- FindStat

edit this statistic or download as text // json

Identifier

St001375: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>3
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>3
[1,3,2,4]=>3
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>3
[2,1,3,4]=>1
[2,1,4,3]=>3
[2,3,1,4]=>2
[2,3,4,1]=>2
[2,4,1,3]=>4
[2,4,3,1]=>3
[3,1,2,4]=>2
[3,1,4,2]=>4
[3,2,1,4]=>1
[3,2,4,1]=>3
[3,4,1,2]=>3
[3,4,2,1]=>2
[4,1,2,3]=>2
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>4
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,2,3,4,5]=>0
[1,2,3,5,4]=>3
[1,2,4,3,5]=>3
[1,2,4,5,3]=>4
[1,2,5,3,4]=>4
[1,2,5,4,3]=>3
[1,3,2,4,5]=>3
[1,3,2,5,4]=>5
[1,3,4,2,5]=>3
[1,3,4,5,2]=>3
[1,3,5,2,4]=>5
[1,3,5,4,2]=>4
[1,4,2,3,5]=>3
[1,4,2,5,3]=>5
[1,4,3,2,5]=>3
[1,4,3,5,2]=>5
[1,4,5,2,3]=>3
[1,4,5,3,2]=>4
[1,5,2,3,4]=>3
[1,5,2,4,3]=>4
[1,5,3,2,4]=>5
[1,5,3,4,2]=>5
[1,5,4,2,3]=>4
[1,5,4,3,2]=>3
[2,1,3,4,5]=>1
[2,1,3,5,4]=>4
[2,1,4,3,5]=>3
[2,1,4,5,3]=>3
[2,1,5,3,4]=>3
[2,1,5,4,3]=>4
[2,3,1,4,5]=>2
[2,3,1,5,4]=>4
[2,3,4,1,5]=>2
[2,3,4,5,1]=>2
[2,3,5,1,4]=>4
[2,3,5,4,1]=>3
[2,4,1,3,5]=>4
[2,4,1,5,3]=>5
[2,4,3,1,5]=>3
[2,4,3,5,1]=>5
[2,4,5,1,3]=>4
[2,4,5,3,1]=>4
[2,5,1,3,4]=>4
[2,5,1,4,3]=>5
[2,5,3,1,4]=>5
[2,5,3,4,1]=>4
[2,5,4,1,3]=>4
[2,5,4,3,1]=>3
[3,1,2,4,5]=>2
[3,1,2,5,4]=>4
[3,1,4,2,5]=>4
[3,1,4,5,2]=>4
[3,1,5,2,4]=>5
[3,1,5,4,2]=>5
[3,2,1,4,5]=>1
[3,2,1,5,4]=>3
[3,2,4,1,5]=>3
[3,2,4,5,1]=>3
[3,2,5,1,4]=>4
[3,2,5,4,1]=>4
[3,4,1,2,5]=>3
[3,4,1,5,2]=>4
[3,4,2,1,5]=>2
[3,4,2,5,1]=>4
[3,4,5,1,2]=>3
[3,4,5,2,1]=>2
[3,5,1,2,4]=>4
[3,5,1,4,2]=>5
[3,5,2,1,4]=>4
[3,5,2,4,1]=>5
[3,5,4,1,2]=>4
[3,5,4,2,1]=>3
[4,1,2,3,5]=>2
[4,1,2,5,3]=>4
[4,1,3,2,5]=>3
[4,1,3,5,2]=>5
[4,1,5,2,3]=>4
[4,1,5,3,2]=>4
[4,2,1,3,5]=>3
[4,2,1,5,3]=>4
[4,2,3,1,5]=>4
[4,2,3,5,1]=>4
[4,2,5,1,3]=>5
[4,2,5,3,1]=>5
[4,3,1,2,5]=>2
[4,3,1,5,2]=>4
[4,3,2,1,5]=>1
[4,3,2,5,1]=>3
[4,3,5,1,2]=>4
[4,3,5,2,1]=>3
[4,5,1,2,3]=>3
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>4
[4,5,3,1,2]=>3
[4,5,3,2,1]=>2
[5,1,2,3,4]=>2
[5,1,2,4,3]=>3
[5,1,3,2,4]=>5
[5,1,3,4,2]=>4
[5,1,4,2,3]=>4
[5,1,4,3,2]=>3
[5,2,1,3,4]=>3
[5,2,1,4,3]=>4
[5,2,3,1,4]=>4
[5,2,3,4,1]=>4
[5,2,4,1,3]=>5
[5,2,4,3,1]=>4
[5,3,1,2,4]=>4
[5,3,1,4,2]=>5
[5,3,2,1,4]=>3
[5,3,2,4,1]=>4
[5,3,4,1,2]=>4
[5,3,4,2,1]=>4
[5,4,1,2,3]=>2
[5,4,1,3,2]=>3
[5,4,2,1,3]=>3
[5,4,2,3,1]=>4
[5,4,3,1,2]=>2
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>3
[1,2,3,5,4,6]=>3
[1,2,3,5,6,4]=>4
[1,2,3,6,4,5]=>4
[1,2,3,6,5,4]=>3
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>5
[1,2,4,5,3,6]=>4
[1,2,4,5,6,3]=>4
[1,2,4,6,3,5]=>6
[1,2,4,6,5,3]=>5
[1,2,5,3,4,6]=>4
[1,2,5,3,6,4]=>6
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>5
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>4
[1,2,6,3,4,5]=>4
[1,2,6,3,5,4]=>5
[1,2,6,4,3,5]=>5
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>4
[1,2,6,5,4,3]=>3
[1,3,2,4,5,6]=>3
[1,3,2,4,6,5]=>6
[1,3,2,5,4,6]=>5
[1,3,2,5,6,4]=>5
[1,3,2,6,4,5]=>5
[1,3,2,6,5,4]=>5
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>5
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>3
[1,3,4,6,2,5]=>5
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>5
[1,3,5,2,6,4]=>6
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>6
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>5
[1,3,6,2,4,5]=>5
[1,3,6,2,5,4]=>6
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>6
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>5
[1,4,2,5,3,6]=>5
[1,4,2,5,6,3]=>5
[1,4,2,6,3,5]=>6
[1,4,2,6,5,3]=>6
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>5
[1,4,3,5,2,6]=>5
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>6
[1,4,3,6,5,2]=>6
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>4
[1,4,5,3,6,2]=>5
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>5
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>5
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>6
[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>6
[1,5,3,2,4,6]=>5
[1,5,3,2,6,4]=>6
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>5
[1,5,3,6,2,4]=>6
[1,5,3,6,4,2]=>6
[1,5,4,2,3,6]=>4
[1,5,4,2,6,3]=>6
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>5
[1,5,4,6,2,3]=>5
[1,5,4,6,3,2]=>5
[1,5,6,2,3,4]=>3
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>5
[1,5,6,3,4,2]=>5
[1,5,6,4,2,3]=>5
[1,5,6,4,3,2]=>4
[1,6,2,3,4,5]=>3
[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>6
[1,6,2,4,5,3]=>5
[1,6,2,5,3,4]=>5
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>5
[1,6,3,2,5,4]=>6
[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>5
[1,6,3,5,2,4]=>6
[1,6,3,5,4,2]=>6
[1,6,4,2,3,5]=>5
[1,6,4,2,5,3]=>6
[1,6,4,3,2,5]=>5
[1,6,4,3,5,2]=>6
[1,6,4,5,2,3]=>5
[1,6,4,5,3,2]=>5
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>5
[1,6,5,3,2,4]=>5
[1,6,5,3,4,2]=>5
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>3
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>5
[2,1,3,6,4,5]=>5
[2,1,3,6,5,4]=>4
[2,1,4,3,5,6]=>3
[2,1,4,3,6,5]=>5
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>3
[2,1,4,6,3,5]=>5
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>5
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>5
[2,1,5,6,3,4]=>3
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>3
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>5
[2,1,6,4,5,3]=>5
[2,1,6,5,3,4]=>4
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>5
[2,3,1,5,4,6]=>4
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>5
[2,3,4,1,5,6]=>2
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>2
[2,3,4,5,6,1]=>2
[2,3,4,6,1,5]=>4
[2,3,4,6,5,1]=>3
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>5
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>4
[2,3,6,1,4,5]=>4
[2,3,6,1,5,4]=>5
[2,3,6,4,1,5]=>5
[2,3,6,4,5,1]=>4
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>3
[2,4,1,3,5,6]=>4
[2,4,1,3,6,5]=>6
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>6
[2,4,1,6,5,3]=>6
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>5
[2,4,3,6,1,5]=>5
[2,4,3,6,5,1]=>5
[2,4,5,1,3,6]=>4
[2,4,5,1,6,3]=>5
[2,4,5,3,1,6]=>4
[2,4,5,3,6,1]=>5
[2,4,5,6,1,3]=>4
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>6
[2,4,6,3,5,1]=>6
[2,4,6,5,1,3]=>5
[2,4,6,5,3,1]=>5
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>6
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>6
[2,5,1,6,3,4]=>5
[2,5,1,6,4,3]=>5
[2,5,3,1,4,6]=>5
[2,5,3,1,6,4]=>6
[2,5,3,4,1,6]=>4
[2,5,3,4,6,1]=>5
[2,5,3,6,1,4]=>6
[2,5,3,6,4,1]=>6
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>5
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>5
[2,5,4,6,1,3]=>6
[2,5,4,6,3,1]=>5
[2,5,6,1,3,4]=>4
[2,5,6,1,4,3]=>5
[2,5,6,3,1,4]=>5
[2,5,6,3,4,1]=>5
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>5
[2,6,1,4,3,5]=>6
[2,6,1,4,5,3]=>5
[2,6,1,5,3,4]=>5
[2,6,1,5,4,3]=>5
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>6
[2,6,3,4,1,5]=>5
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>6
[2,6,3,5,4,1]=>5
[2,6,4,1,3,5]=>6
[2,6,4,1,5,3]=>6
[2,6,4,3,1,5]=>5
[2,6,4,3,5,1]=>5
[2,6,4,5,1,3]=>6
[2,6,4,5,3,1]=>6
[2,6,5,1,3,4]=>4
[2,6,5,1,4,3]=>5
[2,6,5,3,1,4]=>5
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>4
[2,6,5,4,3,1]=>3
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>5
[3,1,2,5,4,6]=>4
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>5
[3,1,4,2,5,6]=>4
[3,1,4,2,6,5]=>6
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>6
[3,1,4,6,5,2]=>5
[3,1,5,2,4,6]=>5
[3,1,5,2,6,4]=>6
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>6
[3,1,5,6,2,4]=>5
[3,1,5,6,4,2]=>5
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>6
[3,1,6,4,2,5]=>6
[3,1,6,4,5,2]=>5
[3,1,6,5,2,4]=>5
[3,1,6,5,4,2]=>5
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>3
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>3
[3,2,4,5,6,1]=>3
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>4
[3,2,5,1,6,4]=>5
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>5
[3,2,5,6,1,4]=>5
[3,2,5,6,4,1]=>5
[3,2,6,1,4,5]=>4
[3,2,6,1,5,4]=>5
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>5
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>3
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>4
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>6
[3,4,1,6,5,2]=>5
[3,4,2,1,5,6]=>2
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>4
[3,4,2,5,6,1]=>4
[3,4,2,6,1,5]=>5
[3,4,2,6,5,1]=>5
[3,4,5,1,2,6]=>3
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>2
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>3
[3,4,5,6,2,1]=>2
[3,4,6,1,2,5]=>5
[3,4,6,1,5,2]=>5
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>5
[3,4,6,5,1,2]=>4
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>4
[3,5,1,2,6,4]=>6
[3,5,1,4,2,6]=>5
[3,5,1,4,6,2]=>6
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>6
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>5
[3,5,2,4,1,6]=>5
[3,5,2,4,6,1]=>6
[3,5,2,6,1,4]=>6
[3,5,2,6,4,1]=>6
[3,5,4,1,2,6]=>4
[3,5,4,1,6,2]=>5
[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>5
[3,5,4,6,1,2]=>6
[3,5,4,6,2,1]=>5
[3,5,6,1,2,4]=>5
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>4
[3,5,6,2,4,1]=>5
[3,5,6,4,1,2]=>5
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>5
[3,6,1,4,2,5]=>6
[3,6,1,4,5,2]=>6
[3,6,1,5,2,4]=>6
[3,6,1,5,4,2]=>5
[3,6,2,1,4,5]=>4
[3,6,2,1,5,4]=>5
[3,6,2,4,1,5]=>6
[3,6,2,4,5,1]=>5
[3,6,2,5,1,4]=>6
[3,6,2,5,4,1]=>5
[3,6,4,1,2,5]=>6
[3,6,4,1,5,2]=>6
[3,6,4,2,1,5]=>5
[3,6,4,2,5,1]=>6
[3,6,4,5,1,2]=>5
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>4
[3,6,5,1,4,2]=>5
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>5
[3,6,5,4,1,2]=>4
[3,6,5,4,2,1]=>3
[4,1,2,3,5,6]=>2
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>4
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>5
[4,1,3,2,5,6]=>3
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>5
[4,1,3,6,2,5]=>6
[4,1,3,6,5,2]=>6
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>6
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>6
[4,1,5,6,2,3]=>4
[4,1,5,6,3,2]=>4
[4,1,6,2,3,5]=>5
[4,1,6,2,5,3]=>6
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>6
[4,1,6,5,2,3]=>5
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>5
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>5
[4,2,1,6,5,3]=>5
[4,2,3,1,5,6]=>4
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>4
[4,2,3,5,6,1]=>4
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>5
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>6
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>6
[4,2,5,6,1,3]=>5
[4,2,5,6,3,1]=>5
[4,2,6,1,3,5]=>6
[4,2,6,1,5,3]=>6
[4,2,6,3,1,5]=>6
[4,2,6,3,5,1]=>6
[4,2,6,5,1,3]=>5
[4,2,6,5,3,1]=>5
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>4
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>4
[4,3,1,6,2,5]=>5
[4,3,1,6,5,2]=>5
[4,3,2,1,5,6]=>1
[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]=>4
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>4
[4,3,5,1,6,2]=>5
[4,3,5,2,1,6]=>3
[4,3,5,2,6,1]=>5
[4,3,5,6,1,2]=>4
[4,3,5,6,2,1]=>3
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>6
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>5
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>5
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>6
[4,5,1,6,2,3]=>5
[4,5,1,6,3,2]=>4
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>4
[4,5,2,3,1,6]=>4
[4,5,2,3,6,1]=>5
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>5
[4,5,3,1,2,6]=>3
[4,5,3,1,6,2]=>5
[4,5,3,2,1,6]=>2
[4,5,3,2,6,1]=>4
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>4
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>4
[4,5,6,2,1,3]=>4
[4,5,6,2,3,1]=>4
[4,5,6,3,1,2]=>3
[4,5,6,3,2,1]=>2
[4,6,1,2,3,5]=>4
[4,6,1,2,5,3]=>5
[4,6,1,3,2,5]=>5
[4,6,1,3,5,2]=>6
[4,6,1,5,2,3]=>6
[4,6,1,5,3,2]=>5
[4,6,2,1,3,5]=>5
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>6
[4,6,2,3,5,1]=>6
[4,6,2,5,1,3]=>7
[4,6,2,5,3,1]=>6
[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>6
[4,6,3,2,1,5]=>4
[4,6,3,2,5,1]=>5
[4,6,3,5,1,2]=>5
[4,6,3,5,2,1]=>5
[4,6,5,1,2,3]=>4
[4,6,5,1,3,2]=>5
[4,6,5,2,1,3]=>5
[4,6,5,2,3,1]=>5
[4,6,5,3,1,2]=>4
[4,6,5,3,2,1]=>3
[5,1,2,3,4,6]=>2
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>5
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>5
[5,1,3,2,4,6]=>5
[5,1,3,2,6,4]=>5
[5,1,3,4,2,6]=>4
[5,1,3,4,6,2]=>5
[5,1,3,6,2,4]=>6
[5,1,3,6,4,2]=>6
[5,1,4,2,3,6]=>4
[5,1,4,2,6,3]=>6
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>5
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>5
[5,1,6,3,2,4]=>6
[5,1,6,3,4,2]=>6
[5,1,6,4,2,3]=>5
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>3
[5,2,1,3,6,4]=>5
[5,2,1,4,3,6]=>4
[5,2,1,4,6,3]=>5
[5,2,1,6,3,4]=>5
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>4
[5,2,3,1,6,4]=>6
[5,2,3,4,1,6]=>4
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>5
[5,2,4,1,3,6]=>5
[5,2,4,1,6,3]=>6
[5,2,4,3,1,6]=>4
[5,2,4,3,6,1]=>5
[5,2,4,6,1,3]=>6
[5,2,4,6,3,1]=>6
[5,2,6,1,3,4]=>5
[5,2,6,1,4,3]=>5
[5,2,6,3,1,4]=>6
[5,2,6,3,4,1]=>6
[5,2,6,4,1,3]=>6
[5,2,6,4,3,1]=>5
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>5
[5,3,1,4,2,6]=>5
[5,3,1,4,6,2]=>6
[5,3,1,6,2,4]=>6
[5,3,1,6,4,2]=>6
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>4
[5,3,2,4,6,1]=>5
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>5
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>6
[5,3,4,2,1,6]=>4
[5,3,4,2,6,1]=>6
[5,3,4,6,1,2]=>5
[5,3,4,6,2,1]=>4
[5,3,6,1,2,4]=>5
[5,3,6,1,4,2]=>7
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>6
[5,3,6,4,1,2]=>5
[5,3,6,4,2,1]=>5
[5,4,1,2,3,6]=>2
[5,4,1,2,6,3]=>4
[5,4,1,3,2,6]=>3
[5,4,1,3,6,2]=>5
[5,4,1,6,2,3]=>4
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>5
[5,4,2,3,1,6]=>4
[5,4,2,3,6,1]=>4
[5,4,2,6,1,3]=>5
[5,4,2,6,3,1]=>5
[5,4,3,1,2,6]=>2
[5,4,3,1,6,2]=>4
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>3
[5,4,3,6,1,2]=>4
[5,4,3,6,2,1]=>3
[5,4,6,1,2,3]=>4
[5,4,6,1,3,2]=>5
[5,4,6,2,1,3]=>5
[5,4,6,2,3,1]=>5
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>3
[5,6,1,2,3,4]=>3
[5,6,1,2,4,3]=>4
[5,6,1,3,2,4]=>6
[5,6,1,3,4,2]=>5
[5,6,1,4,2,3]=>5
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>4
[5,6,2,1,4,3]=>4
[5,6,2,3,1,4]=>5
[5,6,2,3,4,1]=>5
[5,6,2,4,1,3]=>5
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>5
[5,6,3,1,4,2]=>5
[5,6,3,2,1,4]=>4
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>5
[5,6,3,4,2,1]=>4
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>4
[5,6,4,2,3,1]=>5
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>2
[6,1,2,3,4,5]=>2
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>5
[6,1,2,4,5,3]=>4
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>3
[6,1,3,2,4,5]=>5
[6,1,3,2,5,4]=>5
[6,1,3,4,2,5]=>5
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>6
[6,1,3,5,4,2]=>5
[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>6
[6,1,4,3,2,5]=>5
[6,1,4,3,5,2]=>5
[6,1,4,5,2,3]=>5
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>5
[6,1,5,3,2,4]=>5
[6,1,5,3,4,2]=>6
[6,1,5,4,2,3]=>4
[6,1,5,4,3,2]=>3
[6,2,1,3,4,5]=>3
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>5
[6,2,1,4,5,3]=>5
[6,2,1,5,3,4]=>5
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>4
[6,2,3,1,5,4]=>5
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>4
[6,2,3,5,1,4]=>5
[6,2,3,5,4,1]=>5
[6,2,4,1,3,5]=>6
[6,2,4,1,5,3]=>6
[6,2,4,3,1,5]=>5
[6,2,4,3,5,1]=>6
[6,2,4,5,1,3]=>6
[6,2,4,5,3,1]=>5
[6,2,5,1,3,4]=>5
[6,2,5,1,4,3]=>5
[6,2,5,3,1,4]=>6
[6,2,5,3,4,1]=>5
[6,2,5,4,1,3]=>5
[6,2,5,4,3,1]=>4
[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>5
[6,3,1,4,2,5]=>6
[6,3,1,4,5,2]=>5
[6,3,1,5,2,4]=>6
[6,3,1,5,4,2]=>5
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>5
[6,3,2,4,5,1]=>5
[6,3,2,5,1,4]=>5
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>6
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>5
[6,3,4,5,1,2]=>5
[6,3,4,5,2,1]=>4
[6,3,5,1,2,4]=>5
[6,3,5,1,4,2]=>6
[6,3,5,2,1,4]=>5
[6,3,5,2,4,1]=>6
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>4
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>5
[6,4,1,3,2,5]=>5
[6,4,1,3,5,2]=>6
[6,4,1,5,2,3]=>5
[6,4,1,5,3,2]=>5
[6,4,2,1,3,5]=>5
[6,4,2,1,5,3]=>5
[6,4,2,3,1,5]=>6
[6,4,2,3,5,1]=>5
[6,4,2,5,1,3]=>6
[6,4,2,5,3,1]=>6
[6,4,3,1,2,5]=>4
[6,4,3,1,5,2]=>5
[6,4,3,2,1,5]=>3
[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]=>4
[6,4,5,1,3,2]=>5
[6,4,5,2,1,3]=>5
[6,4,5,2,3,1]=>6
[6,4,5,3,1,2]=>5
[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]=>5
[6,5,1,3,4,2]=>4
[6,5,1,4,2,3]=>4
[6,5,1,4,3,2]=>3
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>4
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>5
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>4
[6,5,3,1,4,2]=>5
[6,5,3,2,1,4]=>3
[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]=>2
[6,5,4,1,3,2]=>3
[6,5,4,2,1,3]=>3
[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>2
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>3
[1,2,3,4,6,5,7]=>3
[1,2,3,4,6,7,5]=>4
[1,2,3,4,7,5,6]=>4
[1,2,3,4,7,6,5]=>3
[1,2,3,5,4,6,7]=>3
[1,2,3,5,4,7,6]=>5
[1,2,3,5,6,4,7]=>4
[1,2,3,5,6,7,4]=>4
[1,2,3,5,7,4,6]=>6
[1,2,3,5,7,6,4]=>5
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>6
[1,2,3,6,5,4,7]=>3
[1,2,3,6,5,7,4]=>5
[1,2,3,6,7,4,5]=>4
[1,2,3,6,7,5,4]=>4
[1,2,3,7,4,5,6]=>4
[1,2,3,7,4,6,5]=>5
[1,2,3,7,5,4,6]=>5
[1,2,3,7,5,6,4]=>6
[1,2,3,7,6,4,5]=>4
[1,2,3,7,6,5,4]=>3
[1,2,4,3,5,6,7]=>3
[1,2,4,3,5,7,6]=>6
[1,2,4,3,6,5,7]=>5
[1,2,4,3,6,7,5]=>5
[1,2,4,3,7,5,6]=>5
[1,2,4,3,7,6,5]=>5
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>5
[1,2,4,5,6,3,7]=>4
[1,2,4,5,6,7,3]=>4
[1,2,4,5,7,3,6]=>6
[1,2,4,5,7,6,3]=>5
[1,2,4,6,3,5,7]=>6
[1,2,4,6,3,7,5]=>7
[1,2,4,6,5,3,7]=>5
[1,2,4,6,5,7,3]=>7
[1,2,4,6,7,3,5]=>6
[1,2,4,6,7,5,3]=>6
[1,2,4,7,3,5,6]=>6
[1,2,4,7,3,6,5]=>6
[1,2,4,7,5,3,6]=>7
[1,2,4,7,5,6,3]=>6
[1,2,4,7,6,3,5]=>6
[1,2,4,7,6,5,3]=>5
[1,2,5,3,4,6,7]=>4
[1,2,5,3,4,7,6]=>5
[1,2,5,3,6,4,7]=>6
[1,2,5,3,6,7,4]=>6
[1,2,5,3,7,4,6]=>7
[1,2,5,3,7,6,4]=>6
[1,2,5,4,3,6,7]=>3
[1,2,5,4,3,7,6]=>5
[1,2,5,4,6,3,7]=>5
[1,2,5,4,6,7,3]=>5
[1,2,5,4,7,3,6]=>6
[1,2,5,4,7,6,3]=>6
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>6
[1,2,5,6,4,3,7]=>4
[1,2,5,6,4,7,3]=>6
[1,2,5,6,7,3,4]=>4
[1,2,5,6,7,4,3]=>4
[1,2,5,7,3,4,6]=>6
[1,2,5,7,3,6,4]=>7
[1,2,5,7,4,3,6]=>6
[1,2,5,7,4,6,3]=>7
[1,2,5,7,6,3,4]=>5
[1,2,5,7,6,4,3]=>5
[1,2,6,3,4,5,7]=>4
[1,2,6,3,4,7,5]=>6
[1,2,6,3,5,4,7]=>5
[1,2,6,3,5,7,4]=>7
[1,2,6,3,7,4,5]=>6
[1,2,6,3,7,5,4]=>6
[1,2,6,4,3,5,7]=>5
[1,2,6,4,3,7,5]=>6
[1,2,6,4,5,3,7]=>6
[1,2,6,4,5,7,3]=>6
[1,2,6,4,7,3,5]=>7
[1,2,6,4,7,5,3]=>7
[1,2,6,5,3,4,7]=>4
[1,2,6,5,3,7,4]=>6
[1,2,6,5,4,3,7]=>3
[1,2,6,5,4,7,3]=>5
[1,2,6,5,7,3,4]=>6
[1,2,6,5,7,4,3]=>5
[1,2,6,7,3,4,5]=>4
[1,2,6,7,3,5,4]=>5
[1,2,6,7,4,3,5]=>6
[1,2,6,7,4,5,3]=>6
[1,2,6,7,5,3,4]=>5
[1,2,6,7,5,4,3]=>4
[1,2,7,3,4,5,6]=>4
[1,2,7,3,4,6,5]=>5
[1,2,7,3,5,4,6]=>7
[1,2,7,3,5,6,4]=>6
[1,2,7,3,6,4,5]=>6
[1,2,7,3,6,5,4]=>5
[1,2,7,4,3,5,6]=>5
[1,2,7,4,3,6,5]=>6
[1,2,7,4,5,3,6]=>6
[1,2,7,4,5,6,3]=>6
[1,2,7,4,6,3,5]=>7
[1,2,7,4,6,5,3]=>6
[1,2,7,5,3,4,6]=>6
[1,2,7,5,3,6,4]=>7
[1,2,7,5,4,3,6]=>5
[1,2,7,5,4,6,3]=>6
[1,2,7,5,6,3,4]=>6
[1,2,7,5,6,4,3]=>6
[1,2,7,6,3,4,5]=>4
[1,2,7,6,3,5,4]=>5
[1,2,7,6,4,3,5]=>5
[1,2,7,6,4,5,3]=>6
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>3
[1,3,2,4,5,6,7]=>3
[1,3,2,4,5,7,6]=>6
[1,3,2,4,6,5,7]=>6
[1,3,2,4,6,7,5]=>7
[1,3,2,4,7,5,6]=>7
[1,3,2,4,7,6,5]=>6
[1,3,2,5,4,6,7]=>5
[1,3,2,5,4,7,6]=>7
[1,3,2,5,6,4,7]=>5
[1,3,2,5,6,7,4]=>5
[1,3,2,5,7,4,6]=>7
[1,3,2,5,7,6,4]=>6
[1,3,2,6,4,5,7]=>5
[1,3,2,6,4,7,5]=>7
[1,3,2,6,5,4,7]=>5
[1,3,2,6,5,7,4]=>7
[1,3,2,6,7,4,5]=>5
[1,3,2,6,7,5,4]=>6
[1,3,2,7,4,5,6]=>5
[1,3,2,7,4,6,5]=>6
[1,3,2,7,5,4,6]=>7
[1,3,2,7,5,6,4]=>7
[1,3,2,7,6,4,5]=>6
[1,3,2,7,6,5,4]=>5
[1,3,4,2,5,6,7]=>3
[1,3,4,2,5,7,6]=>6
[1,3,4,2,6,5,7]=>5
[1,3,4,2,6,7,5]=>5
[1,3,4,2,7,5,6]=>5
[1,3,4,2,7,6,5]=>5
[1,3,4,5,2,6,7]=>3
[1,3,4,5,2,7,6]=>5
[1,3,4,5,6,2,7]=>3
[1,3,4,5,6,7,2]=>3
[1,3,4,5,7,2,6]=>5
[1,3,4,5,7,6,2]=>4
[1,3,4,6,2,5,7]=>5
[1,3,4,6,2,7,5]=>6
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>6
[1,3,4,6,7,2,5]=>5
[1,3,4,6,7,5,2]=>5
[1,3,4,7,2,5,6]=>5
[1,3,4,7,2,6,5]=>6
[1,3,4,7,5,2,6]=>6
[1,3,4,7,5,6,2]=>5
[1,3,4,7,6,2,5]=>6
[1,3,4,7,6,5,2]=>4
[1,3,5,2,4,6,7]=>5
[1,3,5,2,4,7,6]=>7
[1,3,5,2,6,4,7]=>6
[1,3,5,2,6,7,4]=>6
[1,3,5,2,7,4,6]=>7
[1,3,5,2,7,6,4]=>7
[1,3,5,4,2,6,7]=>4
[1,3,5,4,2,7,6]=>6
[1,3,5,4,6,2,7]=>6
[1,3,5,4,6,7,2]=>6
[1,3,5,4,7,2,6]=>6
[1,3,5,4,7,6,2]=>6
[1,3,5,6,2,4,7]=>5
[1,3,5,6,2,7,4]=>7
[1,3,5,6,4,2,7]=>5
[1,3,5,6,4,7,2]=>6
[1,3,5,6,7,2,4]=>5
[1,3,5,6,7,4,2]=>5
[1,3,5,7,2,4,6]=>7
[1,3,5,7,2,6,4]=>7
[1,3,5,7,4,2,6]=>7
[1,3,5,7,4,6,2]=>7
[1,3,5,7,6,2,4]=>6
[1,3,5,7,6,4,2]=>6
[1,3,6,2,4,5,7]=>5
[1,3,6,2,4,7,5]=>7
[1,3,6,2,5,4,7]=>6
[1,3,6,2,5,7,4]=>7
[1,3,6,2,7,4,5]=>7
[1,3,6,2,7,5,4]=>6
[1,3,6,4,2,5,7]=>6
[1,3,6,4,2,7,5]=>7
[1,3,6,4,5,2,7]=>5
[1,3,6,4,5,7,2]=>6
[1,3,6,4,7,2,5]=>7
[1,3,6,4,7,5,2]=>7
[1,3,6,5,2,4,7]=>6
[1,3,6,5,2,7,4]=>6
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>6
[1,3,6,5,7,2,4]=>7
[1,3,6,5,7,4,2]=>6
[1,3,6,7,2,4,5]=>5
[1,3,6,7,2,5,4]=>6
[1,3,6,7,4,2,5]=>7
[1,3,6,7,4,5,2]=>6
[1,3,6,7,5,2,4]=>7
[1,3,6,7,5,4,2]=>5
[1,3,7,2,4,5,6]=>5
[1,3,7,2,4,6,5]=>6
[1,3,7,2,5,4,6]=>7
[1,3,7,2,5,6,4]=>7
[1,3,7,2,6,4,5]=>7
[1,3,7,2,6,5,4]=>6
[1,3,7,4,2,5,6]=>6
[1,3,7,4,2,6,5]=>7
[1,3,7,4,5,2,6]=>7
[1,3,7,4,5,6,2]=>5
[1,3,7,4,6,2,5]=>7
[1,3,7,4,6,5,2]=>6
[1,3,7,5,2,4,6]=>7
[1,3,7,5,2,6,4]=>8
[1,3,7,5,4,2,6]=>6
[1,3,7,5,4,6,2]=>6
[1,3,7,5,6,2,4]=>7
[1,3,7,5,6,4,2]=>7
[1,3,7,6,2,4,5]=>6
[1,3,7,6,2,5,4]=>6
[1,3,7,6,4,2,5]=>6
[1,3,7,6,4,5,2]=>5
[1,3,7,6,5,2,4]=>6
[1,3,7,6,5,4,2]=>4
[1,4,2,3,5,6,7]=>3
[1,4,2,3,5,7,6]=>6
[1,4,2,3,6,5,7]=>5
[1,4,2,3,6,7,5]=>5
[1,4,2,3,7,5,6]=>5
[1,4,2,3,7,6,5]=>5
[1,4,2,5,3,6,7]=>5
[1,4,2,5,3,7,6]=>7
[1,4,2,5,6,3,7]=>5
[1,4,2,5,6,7,3]=>5
[1,4,2,5,7,3,6]=>7
[1,4,2,5,7,6,3]=>6
[1,4,2,6,3,5,7]=>6
[1,4,2,6,3,7,5]=>7
[1,4,2,6,5,3,7]=>6
[1,4,2,6,5,7,3]=>7
[1,4,2,6,7,3,5]=>7
[1,4,2,6,7,5,3]=>7
[1,4,2,7,3,5,6]=>6
[1,4,2,7,3,6,5]=>7
[1,4,2,7,5,3,6]=>7
[1,4,2,7,5,6,3]=>7
[1,4,2,7,6,3,5]=>6
[1,4,2,7,6,5,3]=>6
[1,4,3,2,5,6,7]=>3
[1,4,3,2,5,7,6]=>6
[1,4,3,2,6,5,7]=>5
[1,4,3,2,6,7,5]=>5
[1,4,3,2,7,5,6]=>5
[1,4,3,2,7,6,5]=>6
[1,4,3,5,2,6,7]=>5
[1,4,3,5,2,7,6]=>6
[1,4,3,5,6,2,7]=>5
[1,4,3,5,6,7,2]=>5
[1,4,3,5,7,2,6]=>7
[1,4,3,5,7,6,2]=>6
[1,4,3,6,2,5,7]=>6
[1,4,3,6,2,7,5]=>7
[1,4,3,6,5,2,7]=>6
[1,4,3,6,5,7,2]=>7
[1,4,3,6,7,2,5]=>6
[1,4,3,6,7,5,2]=>7
[1,4,3,7,2,5,6]=>6
[1,4,3,7,2,6,5]=>6
[1,4,3,7,5,2,6]=>7
[1,4,3,7,5,6,2]=>7
[1,4,3,7,6,2,5]=>6
[1,4,3,7,6,5,2]=>6
[1,4,5,2,3,6,7]=>3
[1,4,5,2,3,7,6]=>5
[1,4,5,2,6,3,7]=>5
[1,4,5,2,6,7,3]=>5
[1,4,5,2,7,3,6]=>6
[1,4,5,2,7,6,3]=>6
[1,4,5,3,2,6,7]=>4
[1,4,5,3,2,7,6]=>6
[1,4,5,3,6,2,7]=>5
[1,4,5,3,6,7,2]=>5
[1,4,5,3,7,2,6]=>7
[1,4,5,3,7,6,2]=>6
[1,4,5,6,2,3,7]=>3
[1,4,5,6,2,7,3]=>5
[1,4,5,6,3,2,7]=>4
[1,4,5,6,3,7,2]=>5
[1,4,5,6,7,2,3]=>3
[1,4,5,6,7,3,2]=>4
[1,4,5,7,2,3,6]=>5
[1,4,5,7,2,6,3]=>6
[1,4,5,7,3,2,6]=>6
[1,4,5,7,3,6,2]=>6
[1,4,5,7,6,2,3]=>4
[1,4,5,7,6,3,2]=>5
[1,4,6,2,3,5,7]=>5
[1,4,6,2,3,7,5]=>6
[1,4,6,2,5,3,7]=>6
[1,4,6,2,5,7,3]=>7
[1,4,6,2,7,3,5]=>7
[1,4,6,2,7,5,3]=>7
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>7
[1,4,6,3,5,2,7]=>6
[1,4,6,3,5,7,2]=>7
[1,4,6,3,7,2,5]=>7
[1,4,6,3,7,5,2]=>7
[1,4,6,5,2,3,7]=>4
[1,4,6,5,2,7,3]=>6
[1,4,6,5,3,2,7]=>5
                    

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Description

The pancake length of a permutation.
This is the minimal number of pancake moves needed to generate a permutation where a pancake move is a reversal of a prefix in a permutation.

References

[1] Blanco, S. A., Buehrle, C. Some relations on prefix reversal generators of the symmetric and hyperoctahedral group arXiv:1803.01760

Code

@cached_function
def generate_group_from_generators(parent, gens):
    gens = list(gens)
    inds = range(len(gens))

    assert all( gen.parent() == parent for gen in gens )

    one = parent.one()
    level_set_cur  = set([one])
    found_elements = set([one])

    level_sets = []

    while level_set_cur:
        level_sets.append(level_set_cur)
        level_set_new = set()
        for x in level_set_cur:
            for i in inds:
                y = x * gens[i]
                if y not in found_elements:
                    found_elements.add(y)
                    level_set_new.add(y)
        level_set_cur = level_set_new
    return level_sets

@cached_function
def pancake_gens(n):
    return tuple(Permutations(n)(list(range(k,0,-1))+list(range(k+1,n+1))) for k in [2 .. n])

def statistic(sigma):
    n = len(sigma)
    level_sets = generate_group_from_generators(Permutations(n), pancake_gens(n))
    i = 0
    for level in level_sets:
        if sigma not in level:
            i += 1
        else:
            return i

Created

Mar 25, 2019 at 14:37 by Christian Stump

Updated

Mar 09, 2023 at 13:53 by Tilman Möller