- FindStat

edit this statistic or download as text // json

Identifier

St000957: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>2
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>2
[2,3,4,1]=>3
[2,4,1,3]=>3
[2,4,3,1]=>3
[3,1,2,4]=>2
[3,1,4,2]=>3
[3,2,1,4]=>2
[3,2,4,1]=>3
[3,4,1,2]=>4
[3,4,2,1]=>3
[4,1,2,3]=>3
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>4
[4,3,1,2]=>3
[4,3,2,1]=>3
[1,2,3,4,5]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>2
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>2
[1,3,4,5,2]=>3
[1,3,5,2,4]=>3
[1,3,5,4,2]=>3
[1,4,2,3,5]=>2
[1,4,2,5,3]=>3
[1,4,3,2,5]=>2
[1,4,3,5,2]=>3
[1,4,5,2,3]=>4
[1,4,5,3,2]=>3
[1,5,2,3,4]=>3
[1,5,2,4,3]=>3
[1,5,3,2,4]=>3
[1,5,3,4,2]=>4
[1,5,4,2,3]=>3
[1,5,4,3,2]=>3
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>3
[2,1,5,3,4]=>3
[2,1,5,4,3]=>3
[2,3,1,4,5]=>2
[2,3,1,5,4]=>3
[2,3,4,1,5]=>3
[2,3,4,5,1]=>4
[2,3,5,1,4]=>4
[2,3,5,4,1]=>4
[2,4,1,3,5]=>3
[2,4,1,5,3]=>4
[2,4,3,1,5]=>3
[2,4,3,5,1]=>4
[2,4,5,1,3]=>5
[2,4,5,3,1]=>4
[2,5,1,3,4]=>4
[2,5,1,4,3]=>4
[2,5,3,1,4]=>4
[2,5,3,4,1]=>5
[2,5,4,1,3]=>4
[2,5,4,3,1]=>4
[3,1,2,4,5]=>2
[3,1,2,5,4]=>3
[3,1,4,2,5]=>3
[3,1,4,5,2]=>4
[3,1,5,2,4]=>4
[3,1,5,4,2]=>4
[3,2,1,4,5]=>2
[3,2,1,5,4]=>3
[3,2,4,1,5]=>3
[3,2,4,5,1]=>4
[3,2,5,1,4]=>4
[3,2,5,4,1]=>4
[3,4,1,2,5]=>4
[3,4,1,5,2]=>5
[3,4,2,1,5]=>3
[3,4,2,5,1]=>4
[3,4,5,1,2]=>6
[3,4,5,2,1]=>4
[3,5,1,2,4]=>5
[3,5,1,4,2]=>5
[3,5,2,1,4]=>4
[3,5,2,4,1]=>5
[3,5,4,1,2]=>5
[3,5,4,2,1]=>4
[4,1,2,3,5]=>3
[4,1,2,5,3]=>4
[4,1,3,2,5]=>3
[4,1,3,5,2]=>4
[4,1,5,2,3]=>5
[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]=>5
[4,2,5,1,3]=>5
[4,2,5,3,1]=>5
[4,3,1,2,5]=>3
[4,3,1,5,2]=>4
[4,3,2,1,5]=>3
[4,3,2,5,1]=>4
[4,3,5,1,2]=>5
[4,3,5,2,1]=>4
[4,5,1,2,3]=>6
[4,5,1,3,2]=>5
[4,5,2,1,3]=>5
[4,5,2,3,1]=>6
[4,5,3,1,2]=>4
[4,5,3,2,1]=>4
[5,1,2,3,4]=>4
[5,1,2,4,3]=>4
[5,1,3,2,4]=>4
[5,1,3,4,2]=>5
[5,1,4,2,3]=>4
[5,1,4,3,2]=>4
[5,2,1,3,4]=>4
[5,2,1,4,3]=>4
[5,2,3,1,4]=>5
[5,2,3,4,1]=>6
[5,2,4,1,3]=>5
[5,2,4,3,1]=>5
[5,3,1,2,4]=>4
[5,3,1,4,2]=>5
[5,3,2,1,4]=>4
[5,3,2,4,1]=>5
[5,3,4,1,2]=>6
[5,3,4,2,1]=>5
[5,4,1,2,3]=>4
[5,4,1,3,2]=>4
[5,4,2,1,3]=>4
[5,4,2,3,1]=>5
[5,4,3,1,2]=>4
[5,4,3,2,1]=>4
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>2
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>2
[1,2,4,5,6,3]=>3
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>3
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>3
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>3
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>2
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>4
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>4
[1,3,6,4,2,5]=>4
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>3
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>4
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>3
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>4
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>4
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>5
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>5
[1,4,6,5,2,3]=>5
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>4
[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>4
[1,5,3,4,2,6]=>4
[1,5,3,4,6,2]=>5
[1,5,3,6,2,4]=>5
[1,5,3,6,4,2]=>5
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>4
[1,5,4,6,2,3]=>5
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>5
[1,5,6,3,2,4]=>5
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>4
[1,6,2,3,4,5]=>4
[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>4
[1,6,2,4,5,3]=>5
[1,6,2,5,3,4]=>4
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>4
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>6
[1,6,3,5,2,4]=>5
[1,6,3,5,4,2]=>5
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>5
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>5
[1,6,4,5,2,3]=>6
[1,6,4,5,3,2]=>5
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>5
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>4
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>3
[2,1,3,6,5,4]=>3
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>3
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>5
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>4
[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]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>4
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>4
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>5
[2,3,4,6,5,1]=>5
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>4
[2,3,5,4,6,1]=>5
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>5
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>5
[2,3,6,4,1,5]=>5
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>5
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>4
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>5
[2,4,1,6,5,3]=>5
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>4
[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]=>5
[2,4,5,1,6,3]=>6
[2,4,5,3,1,6]=>4
[2,4,5,3,6,1]=>5
[2,4,5,6,1,3]=>7
[2,4,5,6,3,1]=>5
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>5
[2,4,6,3,5,1]=>6
[2,4,6,5,1,3]=>6
[2,4,6,5,3,1]=>5
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>4
[2,5,1,4,6,3]=>5
[2,5,1,6,3,4]=>6
[2,5,1,6,4,3]=>5
[2,5,3,1,4,6]=>4
[2,5,3,1,6,4]=>5
[2,5,3,4,1,6]=>5
[2,5,3,4,6,1]=>6
[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]=>4
[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]=>7
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>7
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>5
[2,6,1,3,4,5]=>5
[2,6,1,3,5,4]=>5
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>6
[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]=>5
[2,6,3,4,1,5]=>6
[2,6,3,4,5,1]=>7
[2,6,3,5,1,4]=>6
[2,6,3,5,4,1]=>6
[2,6,4,1,3,5]=>5
[2,6,4,1,5,3]=>6
[2,6,4,3,1,5]=>5
[2,6,4,3,5,1]=>6
[2,6,4,5,1,3]=>7
[2,6,4,5,3,1]=>6
[2,6,5,1,3,4]=>5
[2,6,5,1,4,3]=>5
[2,6,5,3,1,4]=>5
[2,6,5,3,4,1]=>6
[2,6,5,4,1,3]=>5
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>4
[3,1,4,2,5,6]=>3
[3,1,4,2,6,5]=>4
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>5
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>5
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>5
[3,1,5,4,2,6]=>4
[3,1,5,4,6,2]=>5
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>5
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>5
[3,1,6,4,2,5]=>5
[3,1,6,4,5,2]=>6
[3,1,6,5,2,4]=>5
[3,1,6,5,4,2]=>5
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>3
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>4
[3,2,1,6,4,5]=>4
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>4
[3,2,4,5,6,1]=>5
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>5
[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]=>6
[3,2,5,6,4,1]=>5
[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>5
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>6
[3,2,6,5,1,4]=>5
[3,2,6,5,4,1]=>5
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>6
[3,4,1,6,2,5]=>6
[3,4,1,6,5,2]=>6
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>4
[3,4,2,5,6,1]=>5
[3,4,2,6,1,5]=>5
[3,4,2,6,5,1]=>5
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>7
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>5
[3,4,5,6,1,2]=>8
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>7
[3,4,6,1,5,2]=>7
[3,4,6,2,1,5]=>5
[3,4,6,2,5,1]=>6
[3,4,6,5,1,2]=>7
[3,4,6,5,2,1]=>5
[3,5,1,2,4,6]=>5
[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]=>7
[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]=>5
[3,5,4,1,6,2]=>6
[3,5,4,2,1,6]=>4
[3,5,4,2,6,1]=>5
[3,5,4,6,1,2]=>7
[3,5,4,6,2,1]=>5
[3,5,6,1,2,4]=>8
[3,5,6,1,4,2]=>7
[3,5,6,2,1,4]=>6
[3,5,6,2,4,1]=>7
[3,5,6,4,1,2]=>6
[3,5,6,4,2,1]=>5
[3,6,1,2,4,5]=>6
[3,6,1,2,5,4]=>6
[3,6,1,4,2,5]=>6
[3,6,1,4,5,2]=>7
[3,6,1,5,2,4]=>6
[3,6,1,5,4,2]=>6
[3,6,2,1,4,5]=>5
[3,6,2,1,5,4]=>5
[3,6,2,4,1,5]=>6
[3,6,2,4,5,1]=>7
[3,6,2,5,1,4]=>6
[3,6,2,5,4,1]=>6
[3,6,4,1,2,5]=>6
[3,6,4,1,5,2]=>7
[3,6,4,2,1,5]=>5
[3,6,4,2,5,1]=>6
[3,6,4,5,1,2]=>8
[3,6,4,5,2,1]=>6
[3,6,5,1,2,4]=>6
[3,6,5,1,4,2]=>6
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>6
[3,6,5,4,1,2]=>6
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>4
[4,1,2,5,6,3]=>5
[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]=>4
[4,1,3,5,2,6]=>4
[4,1,3,5,6,2]=>5
[4,1,3,6,2,5]=>5
[4,1,3,6,5,2]=>5
[4,1,5,2,3,6]=>5
[4,1,5,2,6,3]=>6
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>7
[4,1,5,6,3,2]=>5
[4,1,6,2,3,5]=>6
[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]=>6
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>5
[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]=>5
[4,2,3,5,1,6]=>5
[4,2,3,5,6,1]=>6
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>6
[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]=>7
[4,2,5,6,3,1]=>6
[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]=>7
[4,2,6,5,1,3]=>6
[4,2,6,5,3,1]=>6
[4,3,1,2,5,6]=>3
[4,3,1,2,6,5]=>4
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>5
[4,3,1,6,2,5]=>5
[4,3,1,6,5,2]=>5
[4,3,2,1,5,6]=>3
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>4
[4,3,2,5,6,1]=>5
[4,3,2,6,1,5]=>5
[4,3,2,6,5,1]=>5
[4,3,5,1,2,6]=>5
[4,3,5,1,6,2]=>6
[4,3,5,2,1,6]=>4
[4,3,5,2,6,1]=>5
[4,3,5,6,1,2]=>7
[4,3,5,6,2,1]=>5
[4,3,6,1,2,5]=>6
[4,3,6,1,5,2]=>6
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>6
[4,3,6,5,1,2]=>6
[4,3,6,5,2,1]=>5
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>7
[4,5,1,3,2,6]=>5
[4,5,1,3,6,2]=>6
[4,5,1,6,2,3]=>8
[4,5,1,6,3,2]=>6
[4,5,2,1,3,6]=>5
[4,5,2,1,6,3]=>6
[4,5,2,3,1,6]=>6
[4,5,2,3,6,1]=>7
[4,5,2,6,1,3]=>7
[4,5,2,6,3,1]=>7
[4,5,3,1,2,6]=>4
[4,5,3,1,6,2]=>5
[4,5,3,2,1,6]=>4
[4,5,3,2,6,1]=>5
[4,5,3,6,1,2]=>6
[4,5,3,6,2,1]=>5
[4,5,6,1,2,3]=>9
[4,5,6,1,3,2]=>7
[4,5,6,2,1,3]=>7
[4,5,6,2,3,1]=>8
[4,5,6,3,1,2]=>5
[4,5,6,3,2,1]=>5
[4,6,1,2,3,5]=>7
[4,6,1,2,5,3]=>7
[4,6,1,3,2,5]=>6
[4,6,1,3,5,2]=>7
[4,6,1,5,2,3]=>7
[4,6,1,5,3,2]=>6
[4,6,2,1,3,5]=>6
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>7
[4,6,2,3,5,1]=>8
[4,6,2,5,1,3]=>7
[4,6,2,5,3,1]=>7
[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>6
[4,6,3,2,1,5]=>5
[4,6,3,2,5,1]=>6
[4,6,3,5,1,2]=>7
[4,6,3,5,2,1]=>6
[4,6,5,1,2,3]=>7
[4,6,5,1,3,2]=>6
[4,6,5,2,1,3]=>6
[4,6,5,2,3,1]=>7
[4,6,5,3,1,2]=>5
[4,6,5,3,2,1]=>5
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>5
[5,1,2,4,3,6]=>4
[5,1,2,4,6,3]=>5
[5,1,2,6,3,4]=>6
[5,1,2,6,4,3]=>5
[5,1,3,2,4,6]=>4
[5,1,3,2,6,4]=>5
[5,1,3,4,2,6]=>5
[5,1,3,4,6,2]=>6
[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]=>5
[5,1,4,3,2,6]=>4
[5,1,4,3,6,2]=>5
[5,1,4,6,2,3]=>6
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>7
[5,1,6,2,4,3]=>6
[5,1,6,3,2,4]=>6
[5,1,6,3,4,2]=>7
[5,1,6,4,2,3]=>5
[5,1,6,4,3,2]=>5
[5,2,1,3,4,6]=>4
[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]=>6
[5,2,1,6,4,3]=>5
[5,2,3,1,4,6]=>5
[5,2,3,1,6,4]=>6
[5,2,3,4,1,6]=>6
[5,2,3,4,6,1]=>7
[5,2,3,6,1,4]=>7
[5,2,3,6,4,1]=>7
[5,2,4,1,3,6]=>5
[5,2,4,1,6,3]=>6
[5,2,4,3,1,6]=>5
[5,2,4,3,6,1]=>6
[5,2,4,6,1,3]=>7
[5,2,4,6,3,1]=>6
[5,2,6,1,3,4]=>7
[5,2,6,1,4,3]=>6
[5,2,6,3,1,4]=>7
[5,2,6,3,4,1]=>8
[5,2,6,4,1,3]=>6
[5,2,6,4,3,1]=>6
[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]=>4
[5,3,2,1,6,4]=>5
[5,3,2,4,1,6]=>5
[5,3,2,4,6,1]=>6
[5,3,2,6,1,4]=>6
[5,3,2,6,4,1]=>6
[5,3,4,1,2,6]=>6
[5,3,4,1,6,2]=>7
[5,3,4,2,1,6]=>5
[5,3,4,2,6,1]=>6
[5,3,4,6,1,2]=>8
[5,3,4,6,2,1]=>6
[5,3,6,1,2,4]=>7
[5,3,6,1,4,2]=>7
[5,3,6,2,1,4]=>6
[5,3,6,2,4,1]=>7
[5,3,6,4,1,2]=>7
[5,3,6,4,2,1]=>6
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>5
[5,4,1,3,2,6]=>4
[5,4,1,3,6,2]=>5
[5,4,1,6,2,3]=>6
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>4
[5,4,2,1,6,3]=>5
[5,4,2,3,1,6]=>5
[5,4,2,3,6,1]=>6
[5,4,2,6,1,3]=>6
[5,4,2,6,3,1]=>6
[5,4,3,1,2,6]=>4
[5,4,3,1,6,2]=>5
[5,4,3,2,1,6]=>4
[5,4,3,2,6,1]=>5
[5,4,3,6,1,2]=>6
[5,4,3,6,2,1]=>5
[5,4,6,1,2,3]=>7
[5,4,6,1,3,2]=>6
[5,4,6,2,1,3]=>6
[5,4,6,2,3,1]=>7
[5,4,6,3,1,2]=>5
[5,4,6,3,2,1]=>5
[5,6,1,2,3,4]=>8
[5,6,1,2,4,3]=>7
[5,6,1,3,2,4]=>7
[5,6,1,3,4,2]=>8
[5,6,1,4,2,3]=>6
[5,6,1,4,3,2]=>6
[5,6,2,1,3,4]=>7
[5,6,2,1,4,3]=>6
[5,6,2,3,1,4]=>8
[5,6,2,3,4,1]=>9
[5,6,2,4,1,3]=>7
[5,6,2,4,3,1]=>7
[5,6,3,1,2,4]=>6
[5,6,3,1,4,2]=>7
[5,6,3,2,1,4]=>6
[5,6,3,2,4,1]=>7
[5,6,3,4,1,2]=>8
[5,6,3,4,2,1]=>7
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>5
[5,6,4,2,1,3]=>5
[5,6,4,2,3,1]=>6
[5,6,4,3,1,2]=>5
[5,6,4,3,2,1]=>5
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>5
[6,1,2,4,3,5]=>5
[6,1,2,4,5,3]=>6
[6,1,2,5,3,4]=>5
[6,1,2,5,4,3]=>5
[6,1,3,2,4,5]=>5
[6,1,3,2,5,4]=>5
[6,1,3,4,2,5]=>6
[6,1,3,4,5,2]=>7
[6,1,3,5,2,4]=>6
[6,1,3,5,4,2]=>6
[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]=>6
[6,1,4,5,2,3]=>7
[6,1,4,5,3,2]=>6
[6,1,5,2,3,4]=>5
[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]=>5
[6,1,5,4,3,2]=>5
[6,2,1,3,4,5]=>5
[6,2,1,3,5,4]=>5
[6,2,1,4,3,5]=>5
[6,2,1,4,5,3]=>6
[6,2,1,5,3,4]=>5
[6,2,1,5,4,3]=>5
[6,2,3,1,4,5]=>6
[6,2,3,1,5,4]=>6
[6,2,3,4,1,5]=>7
[6,2,3,4,5,1]=>8
[6,2,3,5,1,4]=>7
[6,2,3,5,4,1]=>7
[6,2,4,1,3,5]=>6
[6,2,4,1,5,3]=>7
[6,2,4,3,1,5]=>6
[6,2,4,3,5,1]=>7
[6,2,4,5,1,3]=>8
[6,2,4,5,3,1]=>7
[6,2,5,1,3,4]=>6
[6,2,5,1,4,3]=>6
[6,2,5,3,1,4]=>6
[6,2,5,3,4,1]=>7
[6,2,5,4,1,3]=>6
[6,2,5,4,3,1]=>6
[6,3,1,2,4,5]=>5
[6,3,1,2,5,4]=>5
[6,3,1,4,2,5]=>6
[6,3,1,4,5,2]=>7
[6,3,1,5,2,4]=>6
[6,3,1,5,4,2]=>6
[6,3,2,1,4,5]=>5
[6,3,2,1,5,4]=>5
[6,3,2,4,1,5]=>6
[6,3,2,4,5,1]=>7
[6,3,2,5,1,4]=>6
[6,3,2,5,4,1]=>6
[6,3,4,1,2,5]=>7
[6,3,4,1,5,2]=>8
[6,3,4,2,1,5]=>6
[6,3,4,2,5,1]=>7
[6,3,4,5,1,2]=>9
[6,3,4,5,2,1]=>7
[6,3,5,1,2,4]=>7
[6,3,5,1,4,2]=>7
[6,3,5,2,1,4]=>6
[6,3,5,2,4,1]=>7
[6,3,5,4,1,2]=>7
[6,3,5,4,2,1]=>6
[6,4,1,2,3,5]=>5
[6,4,1,2,5,3]=>6
[6,4,1,3,2,5]=>5
[6,4,1,3,5,2]=>6
[6,4,1,5,2,3]=>7
[6,4,1,5,3,2]=>6
[6,4,2,1,3,5]=>5
[6,4,2,1,5,3]=>6
[6,4,2,3,1,5]=>6
[6,4,2,3,5,1]=>7
[6,4,2,5,1,3]=>7
[6,4,2,5,3,1]=>7
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>6
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>6
[6,4,3,5,1,2]=>7
[6,4,3,5,2,1]=>6
[6,4,5,1,2,3]=>8
[6,4,5,1,3,2]=>7
[6,4,5,2,1,3]=>7
[6,4,5,2,3,1]=>8
[6,4,5,3,1,2]=>6
[6,4,5,3,2,1]=>6
[6,5,1,2,3,4]=>5
[6,5,1,2,4,3]=>5
[6,5,1,3,2,4]=>5
[6,5,1,3,4,2]=>6
[6,5,1,4,2,3]=>5
[6,5,1,4,3,2]=>5
[6,5,2,1,3,4]=>5
[6,5,2,1,4,3]=>5
[6,5,2,3,1,4]=>6
[6,5,2,3,4,1]=>7
[6,5,2,4,1,3]=>6
[6,5,2,4,3,1]=>6
[6,5,3,1,2,4]=>5
[6,5,3,1,4,2]=>6
[6,5,3,2,1,4]=>5
[6,5,3,2,4,1]=>6
[6,5,3,4,1,2]=>7
[6,5,3,4,2,1]=>6
[6,5,4,1,2,3]=>5
[6,5,4,1,3,2]=>5
[6,5,4,2,1,3]=>5
[6,5,4,2,3,1]=>6
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>5
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>1
[1,2,3,4,6,7,5]=>2
[1,2,3,4,7,5,6]=>2
[1,2,3,4,7,6,5]=>2
[1,2,3,5,4,6,7]=>1
[1,2,3,5,4,7,6]=>2
[1,2,3,5,6,4,7]=>2
[1,2,3,5,6,7,4]=>3
[1,2,3,5,7,4,6]=>3
[1,2,3,5,7,6,4]=>3
[1,2,3,6,4,5,7]=>2
[1,2,3,6,4,7,5]=>3
[1,2,3,6,5,4,7]=>2
[1,2,3,6,5,7,4]=>3
[1,2,3,6,7,4,5]=>4
[1,2,3,6,7,5,4]=>3
[1,2,3,7,4,5,6]=>3
[1,2,3,7,4,6,5]=>3
[1,2,3,7,5,4,6]=>3
[1,2,3,7,5,6,4]=>4
[1,2,3,7,6,4,5]=>3
[1,2,3,7,6,5,4]=>3
[1,2,4,3,5,6,7]=>1
[1,2,4,3,5,7,6]=>2
[1,2,4,3,6,5,7]=>2
[1,2,4,3,6,7,5]=>3
[1,2,4,3,7,5,6]=>3
[1,2,4,3,7,6,5]=>3
[1,2,4,5,3,6,7]=>2
[1,2,4,5,3,7,6]=>3
[1,2,4,5,6,3,7]=>3
[1,2,4,5,6,7,3]=>4
[1,2,4,5,7,3,6]=>4
[1,2,4,5,7,6,3]=>4
[1,2,4,6,3,5,7]=>3
[1,2,4,6,3,7,5]=>4
[1,2,4,6,5,3,7]=>3
[1,2,4,6,5,7,3]=>4
[1,2,4,6,7,3,5]=>5
[1,2,4,6,7,5,3]=>4
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>4
[1,2,4,7,5,3,6]=>4
[1,2,4,7,5,6,3]=>5
[1,2,4,7,6,3,5]=>4
[1,2,4,7,6,5,3]=>4
[1,2,5,3,4,6,7]=>2
[1,2,5,3,4,7,6]=>3
[1,2,5,3,6,4,7]=>3
[1,2,5,3,6,7,4]=>4
[1,2,5,3,7,4,6]=>4
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>2
[1,2,5,4,3,7,6]=>3
[1,2,5,4,6,3,7]=>3
[1,2,5,4,6,7,3]=>4
[1,2,5,4,7,3,6]=>4
[1,2,5,4,7,6,3]=>4
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>5
[1,2,5,6,4,3,7]=>3
[1,2,5,6,4,7,3]=>4
[1,2,5,6,7,3,4]=>6
[1,2,5,6,7,4,3]=>4
[1,2,5,7,3,4,6]=>5
[1,2,5,7,3,6,4]=>5
[1,2,5,7,4,3,6]=>4
[1,2,5,7,4,6,3]=>5
[1,2,5,7,6,3,4]=>5
[1,2,5,7,6,4,3]=>4
[1,2,6,3,4,5,7]=>3
[1,2,6,3,4,7,5]=>4
[1,2,6,3,5,4,7]=>3
[1,2,6,3,5,7,4]=>4
[1,2,6,3,7,4,5]=>5
[1,2,6,3,7,5,4]=>4
[1,2,6,4,3,5,7]=>3
[1,2,6,4,3,7,5]=>4
[1,2,6,4,5,3,7]=>4
[1,2,6,4,5,7,3]=>5
[1,2,6,4,7,3,5]=>5
[1,2,6,4,7,5,3]=>5
[1,2,6,5,3,4,7]=>3
[1,2,6,5,3,7,4]=>4
[1,2,6,5,4,3,7]=>3
[1,2,6,5,4,7,3]=>4
[1,2,6,5,7,3,4]=>5
[1,2,6,5,7,4,3]=>4
[1,2,6,7,3,4,5]=>6
[1,2,6,7,3,5,4]=>5
[1,2,6,7,4,3,5]=>5
[1,2,6,7,4,5,3]=>6
[1,2,6,7,5,3,4]=>4
[1,2,6,7,5,4,3]=>4
[1,2,7,3,4,5,6]=>4
[1,2,7,3,4,6,5]=>4
[1,2,7,3,5,4,6]=>4
[1,2,7,3,5,6,4]=>5
[1,2,7,3,6,4,5]=>4
[1,2,7,3,6,5,4]=>4
[1,2,7,4,3,5,6]=>4
[1,2,7,4,3,6,5]=>4
[1,2,7,4,5,3,6]=>5
[1,2,7,4,5,6,3]=>6
[1,2,7,4,6,3,5]=>5
[1,2,7,4,6,5,3]=>5
[1,2,7,5,3,4,6]=>4
[1,2,7,5,3,6,4]=>5
[1,2,7,5,4,3,6]=>4
[1,2,7,5,4,6,3]=>5
[1,2,7,5,6,3,4]=>6
[1,2,7,5,6,4,3]=>5
[1,2,7,6,3,4,5]=>4
[1,2,7,6,3,5,4]=>4
[1,2,7,6,4,3,5]=>4
[1,2,7,6,4,5,3]=>5
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>4
[1,3,2,4,5,6,7]=>1
[1,3,2,4,5,7,6]=>2
[1,3,2,4,6,5,7]=>2
[1,3,2,4,6,7,5]=>3
[1,3,2,4,7,5,6]=>3
[1,3,2,4,7,6,5]=>3
[1,3,2,5,4,6,7]=>2
[1,3,2,5,4,7,6]=>3
[1,3,2,5,6,4,7]=>3
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>4
[1,3,2,5,7,6,4]=>4
[1,3,2,6,4,5,7]=>3
[1,3,2,6,4,7,5]=>4
[1,3,2,6,5,4,7]=>3
[1,3,2,6,5,7,4]=>4
[1,3,2,6,7,4,5]=>5
[1,3,2,6,7,5,4]=>4
[1,3,2,7,4,5,6]=>4
[1,3,2,7,4,6,5]=>4
[1,3,2,7,5,4,6]=>4
[1,3,2,7,5,6,4]=>5
[1,3,2,7,6,4,5]=>4
[1,3,2,7,6,5,4]=>4
[1,3,4,2,5,6,7]=>2
[1,3,4,2,5,7,6]=>3
[1,3,4,2,6,5,7]=>3
[1,3,4,2,6,7,5]=>4
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>4
[1,3,4,5,2,6,7]=>3
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>4
[1,3,4,5,6,7,2]=>5
[1,3,4,5,7,2,6]=>5
[1,3,4,5,7,6,2]=>5
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>5
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>5
[1,3,4,6,7,2,5]=>6
[1,3,4,6,7,5,2]=>5
[1,3,4,7,2,5,6]=>5
[1,3,4,7,2,6,5]=>5
[1,3,4,7,5,2,6]=>5
[1,3,4,7,5,6,2]=>6
[1,3,4,7,6,2,5]=>5
[1,3,4,7,6,5,2]=>5
[1,3,5,2,4,6,7]=>3
[1,3,5,2,4,7,6]=>4
[1,3,5,2,6,4,7]=>4
[1,3,5,2,6,7,4]=>5
[1,3,5,2,7,4,6]=>5
[1,3,5,2,7,6,4]=>5
[1,3,5,4,2,6,7]=>3
[1,3,5,4,2,7,6]=>4
[1,3,5,4,6,2,7]=>4
[1,3,5,4,6,7,2]=>5
[1,3,5,4,7,2,6]=>5
[1,3,5,4,7,6,2]=>5
[1,3,5,6,2,4,7]=>5
[1,3,5,6,2,7,4]=>6
[1,3,5,6,4,2,7]=>4
[1,3,5,6,4,7,2]=>5
[1,3,5,6,7,2,4]=>7
[1,3,5,6,7,4,2]=>5
[1,3,5,7,2,4,6]=>6
[1,3,5,7,2,6,4]=>6
[1,3,5,7,4,2,6]=>5
[1,3,5,7,4,6,2]=>6
[1,3,5,7,6,2,4]=>6
[1,3,5,7,6,4,2]=>5
[1,3,6,2,4,5,7]=>4
[1,3,6,2,4,7,5]=>5
[1,3,6,2,5,4,7]=>4
[1,3,6,2,5,7,4]=>5
[1,3,6,2,7,4,5]=>6
[1,3,6,2,7,5,4]=>5
[1,3,6,4,2,5,7]=>4
[1,3,6,4,2,7,5]=>5
[1,3,6,4,5,2,7]=>5
[1,3,6,4,5,7,2]=>6
[1,3,6,4,7,2,5]=>6
[1,3,6,4,7,5,2]=>6
[1,3,6,5,2,4,7]=>4
[1,3,6,5,2,7,4]=>5
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>5
[1,3,6,5,7,2,4]=>6
[1,3,6,5,7,4,2]=>5
[1,3,6,7,2,4,5]=>7
[1,3,6,7,2,5,4]=>6
[1,3,6,7,4,2,5]=>6
[1,3,6,7,4,5,2]=>7
[1,3,6,7,5,2,4]=>5
[1,3,6,7,5,4,2]=>5
[1,3,7,2,4,5,6]=>5
[1,3,7,2,4,6,5]=>5
[1,3,7,2,5,4,6]=>5
[1,3,7,2,5,6,4]=>6
[1,3,7,2,6,4,5]=>5
[1,3,7,2,6,5,4]=>5
[1,3,7,4,2,5,6]=>5
[1,3,7,4,2,6,5]=>5
[1,3,7,4,5,2,6]=>6
[1,3,7,4,5,6,2]=>7
[1,3,7,4,6,2,5]=>6
[1,3,7,4,6,5,2]=>6
[1,3,7,5,2,4,6]=>5
[1,3,7,5,2,6,4]=>6
[1,3,7,5,4,2,6]=>5
[1,3,7,5,4,6,2]=>6
[1,3,7,5,6,2,4]=>7
[1,3,7,5,6,4,2]=>6
[1,3,7,6,2,4,5]=>5
[1,3,7,6,2,5,4]=>5
[1,3,7,6,4,2,5]=>5
[1,3,7,6,4,5,2]=>6
[1,3,7,6,5,2,4]=>5
[1,3,7,6,5,4,2]=>5
[1,4,2,3,5,6,7]=>2
[1,4,2,3,5,7,6]=>3
[1,4,2,3,6,5,7]=>3
[1,4,2,3,6,7,5]=>4
[1,4,2,3,7,5,6]=>4
[1,4,2,3,7,6,5]=>4
[1,4,2,5,3,6,7]=>3
[1,4,2,5,3,7,6]=>4
[1,4,2,5,6,3,7]=>4
[1,4,2,5,6,7,3]=>5
[1,4,2,5,7,3,6]=>5
[1,4,2,5,7,6,3]=>5
[1,4,2,6,3,5,7]=>4
[1,4,2,6,3,7,5]=>5
[1,4,2,6,5,3,7]=>4
[1,4,2,6,5,7,3]=>5
[1,4,2,6,7,3,5]=>6
[1,4,2,6,7,5,3]=>5
[1,4,2,7,3,5,6]=>5
[1,4,2,7,3,6,5]=>5
[1,4,2,7,5,3,6]=>5
[1,4,2,7,5,6,3]=>6
[1,4,2,7,6,3,5]=>5
[1,4,2,7,6,5,3]=>5
[1,4,3,2,5,6,7]=>2
[1,4,3,2,5,7,6]=>3
[1,4,3,2,6,5,7]=>3
[1,4,3,2,6,7,5]=>4
[1,4,3,2,7,5,6]=>4
[1,4,3,2,7,6,5]=>4
[1,4,3,5,2,6,7]=>3
[1,4,3,5,2,7,6]=>4
[1,4,3,5,6,2,7]=>4
[1,4,3,5,6,7,2]=>5
[1,4,3,5,7,2,6]=>5
[1,4,3,5,7,6,2]=>5
[1,4,3,6,2,5,7]=>4
[1,4,3,6,2,7,5]=>5
[1,4,3,6,5,2,7]=>4
[1,4,3,6,5,7,2]=>5
[1,4,3,6,7,2,5]=>6
[1,4,3,6,7,5,2]=>5
[1,4,3,7,2,5,6]=>5
[1,4,3,7,2,6,5]=>5
[1,4,3,7,5,2,6]=>5
[1,4,3,7,5,6,2]=>6
[1,4,3,7,6,2,5]=>5
[1,4,3,7,6,5,2]=>5
[1,4,5,2,3,6,7]=>4
[1,4,5,2,3,7,6]=>5
[1,4,5,2,6,3,7]=>5
[1,4,5,2,6,7,3]=>6
[1,4,5,2,7,3,6]=>6
[1,4,5,2,7,6,3]=>6
[1,4,5,3,2,6,7]=>3
[1,4,5,3,2,7,6]=>4
[1,4,5,3,6,2,7]=>4
[1,4,5,3,6,7,2]=>5
[1,4,5,3,7,2,6]=>5
[1,4,5,3,7,6,2]=>5
[1,4,5,6,2,3,7]=>6
[1,4,5,6,2,7,3]=>7
[1,4,5,6,3,2,7]=>4
[1,4,5,6,3,7,2]=>5
[1,4,5,6,7,2,3]=>8
[1,4,5,6,7,3,2]=>5
[1,4,5,7,2,3,6]=>7
[1,4,5,7,2,6,3]=>7
[1,4,5,7,3,2,6]=>5
[1,4,5,7,3,6,2]=>6
[1,4,5,7,6,2,3]=>7
[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]=>5
[1,4,6,2,5,7,3]=>6
[1,4,6,2,7,3,5]=>7
[1,4,6,2,7,5,3]=>6
[1,4,6,3,2,5,7]=>4
[1,4,6,3,2,7,5]=>5
[1,4,6,3,5,2,7]=>5
[1,4,6,3,5,7,2]=>6
[1,4,6,3,7,2,5]=>6
[1,4,6,3,7,5,2]=>6
[1,4,6,5,2,3,7]=>5
[1,4,6,5,2,7,3]=>6
[1,4,6,5,3,2,7]=>4
[1,4,6,5,3,7,2]=>5
                    

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Description

The number of Bruhat lower covers of a permutation.
This is, for a permutation $\pi$, the number of permutations $\tau$ with $\operatorname{inv}(\tau) = \operatorname{inv}(\pi) - 1$ such that $\tau*t = \pi$ for a transposition $t$.
This is also the number of occurrences of the boxed pattern $21$: occurrences of the pattern $21$ such that any entry between the two matched entries is either larger or smaller than both of the matched entries.

Code

def statistic(pi):
    return len(PermutationGroupElement(pi).bruhat_lower_covers())

Created

Aug 27, 2017 at 22:50 by Martin Rubey

Updated

Jan 15, 2018 at 08:16 by Martin Rubey