- FindStat

edit this statistic or download as text // json

Identifier

St000401: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

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

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Description

The size of the symmetry class of a permutation.
The symmetry class of a permutation $\pi$ is the set of all permutations that can be obtained from $\pi$ by the three elementary operations inverse (Mp00066inverse), reverse (Mp00064reverse), and complement (Mp00069complement).
Two elements in the same symmetry class are also in the same Wilf-equivalence class, see for example [2].

References

[1] Callan, D., Mansour, T. Five subsets of permutations enumerated as weak sorting permutations arXiv:1602.05182
[2] Stankova-Frenkel, Z., West, J. A New Class of Wilf-Equivalent Permutations arXiv:math/0103152

Code

def eq_class(pi):
    cl = [pi]
    test = [pi]
    while test:
        tau = test.pop()
        tau1 = tau.reverse()
        tau2 = tau.complement()
        tau3 = tau.inverse()
        if tau1 not in cl:
            cl.append(tau1)
            test.append(tau1)
        if tau2 not in cl:
            cl.append(tau2)
            test.append(tau2)
        if tau3 not in cl:
            cl.append(tau3)
            test.append(tau3)
    return cl

def statistic(pi):
    return len(eq_class(pi))

Created

Feb 23, 2016 at 18:09 by Christian Stump

Updated

May 10, 2019 at 17:30 by Henning Ulfarsson