i = len(w)-1
while w1[i] <= w1[i+1]:
i -= 1
if i == -1:
return [w]
else:
return hook_factorization(w[:i]) + [w[i:]]
def statistic(pi):
p0 = hook_factorization(pi)[0]
if len(p0) == 1 or p0[0] < p0[1]:
return len(p0)
else:
return 0
Created
Dec 18, 2015 at 13:44 by Joseph Bernstein
Updated
Apr 06, 2016 at 22:50 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!