- FindStat

edit this statistic or download as text // json

Identifier

St000039: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        []=>0
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>1
[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]=>1
[1,4,2,3]=>0
[1,4,3,2]=>0
[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]=>1
[3,1,2,4]=>0
[3,1,4,2]=>1
[3,2,1,4]=>0
[3,2,4,1]=>1
[3,4,1,2]=>2
[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]=>1
[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]=>1
[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]=>1
[1,3,4,5,2]=>2
[1,3,5,2,4]=>1
[1,3,5,4,2]=>1
[1,4,2,3,5]=>0
[1,4,2,5,3]=>1
[1,4,3,2,5]=>0
[1,4,3,5,2]=>1
[1,4,5,2,3]=>2
[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]=>1
[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]=>1
[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]=>2
[2,4,1,3,5]=>1
[2,4,1,5,3]=>2
[2,4,3,1,5]=>1
[2,4,3,5,1]=>2
[2,4,5,1,3]=>3
[2,4,5,3,1]=>2
[2,5,1,3,4]=>1
[2,5,1,4,3]=>1
[2,5,3,1,4]=>1
[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]=>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]=>0
[3,2,4,1,5]=>1
[3,2,4,5,1]=>2
[3,2,5,1,4]=>1
[3,2,5,4,1]=>1
[3,4,1,2,5]=>2
[3,4,1,5,2]=>3
[3,4,2,1,5]=>1
[3,4,2,5,1]=>2
[3,4,5,1,2]=>4
[3,4,5,2,1]=>3
[3,5,1,2,4]=>2
[3,5,1,4,2]=>2
[3,5,2,1,4]=>1
[3,5,2,4,1]=>1
[3,5,4,1,2]=>3
[3,5,4,2,1]=>2
[4,1,2,3,5]=>0
[4,1,2,5,3]=>1
[4,1,3,2,5]=>0
[4,1,3,5,2]=>1
[4,1,5,2,3]=>2
[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]=>1
[4,2,5,1,3]=>2
[4,2,5,3,1]=>1
[4,3,1,2,5]=>1
[4,3,1,5,2]=>2
[4,3,2,1,5]=>0
[4,3,2,5,1]=>1
[4,3,5,1,2]=>3
[4,3,5,2,1]=>2
[4,5,1,2,3]=>3
[4,5,1,3,2]=>2
[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]=>1
[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]=>1
[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]=>0
[5,3,4,1,2]=>2
[5,3,4,2,1]=>1
[5,4,1,2,3]=>2
[5,4,1,3,2]=>1
[5,4,2,1,3]=>1
[5,4,2,3,1]=>0
[5,4,3,1,2]=>1
[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]=>1
[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]=>1
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>1
[1,2,4,6,5,3]=>1
[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]=>1
[1,2,5,6,3,4]=>2
[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]=>1
[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]=>1
[1,3,2,6,4,5]=>0
[1,3,2,6,5,4]=>0
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>1
[1,3,4,5,2,6]=>2
[1,3,4,5,6,2]=>3
[1,3,4,6,2,5]=>2
[1,3,4,6,5,2]=>2
[1,3,5,2,4,6]=>1
[1,3,5,2,6,4]=>2
[1,3,5,4,2,6]=>1
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>2
[1,3,6,2,4,5]=>1
[1,3,6,2,5,4]=>1
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>1
[1,3,6,5,2,4]=>2
[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]=>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]=>0
[1,4,3,5,2,6]=>1
[1,4,3,5,6,2]=>2
[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]=>3
[1,4,5,3,2,6]=>1
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>4
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>2
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>1
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>2
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>1
[1,5,2,4,3,6]=>0
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>2
[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]=>1
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>1
[1,5,4,2,3,6]=>1
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>1
[1,5,4,6,2,3]=>3
[1,5,4,6,3,2]=>2
[1,5,6,2,3,4]=>3
[1,5,6,2,4,3]=>2
[1,5,6,3,2,4]=>2
[1,5,6,3,4,2]=>1
[1,5,6,4,2,3]=>2
[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]=>1
[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]=>1
[1,6,3,5,4,2]=>0
[1,6,4,2,3,5]=>1
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>0
[1,6,4,3,5,2]=>0
[1,6,4,5,2,3]=>2
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>2
[1,6,5,2,4,3]=>1
[1,6,5,3,2,4]=>1
[1,6,5,3,4,2]=>0
[1,6,5,4,2,3]=>1
[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]=>1
[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]=>1
[2,1,4,5,6,3]=>2
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>1
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>1
[2,1,5,6,3,4]=>2
[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]=>1
[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]=>2
[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]=>3
[2,3,5,1,4,6]=>2
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>3
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>3
[2,3,6,1,4,5]=>2
[2,3,6,1,5,4]=>2
[2,3,6,4,1,5]=>2
[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]=>2
[2,4,1,5,6,3]=>3
[2,4,1,6,3,5]=>2
[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]=>2
[2,4,3,5,6,1]=>3
[2,4,3,6,1,5]=>2
[2,4,3,6,5,1]=>2
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>2
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>5
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>3
[2,4,6,3,1,5]=>2
[2,4,6,3,5,1]=>2
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>3
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>2
[2,5,1,6,3,4]=>3
[2,5,1,6,4,3]=>2
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>2
[2,5,3,4,1,6]=>1
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>3
[2,5,3,6,4,1]=>2
[2,5,4,1,3,6]=>2
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>1
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>4
[2,5,6,1,4,3]=>3
[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]=>2
[2,6,1,5,4,3]=>1
[2,6,3,1,4,5]=>1
[2,6,3,1,5,4]=>1
[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]=>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]=>1
[2,6,4,5,1,3]=>3
[2,6,4,5,3,1]=>2
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>2
[2,6,5,3,1,4]=>2
[2,6,5,3,4,1]=>1
[2,6,5,4,1,3]=>2
[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]=>1
[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>0
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>1
[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]=>2
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>2
[3,1,5,6,2,4]=>3
[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]=>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]=>1
[3,2,1,6,4,5]=>0
[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>1
[3,2,4,5,1,6]=>2
[3,2,4,5,6,1]=>3
[3,2,4,6,1,5]=>2
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>1
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>1
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>3
[3,2,5,6,4,1]=>2
[3,2,6,1,4,5]=>1
[3,2,6,1,5,4]=>1
[3,2,6,4,1,5]=>1
[3,2,6,4,5,1]=>1
[3,2,6,5,1,4]=>2
[3,2,6,5,4,1]=>1
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>3
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>3
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>1
[3,4,2,5,1,6]=>2
[3,4,2,5,6,1]=>3
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>2
[3,4,5,1,2,6]=>4
[3,4,5,1,6,2]=>5
[3,4,5,2,1,6]=>3
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>6
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>4
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>4
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>3
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>3
[3,5,1,6,2,4]=>4
[3,5,1,6,4,2]=>3
[3,5,2,1,4,6]=>1
[3,5,2,1,6,4]=>2
[3,5,2,4,1,6]=>1
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>3
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>3
[3,5,4,6,1,2]=>5
[3,5,4,6,2,1]=>4
[3,5,6,1,2,4]=>5
[3,5,6,1,4,2]=>4
[3,5,6,2,1,4]=>4
[3,5,6,2,4,1]=>3
[3,5,6,4,1,2]=>4
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>2
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>2
[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]=>2
[3,6,2,5,4,1]=>1
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>2
[3,6,4,2,5,1]=>2
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>4
[3,6,5,1,4,2]=>3
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>2
[3,6,5,4,1,2]=>3
[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]=>1
[4,1,2,5,6,3]=>2
[4,1,2,6,3,5]=>1
[4,1,2,6,5,3]=>1
[4,1,3,2,5,6]=>0
[4,1,3,2,6,5]=>0
[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]=>2
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>2
[4,1,5,6,2,3]=>4
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>2
[4,1,6,3,2,5]=>1
[4,1,6,3,5,2]=>1
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>2
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>0
[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]=>0
[4,2,3,5,1,6]=>1
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>1
[4,2,3,6,5,1]=>1
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>3
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>2
[4,2,5,6,1,3]=>4
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>2
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>3
[4,2,6,5,3,1]=>2
[4,3,1,2,5,6]=>1
[4,3,1,2,6,5]=>1
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>2
[4,3,1,6,5,2]=>2
[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]=>2
[4,3,2,6,1,5]=>1
[4,3,2,6,5,1]=>1
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>2
[4,3,5,2,6,1]=>3
[4,3,5,6,1,2]=>5
[4,3,5,6,2,1]=>4
[4,3,6,1,2,5]=>3
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>2
[4,3,6,2,5,1]=>2
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>3
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>4
[4,5,1,3,2,6]=>2
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>5
[4,5,1,6,3,2]=>4
[4,5,2,1,3,6]=>2
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>4
[4,5,2,6,3,1]=>3
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>2
[4,5,3,6,1,2]=>4
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>6
[4,5,6,1,3,2]=>5
[4,5,6,2,1,3]=>5
[4,5,6,2,3,1]=>4
[4,5,6,3,1,2]=>4
[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>2
[4,6,1,5,2,3]=>4
[4,6,1,5,3,2]=>3
[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]=>3
[4,6,2,5,3,1]=>2
[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]=>1
[4,6,3,5,1,2]=>3
[4,6,3,5,2,1]=>2
[4,6,5,1,2,3]=>5
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>4
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>1
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>1
[5,1,2,6,3,4]=>2
[5,1,2,6,4,3]=>1
[5,1,3,2,4,6]=>0
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>0
[5,1,3,4,6,2]=>1
[5,1,3,6,2,4]=>2
[5,1,3,6,4,2]=>1
[5,1,4,2,3,6]=>1
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>0
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>3
[5,1,4,6,3,2]=>2
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>2
[5,1,6,3,2,4]=>2
[5,1,6,3,4,2]=>1
[5,1,6,4,2,3]=>2
[5,1,6,4,3,2]=>1
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>1
[5,2,1,4,3,6]=>0
[5,2,1,4,6,3]=>1
[5,2,1,6,3,4]=>2
[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]=>1
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>1
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>2
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>1
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>2
[5,2,6,1,3,4]=>3
[5,2,6,1,4,3]=>2
[5,2,6,3,1,4]=>2
[5,2,6,3,4,1]=>1
[5,2,6,4,1,3]=>2
[5,2,6,4,3,1]=>1
[5,3,1,2,4,6]=>1
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>1
[5,3,1,4,6,2]=>2
[5,3,1,6,2,4]=>3
[5,3,1,6,4,2]=>2
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>1
[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>1
[5,3,2,6,1,4]=>2
[5,3,2,6,4,1]=>1
[5,3,4,1,2,6]=>2
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>2
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>4
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>3
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>2
[5,4,1,2,3,6]=>2
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>1
[5,4,1,3,6,2]=>2
[5,4,1,6,2,3]=>4
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>1
[5,4,2,1,6,3]=>2
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>3
[5,4,2,6,3,1]=>2
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>2
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>1
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>2
[5,4,6,1,2,3]=>5
[5,4,6,1,3,2]=>4
[5,4,6,2,1,3]=>4
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>3
[5,4,6,3,2,1]=>2
[5,6,1,2,3,4]=>4
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>3
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>2
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>1
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>1
[5,6,3,1,2,4]=>3
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>2
[5,6,3,2,4,1]=>1
[5,6,3,4,1,2]=>2
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>4
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>2
[5,6,4,3,2,1]=>1
[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]=>1
[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]=>1
[6,1,3,5,4,2]=>0
[6,1,4,2,3,5]=>1
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>0
[6,1,4,5,2,3]=>2
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>2
[6,1,5,2,4,3]=>1
[6,1,5,3,2,4]=>1
[6,1,5,3,4,2]=>0
[6,1,5,4,2,3]=>1
[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]=>1
[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]=>1
[6,2,3,5,4,1]=>0
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>1
[6,2,4,3,1,5]=>0
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>2
[6,2,4,5,3,1]=>1
[6,2,5,1,3,4]=>2
[6,2,5,1,4,3]=>1
[6,2,5,3,1,4]=>1
[6,2,5,3,4,1]=>0
[6,2,5,4,1,3]=>1
[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]=>2
[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]=>0
[6,3,4,1,2,5]=>2
[6,3,4,1,5,2]=>2
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>1
[6,3,4,5,1,2]=>3
[6,3,4,5,2,1]=>2
[6,3,5,1,2,4]=>3
[6,3,5,1,4,2]=>2
[6,3,5,2,1,4]=>2
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>2
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>2
[6,4,1,2,5,3]=>2
[6,4,1,3,2,5]=>1
[6,4,1,3,5,2]=>1
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>2
[6,4,2,1,3,5]=>1
[6,4,2,1,5,3]=>1
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>2
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>1
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>2
[6,4,3,5,2,1]=>1
[6,4,5,1,2,3]=>4
[6,4,5,1,3,2]=>3
[6,4,5,2,1,3]=>3
[6,4,5,2,3,1]=>2
[6,4,5,3,1,2]=>2
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>3
[6,5,1,2,4,3]=>2
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>1
[6,5,1,4,2,3]=>2
[6,5,1,4,3,2]=>1
[6,5,2,1,3,4]=>2
[6,5,2,1,4,3]=>1
[6,5,2,3,1,4]=>1
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>1
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>2
[6,5,3,1,4,2]=>1
[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]=>0
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>2
[6,5,4,2,1,3]=>2
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>0
                    

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Description

The number of crossings of a permutation.
A crossing of a permutation $\pi$ is given by a pair $(i,j)$ such that either $i < j \leq \pi(i) \leq \pi(j)$ or $\pi(i) < \pi(j) < i < j$.
Pictorially, the diagram of a permutation is obtained by writing the numbers from $1$ to $n$ in this order on a line, and connecting $i$ and $\pi(i)$ with an arc above the line if $i\leq\pi(i)$ and with an arc below the line if $i > \pi(i)$. Then the number of crossings is the number of pairs of arcs above the line that cross or touch, plus the number of arcs below the line that cross.

References

[1] Corteel, S. Crossings and alignments of permutations MathSciNet:2290808

Code

def statistic(pi):
    n = len(pi)
    return sum( 1 for i in range(1,n+1) for j in range(1,n+1) if i < j <= pi(i) < pi(j) or pi(i) < pi(j) < i < j )

Created

Feb 21, 2013 at 01:01 by Mirkó Visontai

Updated

May 10, 2019 at 17:13 by Henning Ulfarsson