- FindStat

edit this statistic or download as text // json

Identifier

St000458: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,2]=>2
[2,1]=>2
[1,2,3]=>3
[1,3,2]=>3
[2,1,3]=>3
[2,3,1]=>3
[3,1,2]=>3
[3,2,1]=>3
[1,2,3,4]=>5
[1,2,4,3]=>5
[1,3,2,4]=>5
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>3
[2,1,3,4]=>5
[2,1,4,3]=>5
[2,3,1,4]=>3
[2,3,4,1]=>3
[2,4,1,3]=>1
[2,4,3,1]=>3
[3,1,2,4]=>3
[3,1,4,2]=>1
[3,2,1,4]=>3
[3,2,4,1]=>3
[3,4,1,2]=>5
[3,4,2,1]=>5
[4,1,2,3]=>3
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>5
[4,3,1,2]=>5
[4,3,2,1]=>5
[1,2,3,4,5]=>8
[1,2,3,5,4]=>8
[1,2,4,3,5]=>8
[1,2,4,5,3]=>6
[1,2,5,3,4]=>6
[1,2,5,4,3]=>6
[1,3,2,4,5]=>8
[1,3,2,5,4]=>8
[1,3,4,2,5]=>3
[1,3,4,5,2]=>3
[1,3,5,2,4]=>1
[1,3,5,4,2]=>3
[1,4,2,3,5]=>3
[1,4,2,5,3]=>1
[1,4,3,2,5]=>3
[1,4,3,5,2]=>3
[1,4,5,2,3]=>5
[1,4,5,3,2]=>5
[1,5,2,3,4]=>3
[1,5,2,4,3]=>3
[1,5,3,2,4]=>3
[1,5,3,4,2]=>5
[1,5,4,2,3]=>5
[1,5,4,3,2]=>5
[2,1,3,4,5]=>8
[2,1,3,5,4]=>8
[2,1,4,3,5]=>8
[2,1,4,5,3]=>6
[2,1,5,3,4]=>6
[2,1,5,4,3]=>6
[2,3,1,4,5]=>6
[2,3,1,5,4]=>6
[2,3,4,1,5]=>3
[2,3,4,5,1]=>5
[2,3,5,1,4]=>2
[2,3,5,4,1]=>5
[2,4,1,3,5]=>1
[2,4,1,5,3]=>1
[2,4,3,1,5]=>3
[2,4,3,5,1]=>5
[2,4,5,1,3]=>2
[2,4,5,3,1]=>3
[2,5,1,3,4]=>2
[2,5,1,4,3]=>2
[2,5,3,1,4]=>1
[2,5,3,4,1]=>3
[2,5,4,1,3]=>2
[2,5,4,3,1]=>3
[3,1,2,4,5]=>6
[3,1,2,5,4]=>6
[3,1,4,2,5]=>1
[3,1,4,5,2]=>2
[3,1,5,2,4]=>1
[3,1,5,4,2]=>2
[3,2,1,4,5]=>6
[3,2,1,5,4]=>6
[3,2,4,1,5]=>3
[3,2,4,5,1]=>5
[3,2,5,1,4]=>2
[3,2,5,4,1]=>5
[3,4,1,2,5]=>5
[3,4,1,5,2]=>2
[3,4,2,1,5]=>5
[3,4,2,5,1]=>3
[3,4,5,1,2]=>6
[3,4,5,2,1]=>6
[3,5,1,2,4]=>2
[3,5,1,4,2]=>1
[3,5,2,1,4]=>2
[3,5,2,4,1]=>1
[3,5,4,1,2]=>6
[3,5,4,2,1]=>6
[4,1,2,3,5]=>3
[4,1,2,5,3]=>2
[4,1,3,2,5]=>3
[4,1,3,5,2]=>1
[4,1,5,2,3]=>2
[4,1,5,3,2]=>2
[4,2,1,3,5]=>3
[4,2,1,5,3]=>2
[4,2,3,1,5]=>5
[4,2,3,5,1]=>3
[4,2,5,1,3]=>1
[4,2,5,3,1]=>1
[4,3,1,2,5]=>5
[4,3,1,5,2]=>2
[4,3,2,1,5]=>5
[4,3,2,5,1]=>3
[4,3,5,1,2]=>6
[4,3,5,2,1]=>6
[4,5,1,2,3]=>6
[4,5,1,3,2]=>6
[4,5,2,1,3]=>6
[4,5,2,3,1]=>8
[4,5,3,1,2]=>8
[4,5,3,2,1]=>8
[5,1,2,3,4]=>5
[5,1,2,4,3]=>5
[5,1,3,2,4]=>5
[5,1,3,4,2]=>3
[5,1,4,2,3]=>3
[5,1,4,3,2]=>3
[5,2,1,3,4]=>5
[5,2,1,4,3]=>5
[5,2,3,1,4]=>3
[5,2,3,4,1]=>3
[5,2,4,1,3]=>1
[5,2,4,3,1]=>3
[5,3,1,2,4]=>3
[5,3,1,4,2]=>1
[5,3,2,1,4]=>3
[5,3,2,4,1]=>3
[5,3,4,1,2]=>8
[5,3,4,2,1]=>8
[5,4,1,2,3]=>6
[5,4,1,3,2]=>6
[5,4,2,1,3]=>6
[5,4,2,3,1]=>8
[5,4,3,1,2]=>8
[5,4,3,2,1]=>8
[1,2,3,4,5,6]=>13
[1,2,3,4,6,5]=>13
[1,2,3,5,4,6]=>13
[1,2,3,5,6,4]=>9
[1,2,3,6,4,5]=>9
[1,2,3,6,5,4]=>9
[1,2,4,3,5,6]=>13
[1,2,4,3,6,5]=>13
[1,2,4,5,3,6]=>6
[1,2,4,5,6,3]=>6
[1,2,4,6,3,5]=>2
[1,2,4,6,5,3]=>6
[1,2,5,3,4,6]=>6
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>6
[1,2,5,4,6,3]=>6
[1,2,5,6,3,4]=>10
[1,2,5,6,4,3]=>10
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>6
[1,2,6,4,3,5]=>6
[1,2,6,4,5,3]=>10
[1,2,6,5,3,4]=>10
[1,2,6,5,4,3]=>10
[1,3,2,4,5,6]=>13
[1,3,2,4,6,5]=>13
[1,3,2,5,4,6]=>13
[1,3,2,5,6,4]=>9
[1,3,2,6,4,5]=>9
[1,3,2,6,5,4]=>9
[1,3,4,2,5,6]=>6
[1,3,4,2,6,5]=>6
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>2
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>1
[1,3,5,2,6,4]=>1
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>2
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>2
[1,3,6,2,5,4]=>2
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>3
[1,3,6,5,2,4]=>2
[1,3,6,5,4,2]=>3
[1,4,2,3,5,6]=>6
[1,4,2,3,6,5]=>6
[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]=>2
[1,4,3,2,5,6]=>6
[1,4,3,2,6,5]=>6
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>2
[1,4,3,6,5,2]=>5
[1,4,5,2,3,6]=>5
[1,4,5,2,6,3]=>2
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>3
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>6
[1,4,6,2,3,5]=>2
[1,4,6,2,5,3]=>1
[1,4,6,3,2,5]=>2
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>6
[1,4,6,5,3,2]=>6
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>2
[1,5,2,6,4,3]=>2
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>2
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>3
[1,5,3,6,2,4]=>1
[1,5,3,6,4,2]=>1
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>5
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>6
[1,5,4,6,3,2]=>6
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>6
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>8
[1,5,6,4,2,3]=>8
[1,5,6,4,3,2]=>8
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>5
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>3
[1,6,2,5,3,4]=>3
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>5
[1,6,3,2,5,4]=>5
[1,6,3,4,2,5]=>3
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>1
[1,6,3,5,4,2]=>3
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>3
[1,6,4,5,2,3]=>8
[1,6,4,5,3,2]=>8
[1,6,5,2,3,4]=>6
[1,6,5,2,4,3]=>6
[1,6,5,3,2,4]=>6
[1,6,5,3,4,2]=>8
[1,6,5,4,2,3]=>8
[1,6,5,4,3,2]=>8
[2,1,3,4,5,6]=>13
[2,1,3,4,6,5]=>13
[2,1,3,5,4,6]=>13
[2,1,3,5,6,4]=>9
[2,1,3,6,4,5]=>9
[2,1,3,6,5,4]=>9
[2,1,4,3,5,6]=>13
[2,1,4,3,6,5]=>13
[2,1,4,5,3,6]=>6
[2,1,4,5,6,3]=>6
[2,1,4,6,3,5]=>2
[2,1,4,6,5,3]=>6
[2,1,5,3,4,6]=>6
[2,1,5,3,6,4]=>2
[2,1,5,4,3,6]=>6
[2,1,5,4,6,3]=>6
[2,1,5,6,3,4]=>10
[2,1,5,6,4,3]=>10
[2,1,6,3,4,5]=>6
[2,1,6,3,5,4]=>6
[2,1,6,4,3,5]=>6
[2,1,6,4,5,3]=>10
[2,1,6,5,3,4]=>10
[2,1,6,5,4,3]=>10
[2,3,1,4,5,6]=>9
[2,3,1,4,6,5]=>9
[2,3,1,5,4,6]=>9
[2,3,1,5,6,4]=>9
[2,3,1,6,4,5]=>9
[2,3,1,6,5,4]=>9
[2,3,4,1,5,6]=>6
[2,3,4,1,6,5]=>6
[2,3,4,5,1,6]=>5
[2,3,4,5,6,1]=>8
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>8
[2,3,5,1,4,6]=>2
[2,3,5,1,6,4]=>2
[2,3,5,4,1,6]=>5
[2,3,5,4,6,1]=>8
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>6
[2,3,6,1,4,5]=>4
[2,3,6,1,5,4]=>4
[2,3,6,4,1,5]=>2
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>4
[2,3,6,5,4,1]=>6
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>2
[2,4,1,5,3,6]=>1
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>1
[2,4,1,6,5,3]=>2
[2,4,3,1,5,6]=>6
[2,4,3,1,6,5]=>6
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>8
[2,4,3,6,1,5]=>3
[2,4,3,6,5,1]=>8
[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]=>3
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>3
[2,4,6,1,3,5]=>1
[2,4,6,1,5,3]=>1
[2,4,6,3,1,5]=>1
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>3
[2,4,6,5,3,1]=>3
[2,5,1,3,4,6]=>2
[2,5,1,3,6,4]=>1
[2,5,1,4,3,6]=>2
[2,5,1,4,6,3]=>1
[2,5,1,6,3,4]=>2
[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]=>3
[2,5,3,4,6,1]=>3
[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]=>3
[2,5,4,3,6,1]=>3
[2,5,4,6,1,3]=>3
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>4
[2,5,6,1,4,3]=>4
[2,5,6,3,1,4]=>2
[2,5,6,3,4,1]=>5
[2,5,6,4,1,3]=>3
[2,5,6,4,3,1]=>5
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>3
[2,6,1,4,3,5]=>3
[2,6,1,4,5,3]=>3
[2,6,1,5,3,4]=>3
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>2
[2,6,3,1,5,4]=>2
[2,6,3,4,1,5]=>2
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>1
[2,6,3,5,4,1]=>3
[2,6,4,1,3,5]=>1
[2,6,4,1,5,3]=>1
[2,6,4,3,1,5]=>2
[2,6,4,3,5,1]=>3
[2,6,4,5,1,3]=>3
[2,6,4,5,3,1]=>5
[2,6,5,1,3,4]=>4
[2,6,5,1,4,3]=>4
[2,6,5,3,1,4]=>2
[2,6,5,3,4,1]=>5
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>9
[3,1,2,4,6,5]=>9
[3,1,2,5,4,6]=>9
[3,1,2,5,6,4]=>9
[3,1,2,6,4,5]=>9
[3,1,2,6,5,4]=>9
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>2
[3,1,4,5,2,6]=>2
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>1
[3,1,4,6,5,2]=>3
[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]=>3
[3,1,5,6,2,4]=>2
[3,1,5,6,4,2]=>3
[3,1,6,2,4,5]=>2
[3,1,6,2,5,4]=>2
[3,1,6,4,2,5]=>1
[3,1,6,4,5,2]=>3
[3,1,6,5,2,4]=>2
[3,1,6,5,4,2]=>3
[3,2,1,4,5,6]=>9
[3,2,1,4,6,5]=>9
[3,2,1,5,4,6]=>9
[3,2,1,5,6,4]=>9
[3,2,1,6,4,5]=>9
[3,2,1,6,5,4]=>9
[3,2,4,1,5,6]=>6
[3,2,4,1,6,5]=>6
[3,2,4,5,1,6]=>5
[3,2,4,5,6,1]=>8
[3,2,4,6,1,5]=>3
[3,2,4,6,5,1]=>8
[3,2,5,1,4,6]=>2
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>5
[3,2,5,4,6,1]=>8
[3,2,5,6,1,4]=>4
[3,2,5,6,4,1]=>6
[3,2,6,1,4,5]=>4
[3,2,6,1,5,4]=>4
[3,2,6,4,1,5]=>2
[3,2,6,4,5,1]=>6
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>6
[3,4,1,2,5,6]=>10
[3,4,1,2,6,5]=>10
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>2
[3,4,1,6,5,2]=>4
[3,4,2,1,5,6]=>10
[3,4,2,1,6,5]=>10
[3,4,2,5,1,6]=>3
[3,4,2,5,6,1]=>6
[3,4,2,6,1,5]=>3
[3,4,2,6,5,1]=>6
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>3
[3,4,5,2,1,6]=>6
[3,4,5,2,6,1]=>3
[3,4,5,6,1,2]=>10
[3,4,5,6,2,1]=>10
[3,4,6,1,2,5]=>4
[3,4,6,1,5,2]=>2
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>10
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>2
[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]=>6
[3,5,4,1,6,2]=>3
[3,5,4,2,1,6]=>6
[3,5,4,2,6,1]=>3
[3,5,4,6,1,2]=>10
[3,5,4,6,2,1]=>10
[3,5,6,1,2,4]=>4
[3,5,6,1,4,2]=>2
[3,5,6,2,1,4]=>4
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>6
[3,5,6,4,2,1]=>6
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>4
[3,6,1,4,2,5]=>1
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>1
[3,6,1,5,4,2]=>2
[3,6,2,1,4,5]=>4
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>1
[3,6,2,4,5,1]=>2
[3,6,2,5,1,4]=>1
[3,6,2,5,4,1]=>2
[3,6,4,1,2,5]=>2
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>2
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>6
[3,6,4,5,2,1]=>6
[3,6,5,1,2,4]=>4
[3,6,5,1,4,2]=>2
[3,6,5,2,1,4]=>4
[3,6,5,2,4,1]=>2
[3,6,5,4,1,2]=>6
[3,6,5,4,2,1]=>6
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>6
[4,1,2,5,3,6]=>2
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>2
[4,1,2,6,5,3]=>4
[4,1,3,2,5,6]=>6
[4,1,3,2,6,5]=>6
[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]=>2
[4,1,5,2,3,6]=>2
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>1
[4,1,5,6,2,3]=>4
[4,1,5,6,3,2]=>4
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>1
[4,1,6,3,2,5]=>2
[4,1,6,3,5,2]=>1
[4,1,6,5,2,3]=>4
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>6
[4,2,1,3,6,5]=>6
[4,2,1,5,3,6]=>2
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>2
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>10
[4,2,3,1,6,5]=>10
[4,2,3,5,1,6]=>3
[4,2,3,5,6,1]=>6
[4,2,3,6,1,5]=>3
[4,2,3,6,5,1]=>6
[4,2,5,1,3,6]=>1
[4,2,5,1,6,3]=>1
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>2
[4,2,6,1,3,5]=>1
[4,2,6,1,5,3]=>1
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>2
[4,2,6,5,3,1]=>2
[4,3,1,2,5,6]=>10
[4,3,1,2,6,5]=>10
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>4
[4,3,1,6,2,5]=>2
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>10
[4,3,2,1,6,5]=>10
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>6
[4,3,2,6,1,5]=>3
[4,3,2,6,5,1]=>6
[4,3,5,1,2,6]=>6
[4,3,5,1,6,2]=>3
[4,3,5,2,1,6]=>6
[4,3,5,2,6,1]=>3
[4,3,5,6,1,2]=>10
[4,3,5,6,2,1]=>10
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>2
[4,3,6,2,1,5]=>4
[4,3,6,2,5,1]=>2
[4,3,6,5,1,2]=>10
[4,3,6,5,2,1]=>10
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>4
[4,5,1,3,2,6]=>6
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>4
[4,5,1,6,3,2]=>4
[4,5,2,1,3,6]=>6
[4,5,2,1,6,3]=>4
[4,5,2,3,1,6]=>8
[4,5,2,3,6,1]=>5
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>2
[4,5,3,1,2,6]=>8
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>8
[4,5,3,2,6,1]=>5
[4,5,3,6,1,2]=>6
[4,5,3,6,2,1]=>6
[4,5,6,1,2,3]=>9
[4,5,6,1,3,2]=>9
[4,5,6,2,1,3]=>9
[4,5,6,2,3,1]=>9
[4,5,6,3,1,2]=>9
[4,5,6,3,2,1]=>9
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>2
[4,6,1,3,2,5]=>3
[4,6,1,3,5,2]=>1
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>2
[4,6,2,1,3,5]=>3
[4,6,2,1,5,3]=>2
[4,6,2,3,1,5]=>3
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>1
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>1
[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>2
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>2
[4,6,5,1,2,3]=>9
[4,6,5,1,3,2]=>9
[4,6,5,2,1,3]=>9
[4,6,5,2,3,1]=>9
[4,6,5,3,1,2]=>9
[4,6,5,3,2,1]=>9
[5,1,2,3,4,6]=>5
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>5
[5,1,2,4,6,3]=>2
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>4
[5,1,3,2,4,6]=>5
[5,1,3,2,6,4]=>3
[5,1,3,4,2,6]=>3
[5,1,3,4,6,2]=>2
[5,1,3,6,2,4]=>1
[5,1,3,6,4,2]=>1
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>1
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>2
[5,1,4,6,2,3]=>2
[5,1,4,6,3,2]=>2
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>3
[5,1,6,3,2,4]=>3
[5,1,6,3,4,2]=>3
[5,1,6,4,2,3]=>3
[5,1,6,4,3,2]=>3
[5,2,1,3,4,6]=>5
[5,2,1,3,6,4]=>3
[5,2,1,4,3,6]=>5
[5,2,1,4,6,3]=>2
[5,2,1,6,3,4]=>4
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>3
[5,2,3,1,6,4]=>3
[5,2,3,4,1,6]=>3
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>2
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>1
[5,2,4,3,1,6]=>3
[5,2,4,3,6,1]=>3
[5,2,4,6,1,3]=>1
[5,2,4,6,3,1]=>1
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>2
[5,2,6,3,1,4]=>1
[5,2,6,3,4,1]=>2
[5,2,6,4,1,3]=>1
[5,2,6,4,3,1]=>2
[5,3,1,2,4,6]=>3
[5,3,1,2,6,4]=>3
[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]=>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]=>2
[5,3,2,6,4,1]=>2
[5,3,4,1,2,6]=>8
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>8
[5,3,4,2,6,1]=>5
[5,3,4,6,1,2]=>6
[5,3,4,6,2,1]=>6
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>1
[5,3,6,2,1,4]=>2
[5,3,6,2,4,1]=>1
[5,3,6,4,1,2]=>2
[5,3,6,4,2,1]=>2
[5,4,1,2,3,6]=>6
[5,4,1,2,6,3]=>4
[5,4,1,3,2,6]=>6
[5,4,1,3,6,2]=>2
[5,4,1,6,2,3]=>4
[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>6
[5,4,2,1,6,3]=>4
[5,4,2,3,1,6]=>8
[5,4,2,3,6,1]=>5
[5,4,2,6,1,3]=>2
[5,4,2,6,3,1]=>2
[5,4,3,1,2,6]=>8
[5,4,3,1,6,2]=>3
[5,4,3,2,1,6]=>8
[5,4,3,2,6,1]=>5
[5,4,3,6,1,2]=>6
[5,4,3,6,2,1]=>6
[5,4,6,1,2,3]=>9
[5,4,6,1,3,2]=>9
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>9
[5,4,6,3,1,2]=>9
[5,4,6,3,2,1]=>9
[5,6,1,2,3,4]=>10
[5,6,1,2,4,3]=>10
[5,6,1,3,2,4]=>10
[5,6,1,3,4,2]=>6
[5,6,1,4,2,3]=>6
[5,6,1,4,3,2]=>6
[5,6,2,1,3,4]=>10
[5,6,2,1,4,3]=>10
[5,6,2,3,1,4]=>6
[5,6,2,3,4,1]=>6
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>6
[5,6,3,1,2,4]=>6
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>6
[5,6,3,2,4,1]=>6
[5,6,3,4,1,2]=>13
[5,6,3,4,2,1]=>13
[5,6,4,1,2,3]=>9
[5,6,4,1,3,2]=>9
[5,6,4,2,1,3]=>9
[5,6,4,2,3,1]=>13
[5,6,4,3,1,2]=>13
[5,6,4,3,2,1]=>13
[6,1,2,3,4,5]=>8
[6,1,2,3,5,4]=>8
[6,1,2,4,3,5]=>8
[6,1,2,4,5,3]=>6
[6,1,2,5,3,4]=>6
[6,1,2,5,4,3]=>6
[6,1,3,2,4,5]=>8
[6,1,3,2,5,4]=>8
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>1
[6,1,3,5,4,2]=>3
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>3
[6,1,4,5,2,3]=>5
[6,1,4,5,3,2]=>5
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>3
[6,1,5,3,2,4]=>3
[6,1,5,3,4,2]=>5
[6,1,5,4,2,3]=>5
[6,1,5,4,3,2]=>5
[6,2,1,3,4,5]=>8
[6,2,1,3,5,4]=>8
[6,2,1,4,3,5]=>8
[6,2,1,4,5,3]=>6
[6,2,1,5,3,4]=>6
[6,2,1,5,4,3]=>6
[6,2,3,1,4,5]=>6
[6,2,3,1,5,4]=>6
[6,2,3,4,1,5]=>3
[6,2,3,4,5,1]=>5
[6,2,3,5,1,4]=>2
[6,2,3,5,4,1]=>5
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>1
[6,2,4,3,1,5]=>3
[6,2,4,3,5,1]=>5
[6,2,4,5,1,3]=>2
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>2
[6,2,5,1,4,3]=>2
[6,2,5,3,1,4]=>1
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>2
[6,2,5,4,3,1]=>3
[6,3,1,2,4,5]=>6
[6,3,1,2,5,4]=>6
[6,3,1,4,2,5]=>1
[6,3,1,4,5,2]=>2
[6,3,1,5,2,4]=>1
[6,3,1,5,4,2]=>2
[6,3,2,1,4,5]=>6
[6,3,2,1,5,4]=>6
[6,3,2,4,1,5]=>3
[6,3,2,4,5,1]=>5
[6,3,2,5,1,4]=>2
[6,3,2,5,4,1]=>5
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>2
[6,3,4,2,1,5]=>5
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>6
[6,3,4,5,2,1]=>6
[6,3,5,1,2,4]=>2
[6,3,5,1,4,2]=>1
[6,3,5,2,1,4]=>2
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>6
[6,3,5,4,2,1]=>6
[6,4,1,2,3,5]=>3
[6,4,1,2,5,3]=>2
[6,4,1,3,2,5]=>3
[6,4,1,3,5,2]=>1
[6,4,1,5,2,3]=>2
[6,4,1,5,3,2]=>2
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>2
[6,4,2,3,1,5]=>5
[6,4,2,3,5,1]=>3
[6,4,2,5,1,3]=>1
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>2
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>3
[6,4,3,5,1,2]=>6
[6,4,3,5,2,1]=>6
[6,4,5,1,2,3]=>9
[6,4,5,1,3,2]=>9
[6,4,5,2,1,3]=>9
[6,4,5,2,3,1]=>13
[6,4,5,3,1,2]=>13
[6,4,5,3,2,1]=>13
[6,5,1,2,3,4]=>10
[6,5,1,2,4,3]=>10
[6,5,1,3,2,4]=>10
[6,5,1,3,4,2]=>6
[6,5,1,4,2,3]=>6
[6,5,1,4,3,2]=>6
[6,5,2,1,3,4]=>10
[6,5,2,1,4,3]=>10
[6,5,2,3,1,4]=>6
[6,5,2,3,4,1]=>6
[6,5,2,4,1,3]=>2
[6,5,2,4,3,1]=>6
[6,5,3,1,2,4]=>6
[6,5,3,1,4,2]=>2
[6,5,3,2,1,4]=>6
[6,5,3,2,4,1]=>6
[6,5,3,4,1,2]=>13
[6,5,3,4,2,1]=>13
[6,5,4,1,2,3]=>9
[6,5,4,1,3,2]=>9
[6,5,4,2,1,3]=>9
[6,5,4,2,3,1]=>13
[6,5,4,3,1,2]=>13
[6,5,4,3,2,1]=>13
[1,2,3,4,5,6,7]=>21
[1,2,3,4,5,7,6]=>21
[1,2,3,4,6,5,7]=>21
[1,2,3,4,6,7,5]=>15
[1,2,3,4,7,5,6]=>15
[1,2,3,4,7,6,5]=>15
[1,2,3,5,4,6,7]=>21
[1,2,3,5,4,7,6]=>21
[1,2,3,5,6,4,7]=>9
[1,2,3,5,6,7,4]=>9
[1,2,3,5,7,4,6]=>3
[1,2,3,5,7,6,4]=>9
[1,2,3,6,4,5,7]=>9
[1,2,3,6,4,7,5]=>3
[1,2,3,6,5,4,7]=>9
[1,2,3,6,5,7,4]=>9
[1,2,3,6,7,4,5]=>15
[1,2,3,6,7,5,4]=>15
[1,2,3,7,4,5,6]=>9
[1,2,3,7,4,6,5]=>9
[1,2,3,7,5,4,6]=>9
[1,2,3,7,5,6,4]=>15
[1,2,3,7,6,4,5]=>15
[1,2,3,7,6,5,4]=>15
[1,2,4,3,5,6,7]=>21
[1,2,4,3,5,7,6]=>21
[1,2,4,3,6,5,7]=>21
[1,2,4,3,6,7,5]=>15
[1,2,4,3,7,5,6]=>15
[1,2,4,3,7,6,5]=>15
[1,2,4,5,3,6,7]=>12
[1,2,4,5,3,7,6]=>12
[1,2,4,5,6,3,7]=>6
[1,2,4,5,6,7,3]=>10
[1,2,4,5,7,3,6]=>4
[1,2,4,5,7,6,3]=>10
[1,2,4,6,3,5,7]=>2
[1,2,4,6,3,7,5]=>2
[1,2,4,6,5,3,7]=>6
[1,2,4,6,5,7,3]=>10
[1,2,4,6,7,3,5]=>4
[1,2,4,6,7,5,3]=>6
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>4
[1,2,4,7,5,3,6]=>2
[1,2,4,7,5,6,3]=>6
[1,2,4,7,6,3,5]=>4
[1,2,4,7,6,5,3]=>6
[1,2,5,3,4,6,7]=>12
[1,2,5,3,4,7,6]=>12
[1,2,5,3,6,4,7]=>2
[1,2,5,3,6,7,4]=>4
[1,2,5,3,7,4,6]=>2
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>12
[1,2,5,4,3,7,6]=>12
[1,2,5,4,6,3,7]=>6
[1,2,5,4,6,7,3]=>10
[1,2,5,4,7,3,6]=>4
[1,2,5,4,7,6,3]=>10
[1,2,5,6,3,4,7]=>10
[1,2,5,6,3,7,4]=>4
[1,2,5,6,4,3,7]=>10
[1,2,5,6,4,7,3]=>6
[1,2,5,6,7,3,4]=>12
[1,2,5,6,7,4,3]=>12
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>2
[1,2,5,7,4,3,6]=>4
[1,2,5,7,4,6,3]=>2
[1,2,5,7,6,3,4]=>12
[1,2,5,7,6,4,3]=>12
[1,2,6,3,4,5,7]=>6
[1,2,6,3,4,7,5]=>4
[1,2,6,3,5,4,7]=>6
[1,2,6,3,5,7,4]=>2
[1,2,6,3,7,4,5]=>4
[1,2,6,3,7,5,4]=>4
[1,2,6,4,3,5,7]=>6
[1,2,6,4,3,7,5]=>4
[1,2,6,4,5,3,7]=>10
[1,2,6,4,5,7,3]=>6
[1,2,6,4,7,3,5]=>2
[1,2,6,4,7,5,3]=>2
[1,2,6,5,3,4,7]=>10
[1,2,6,5,3,7,4]=>4
[1,2,6,5,4,3,7]=>10
[1,2,6,5,4,7,3]=>6
[1,2,6,5,7,3,4]=>12
[1,2,6,5,7,4,3]=>12
[1,2,6,7,3,4,5]=>12
[1,2,6,7,3,5,4]=>12
[1,2,6,7,4,3,5]=>12
[1,2,6,7,4,5,3]=>16
[1,2,6,7,5,3,4]=>16
[1,2,6,7,5,4,3]=>16
[1,2,7,3,4,5,6]=>10
[1,2,7,3,4,6,5]=>10
[1,2,7,3,5,4,6]=>10
[1,2,7,3,5,6,4]=>6
[1,2,7,3,6,4,5]=>6
[1,2,7,3,6,5,4]=>6
[1,2,7,4,3,5,6]=>10
[1,2,7,4,3,6,5]=>10
[1,2,7,4,5,3,6]=>6
[1,2,7,4,5,6,3]=>6
[1,2,7,4,6,3,5]=>2
[1,2,7,4,6,5,3]=>6
[1,2,7,5,3,4,6]=>6
[1,2,7,5,3,6,4]=>2
[1,2,7,5,4,3,6]=>6
[1,2,7,5,4,6,3]=>6
[1,2,7,5,6,3,4]=>16
[1,2,7,5,6,4,3]=>16
[1,2,7,6,3,4,5]=>12
[1,2,7,6,3,5,4]=>12
[1,2,7,6,4,3,5]=>12
[1,2,7,6,4,5,3]=>16
[1,2,7,6,5,3,4]=>16
[1,2,7,6,5,4,3]=>16
[1,3,2,4,5,6,7]=>21
[1,3,2,4,5,7,6]=>21
[1,3,2,4,6,5,7]=>21
[1,3,2,4,6,7,5]=>15
[1,3,2,4,7,5,6]=>15
[1,3,2,4,7,6,5]=>15
[1,3,2,5,4,6,7]=>21
[1,3,2,5,4,7,6]=>21
[1,3,2,5,6,4,7]=>9
[1,3,2,5,6,7,4]=>9
[1,3,2,5,7,4,6]=>3
[1,3,2,5,7,6,4]=>9
[1,3,2,6,4,5,7]=>9
[1,3,2,6,4,7,5]=>3
[1,3,2,6,5,4,7]=>9
[1,3,2,6,5,7,4]=>9
[1,3,2,6,7,4,5]=>15
[1,3,2,6,7,5,4]=>15
[1,3,2,7,4,5,6]=>9
[1,3,2,7,4,6,5]=>9
[1,3,2,7,5,4,6]=>9
[1,3,2,7,5,6,4]=>15
[1,3,2,7,6,4,5]=>15
[1,3,2,7,6,5,4]=>15
[1,3,4,2,5,6,7]=>9
[1,3,4,2,5,7,6]=>9
[1,3,4,2,6,5,7]=>9
[1,3,4,2,6,7,5]=>9
[1,3,4,2,7,5,6]=>9
[1,3,4,2,7,6,5]=>9
[1,3,4,5,2,6,7]=>6
[1,3,4,5,2,7,6]=>6
[1,3,4,5,6,2,7]=>5
[1,3,4,5,6,7,2]=>8
[1,3,4,5,7,2,6]=>3
[1,3,4,5,7,6,2]=>8
[1,3,4,6,2,5,7]=>2
[1,3,4,6,2,7,5]=>2
[1,3,4,6,5,2,7]=>5
[1,3,4,6,5,7,2]=>8
[1,3,4,6,7,2,5]=>4
[1,3,4,6,7,5,2]=>6
[1,3,4,7,2,5,6]=>4
[1,3,4,7,2,6,5]=>4
[1,3,4,7,5,2,6]=>2
[1,3,4,7,5,6,2]=>6
[1,3,4,7,6,2,5]=>4
[1,3,4,7,6,5,2]=>6
[1,3,5,2,4,6,7]=>2
[1,3,5,2,4,7,6]=>2
[1,3,5,2,6,4,7]=>1
[1,3,5,2,6,7,4]=>2
[1,3,5,2,7,4,6]=>1
[1,3,5,2,7,6,4]=>2
[1,3,5,4,2,6,7]=>6
[1,3,5,4,2,7,6]=>6
[1,3,5,4,6,2,7]=>5
[1,3,5,4,6,7,2]=>8
[1,3,5,4,7,2,6]=>3
[1,3,5,4,7,6,2]=>8
[1,3,5,6,2,4,7]=>2
[1,3,5,6,2,7,4]=>2
[1,3,5,6,4,2,7]=>3
[1,3,5,6,4,7,2]=>3
[1,3,5,6,7,2,4]=>3
[1,3,5,6,7,4,2]=>3
[1,3,5,7,2,4,6]=>1
[1,3,5,7,2,6,4]=>1
[1,3,5,7,4,2,6]=>1
[1,3,5,7,4,6,2]=>1
[1,3,5,7,6,2,4]=>3
[1,3,5,7,6,4,2]=>3
[1,3,6,2,4,5,7]=>2
[1,3,6,2,4,7,5]=>1
[1,3,6,2,5,4,7]=>2
[1,3,6,2,5,7,4]=>1
[1,3,6,2,7,4,5]=>2
[1,3,6,2,7,5,4]=>2
[1,3,6,4,2,5,7]=>1
[1,3,6,4,2,7,5]=>1
[1,3,6,4,5,2,7]=>3
[1,3,6,4,5,7,2]=>3
[1,3,6,4,7,2,5]=>1
[1,3,6,4,7,5,2]=>1
[1,3,6,5,2,4,7]=>2
[1,3,6,5,2,7,4]=>2
[1,3,6,5,4,2,7]=>3
[1,3,6,5,4,7,2]=>3
[1,3,6,5,7,2,4]=>3
[1,3,6,5,7,4,2]=>3
[1,3,6,7,2,4,5]=>4
[1,3,6,7,2,5,4]=>4
[1,3,6,7,4,2,5]=>2
[1,3,6,7,4,5,2]=>5
[1,3,6,7,5,2,4]=>3
[1,3,6,7,5,4,2]=>5
[1,3,7,2,4,5,6]=>3
[1,3,7,2,4,6,5]=>3
[1,3,7,2,5,4,6]=>3
[1,3,7,2,5,6,4]=>3
[1,3,7,2,6,4,5]=>3
[1,3,7,2,6,5,4]=>3
[1,3,7,4,2,5,6]=>2
[1,3,7,4,2,6,5]=>2
[1,3,7,4,5,2,6]=>2
[1,3,7,4,5,6,2]=>3
[1,3,7,4,6,2,5]=>1
[1,3,7,4,6,5,2]=>3
[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]=>3
[1,3,7,5,6,2,4]=>3
[1,3,7,5,6,4,2]=>5
[1,3,7,6,2,4,5]=>4
[1,3,7,6,2,5,4]=>4
[1,3,7,6,4,2,5]=>2
[1,3,7,6,4,5,2]=>5
[1,3,7,6,5,2,4]=>3
[1,3,7,6,5,4,2]=>5
[1,4,2,3,5,6,7]=>9
[1,4,2,3,5,7,6]=>9
[1,4,2,3,6,5,7]=>9
[1,4,2,3,6,7,5]=>9
[1,4,2,3,7,5,6]=>9
[1,4,2,3,7,6,5]=>9
[1,4,2,5,3,6,7]=>2
[1,4,2,5,3,7,6]=>2
[1,4,2,5,6,3,7]=>2
[1,4,2,5,6,7,3]=>3
[1,4,2,5,7,3,6]=>1
[1,4,2,5,7,6,3]=>3
[1,4,2,6,3,5,7]=>1
[1,4,2,6,3,7,5]=>1
[1,4,2,6,5,3,7]=>2
[1,4,2,6,5,7,3]=>3
[1,4,2,6,7,3,5]=>2
[1,4,2,6,7,5,3]=>3
[1,4,2,7,3,5,6]=>2
[1,4,2,7,3,6,5]=>2
[1,4,2,7,5,3,6]=>1
[1,4,2,7,5,6,3]=>3
[1,4,2,7,6,3,5]=>2
[1,4,2,7,6,5,3]=>3
[1,4,3,2,5,6,7]=>9
[1,4,3,2,5,7,6]=>9
[1,4,3,2,6,5,7]=>9
[1,4,3,2,6,7,5]=>9
[1,4,3,2,7,5,6]=>9
[1,4,3,2,7,6,5]=>9
[1,4,3,5,2,6,7]=>6
[1,4,3,5,2,7,6]=>6
[1,4,3,5,6,2,7]=>5
[1,4,3,5,6,7,2]=>8
[1,4,3,5,7,2,6]=>3
[1,4,3,5,7,6,2]=>8
[1,4,3,6,2,5,7]=>2
[1,4,3,6,2,7,5]=>2
[1,4,3,6,5,2,7]=>5
[1,4,3,6,5,7,2]=>8
[1,4,3,6,7,2,5]=>4
[1,4,3,6,7,5,2]=>6
[1,4,3,7,2,5,6]=>4
[1,4,3,7,2,6,5]=>4
[1,4,3,7,5,2,6]=>2
[1,4,3,7,5,6,2]=>6
[1,4,3,7,6,2,5]=>4
[1,4,3,7,6,5,2]=>6
[1,4,5,2,3,6,7]=>10
[1,4,5,2,3,7,6]=>10
[1,4,5,2,6,3,7]=>2
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>2
[1,4,5,2,7,6,3]=>4
[1,4,5,3,2,6,7]=>10
[1,4,5,3,2,7,6]=>10
[1,4,5,3,6,2,7]=>3
[1,4,5,3,6,7,2]=>6
[1,4,5,3,7,2,6]=>3
[1,4,5,3,7,6,2]=>6
[1,4,5,6,2,3,7]=>6
[1,4,5,6,2,7,3]=>3
[1,4,5,6,3,2,7]=>6
[1,4,5,6,3,7,2]=>3
[1,4,5,6,7,2,3]=>10
[1,4,5,6,7,3,2]=>10
[1,4,5,7,2,3,6]=>4
[1,4,5,7,2,6,3]=>2
[1,4,5,7,3,2,6]=>4
[1,4,5,7,3,6,2]=>2
[1,4,5,7,6,2,3]=>10
[1,4,5,7,6,3,2]=>10
[1,4,6,2,3,5,7]=>2
[1,4,6,2,3,7,5]=>2
[1,4,6,2,5,3,7]=>1
[1,4,6,2,5,7,3]=>1
[1,4,6,2,7,3,5]=>1
[1,4,6,2,7,5,3]=>1
[1,4,6,3,2,5,7]=>2
[1,4,6,3,2,7,5]=>2
[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]=>6
[1,4,6,5,2,7,3]=>3
[1,4,6,5,3,2,7]=>6
[1,4,6,5,3,7,2]=>3
                    

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Description

The number of permutations obtained by switching adjacencies or successions.
For a permutation $\pi$, this statistic is the size of its equivalence class of the equivalence relation generated by the interchange of any two adjacent elements $\pi_i$ and $\pi_{i+1}$ such that $|\pi_i - \pi_{i+1}| = 1$.

References

[1] Stanley, R. P. An equivalence relation on the symmetric group and multiplicity-free flag $h$-vectors MathSciNet:3029438 arXiv:1208.3540
[2] Amdeberhan, T. "flavored" equivalence classes of permutations MathOverflow:256673

Code

def statistic(pi):
    def children(a):
        for i in range(len(a)-1):
            d = a[i] - a[i+1]
            if d == 1 or d == -1:
                yield Permutation(a[:i] + [a[i+1], a[i]] + a[i+2:])

    return len([1 for pi in RecursivelyEnumeratedSet([Permutation(pi)], children)])

Created

Apr 05, 2016 at 17:34 by Jiang Zeng

Updated

May 10, 2019 at 17:36 by Henning Ulfarsson