- FindStat

edit this statistic or download as text // json

Identifier

St001411: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>0
[1,3,2,4]=>0
[1,3,4,2]=>0
[1,4,2,3]=>0
[1,4,3,2]=>1
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,3,1]=>1
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>1
[3,2,4,1]=>1
[3,4,1,2]=>1
[3,4,2,1]=>2
[4,1,2,3]=>0
[4,1,3,2]=>1
[4,2,1,3]=>1
[4,2,3,1]=>2
[4,3,1,2]=>2
[4,3,2,1]=>4
[1,2,3,4,5]=>0
[1,2,3,5,4]=>0
[1,2,4,3,5]=>0
[1,2,4,5,3]=>0
[1,2,5,3,4]=>0
[1,2,5,4,3]=>1
[1,3,2,4,5]=>0
[1,3,2,5,4]=>0
[1,3,4,2,5]=>0
[1,3,4,5,2]=>0
[1,3,5,2,4]=>0
[1,3,5,4,2]=>1
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>1
[1,4,3,5,2]=>1
[1,4,5,2,3]=>1
[1,4,5,3,2]=>2
[1,5,2,3,4]=>0
[1,5,2,4,3]=>1
[1,5,3,2,4]=>1
[1,5,3,4,2]=>2
[1,5,4,2,3]=>2
[1,5,4,3,2]=>4
[2,1,3,4,5]=>0
[2,1,3,5,4]=>0
[2,1,4,3,5]=>0
[2,1,4,5,3]=>0
[2,1,5,3,4]=>0
[2,1,5,4,3]=>1
[2,3,1,4,5]=>0
[2,3,1,5,4]=>0
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>0
[2,3,5,4,1]=>1
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>1
[2,4,3,5,1]=>1
[2,4,5,1,3]=>1
[2,4,5,3,1]=>2
[2,5,1,3,4]=>0
[2,5,1,4,3]=>1
[2,5,3,1,4]=>1
[2,5,3,4,1]=>2
[2,5,4,1,3]=>2
[2,5,4,3,1]=>4
[3,1,2,4,5]=>0
[3,1,2,5,4]=>0
[3,1,4,2,5]=>0
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,4,2]=>1
[3,2,1,4,5]=>1
[3,2,1,5,4]=>1
[3,2,4,1,5]=>1
[3,2,4,5,1]=>1
[3,2,5,1,4]=>1
[3,2,5,4,1]=>2
[3,4,1,2,5]=>1
[3,4,1,5,2]=>1
[3,4,2,1,5]=>2
[3,4,2,5,1]=>2
[3,4,5,1,2]=>3
[3,4,5,2,1]=>3
[3,5,1,2,4]=>1
[3,5,1,4,2]=>2
[3,5,2,1,4]=>2
[3,5,2,4,1]=>3
[3,5,4,1,2]=>4
[3,5,4,2,1]=>5
[4,1,2,3,5]=>0
[4,1,2,5,3]=>0
[4,1,3,2,5]=>1
[4,1,3,5,2]=>1
[4,1,5,2,3]=>1
[4,1,5,3,2]=>2
[4,2,1,3,5]=>1
[4,2,1,5,3]=>1
[4,2,3,1,5]=>2
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>2
[4,3,1,5,2]=>2
[4,3,2,1,5]=>4
[4,3,2,5,1]=>4
[4,3,5,1,2]=>4
[4,3,5,2,1]=>5
[4,5,1,2,3]=>3
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>5
[4,5,3,1,2]=>5
[4,5,3,2,1]=>7
[5,1,2,3,4]=>0
[5,1,2,4,3]=>1
[5,1,3,2,4]=>1
[5,1,3,4,2]=>2
[5,1,4,2,3]=>2
[5,1,4,3,2]=>4
[5,2,1,3,4]=>1
[5,2,1,4,3]=>2
[5,2,3,1,4]=>2
[5,2,3,4,1]=>3
[5,2,4,1,3]=>3
[5,2,4,3,1]=>5
[5,3,1,2,4]=>2
[5,3,1,4,2]=>3
[5,3,2,1,4]=>4
[5,3,2,4,1]=>5
[5,3,4,1,2]=>5
[5,3,4,2,1]=>7
[5,4,1,2,3]=>3
[5,4,1,3,2]=>5
[5,4,2,1,3]=>5
[5,4,2,3,1]=>7
[5,4,3,1,2]=>7
[5,4,3,2,1]=>10
[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]=>0
[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>1
[1,2,4,3,5,6]=>0
[1,2,4,3,6,5]=>0
[1,2,4,5,3,6]=>0
[1,2,4,5,6,3]=>0
[1,2,4,6,3,5]=>0
[1,2,4,6,5,3]=>1
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>1
[1,2,5,4,6,3]=>1
[1,2,5,6,3,4]=>1
[1,2,5,6,4,3]=>2
[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>1
[1,2,6,4,3,5]=>1
[1,2,6,4,5,3]=>2
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>4
[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]=>0
[1,3,2,6,4,5]=>0
[1,3,2,6,5,4]=>1
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>0
[1,3,4,5,2,6]=>0
[1,3,4,5,6,2]=>0
[1,3,4,6,2,5]=>0
[1,3,4,6,5,2]=>1
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>1
[1,3,5,4,6,2]=>1
[1,3,5,6,2,4]=>1
[1,3,5,6,4,2]=>2
[1,3,6,2,4,5]=>0
[1,3,6,2,5,4]=>1
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>2
[1,3,6,5,2,4]=>2
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>0
[1,4,2,5,3,6]=>0
[1,4,2,5,6,3]=>0
[1,4,2,6,3,5]=>0
[1,4,2,6,5,3]=>1
[1,4,3,2,5,6]=>1
[1,4,3,2,6,5]=>1
[1,4,3,5,2,6]=>1
[1,4,3,5,6,2]=>1
[1,4,3,6,2,5]=>1
[1,4,3,6,5,2]=>2
[1,4,5,2,3,6]=>1
[1,4,5,2,6,3]=>1
[1,4,5,3,2,6]=>2
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>1
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>2
[1,4,6,3,5,2]=>3
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>5
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>0
[1,5,2,4,3,6]=>1
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>1
[1,5,2,6,4,3]=>2
[1,5,3,2,4,6]=>1
[1,5,3,2,6,4]=>1
[1,5,3,4,2,6]=>2
[1,5,3,4,6,2]=>2
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>3
[1,5,4,2,3,6]=>2
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>4
[1,5,4,3,6,2]=>4
[1,5,4,6,2,3]=>4
[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]=>4
[1,5,6,3,4,2]=>5
[1,5,6,4,2,3]=>5
[1,5,6,4,3,2]=>7
[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>1
[1,6,2,4,3,5]=>1
[1,6,2,4,5,3]=>2
[1,6,2,5,3,4]=>2
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>1
[1,6,3,2,5,4]=>2
[1,6,3,4,2,5]=>2
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>5
[1,6,4,2,3,5]=>2
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>5
[1,6,4,5,2,3]=>5
[1,6,4,5,3,2]=>7
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>5
[1,6,5,3,2,4]=>5
[1,6,5,3,4,2]=>7
[1,6,5,4,2,3]=>7
[1,6,5,4,3,2]=>10
[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]=>0
[2,1,3,6,4,5]=>0
[2,1,3,6,5,4]=>1
[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>0
[2,1,4,5,6,3]=>0
[2,1,4,6,3,5]=>0
[2,1,4,6,5,3]=>1
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>0
[2,1,5,4,3,6]=>1
[2,1,5,4,6,3]=>1
[2,1,5,6,3,4]=>1
[2,1,5,6,4,3]=>2
[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>1
[2,1,6,4,3,5]=>1
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>2
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>0
[2,3,1,5,4,6]=>0
[2,3,1,5,6,4]=>0
[2,3,1,6,4,5]=>0
[2,3,1,6,5,4]=>1
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>0
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>0
[2,3,4,6,5,1]=>1
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>1
[2,3,5,4,6,1]=>1
[2,3,5,6,1,4]=>1
[2,3,5,6,4,1]=>2
[2,3,6,1,4,5]=>0
[2,3,6,1,5,4]=>1
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>2
[2,3,6,5,1,4]=>2
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>0
[2,4,1,3,6,5]=>0
[2,4,1,5,3,6]=>0
[2,4,1,5,6,3]=>0
[2,4,1,6,3,5]=>0
[2,4,1,6,5,3]=>1
[2,4,3,1,5,6]=>1
[2,4,3,1,6,5]=>1
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>1
[2,4,3,6,5,1]=>2
[2,4,5,1,3,6]=>1
[2,4,5,1,6,3]=>1
[2,4,5,3,1,6]=>2
[2,4,5,3,6,1]=>2
[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]=>2
[2,4,6,3,1,5]=>2
[2,4,6,3,5,1]=>3
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>5
[2,5,1,3,4,6]=>0
[2,5,1,3,6,4]=>0
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>1
[2,5,1,6,3,4]=>1
[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]=>2
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>2
[2,5,3,6,4,1]=>3
[2,5,4,1,3,6]=>2
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>4
[2,5,4,3,6,1]=>4
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>5
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>4
[2,5,6,3,1,4]=>4
[2,5,6,3,4,1]=>5
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>7
[2,6,1,3,4,5]=>0
[2,6,1,3,5,4]=>1
[2,6,1,4,3,5]=>1
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>1
[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]=>3
[2,6,3,5,4,1]=>5
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>3
[2,6,4,3,1,5]=>4
[2,6,4,3,5,1]=>5
[2,6,4,5,1,3]=>5
[2,6,4,5,3,1]=>7
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>5
[2,6,5,3,1,4]=>5
[2,6,5,3,4,1]=>7
[2,6,5,4,1,3]=>7
[2,6,5,4,3,1]=>10
[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]=>0
[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>1
[3,1,4,2,5,6]=>0
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>0
[3,1,4,5,6,2]=>0
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>1
[3,1,5,6,4,2]=>2
[3,1,6,2,4,5]=>0
[3,1,6,2,5,4]=>1
[3,1,6,4,2,5]=>1
[3,1,6,4,5,2]=>2
[3,1,6,5,2,4]=>2
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>1
[3,2,1,5,4,6]=>1
[3,2,1,5,6,4]=>1
[3,2,1,6,4,5]=>1
[3,2,1,6,5,4]=>2
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>1
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>1
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>1
[3,2,5,1,6,4]=>1
[3,2,5,4,1,6]=>2
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>2
[3,2,5,6,4,1]=>3
[3,2,6,1,4,5]=>1
[3,2,6,1,5,4]=>2
[3,2,6,4,1,5]=>2
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>5
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>1
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>1
[3,4,1,6,2,5]=>1
[3,4,1,6,5,2]=>2
[3,4,2,1,5,6]=>2
[3,4,2,1,6,5]=>2
[3,4,2,5,1,6]=>2
[3,4,2,5,6,1]=>2
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>3
[3,4,5,1,6,2]=>3
[3,4,5,2,1,6]=>3
[3,4,5,2,6,1]=>3
[3,4,5,6,1,2]=>6
[3,4,5,6,2,1]=>4
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>4
[3,4,6,5,1,2]=>7
[3,4,6,5,2,1]=>6
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>1
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>2
[3,5,1,6,2,4]=>2
[3,5,1,6,4,2]=>3
[3,5,2,1,4,6]=>2
[3,5,2,1,6,4]=>2
[3,5,2,4,1,6]=>3
[3,5,2,4,6,1]=>3
[3,5,2,6,1,4]=>3
[3,5,2,6,4,1]=>4
[3,5,4,1,2,6]=>4
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>5
[3,5,4,2,6,1]=>5
[3,5,4,6,1,2]=>7
[3,5,4,6,2,1]=>6
[3,5,6,1,2,4]=>5
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>6
[3,5,6,4,1,2]=>8
[3,5,6,4,2,1]=>8
[3,6,1,2,4,5]=>1
[3,6,1,2,5,4]=>2
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>3
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>5
[3,6,2,1,4,5]=>2
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>3
[3,6,2,4,5,1]=>4
[3,6,2,5,1,4]=>4
[3,6,2,5,4,1]=>6
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>5
[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]=>8
[3,6,5,1,2,4]=>5
[3,6,5,1,4,2]=>7
[3,6,5,2,1,4]=>6
[3,6,5,2,4,1]=>8
[3,6,5,4,1,2]=>10
[3,6,5,4,2,1]=>11
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>0
[4,1,2,5,3,6]=>0
[4,1,2,5,6,3]=>0
[4,1,2,6,3,5]=>0
[4,1,2,6,5,3]=>1
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>1
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>1
[4,1,3,6,2,5]=>1
[4,1,3,6,5,2]=>2
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>2
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>1
[4,1,6,2,5,3]=>2
[4,1,6,3,2,5]=>2
[4,1,6,3,5,2]=>3
[4,1,6,5,2,3]=>4
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>1
[4,2,1,3,6,5]=>1
[4,2,1,5,3,6]=>1
[4,2,1,5,6,3]=>1
[4,2,1,6,3,5]=>1
[4,2,1,6,5,3]=>2
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>2
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>2
[4,2,3,6,5,1]=>3
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>2
[4,2,5,3,1,6]=>3
[4,2,5,3,6,1]=>3
[4,2,5,6,1,3]=>4
[4,2,5,6,3,1]=>4
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>3
[4,2,6,3,1,5]=>3
[4,2,6,3,5,1]=>4
[4,2,6,5,1,3]=>5
[4,2,6,5,3,1]=>6
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>2
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>2
[4,3,1,6,2,5]=>2
[4,3,1,6,5,2]=>3
[4,3,2,1,5,6]=>4
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>4
[4,3,2,5,6,1]=>4
[4,3,2,6,1,5]=>4
[4,3,2,6,5,1]=>5
[4,3,5,1,2,6]=>4
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>5
[4,3,5,2,6,1]=>5
[4,3,5,6,1,2]=>7
[4,3,5,6,2,1]=>6
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>5
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>6
[4,3,6,5,1,2]=>8
[4,3,6,5,2,1]=>8
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>5
[4,5,1,6,3,2]=>5
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>4
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>5
[4,5,2,6,1,3]=>6
[4,5,2,6,3,1]=>6
[4,5,3,1,2,6]=>5
[4,5,3,1,6,2]=>5
[4,5,3,2,1,6]=>7
[4,5,3,2,6,1]=>7
[4,5,3,6,1,2]=>8
[4,5,3,6,2,1]=>8
[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]=>10
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>5
[4,6,1,5,2,3]=>6
[4,6,1,5,3,2]=>7
[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>5
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>6
[4,6,2,5,1,3]=>7
[4,6,2,5,3,1]=>8
[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>6
[4,6,3,2,1,5]=>7
[4,6,3,2,5,1]=>8
[4,6,3,5,1,2]=>9
[4,6,3,5,2,1]=>10
[4,6,5,1,2,3]=>9
[4,6,5,1,3,2]=>10
[4,6,5,2,1,3]=>10
[4,6,5,2,3,1]=>11
[4,6,5,3,1,2]=>11
[4,6,5,3,2,1]=>13
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>0
[5,1,2,4,3,6]=>1
[5,1,2,4,6,3]=>1
[5,1,2,6,3,4]=>1
[5,1,2,6,4,3]=>2
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>2
[5,1,3,6,2,4]=>2
[5,1,3,6,4,2]=>3
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>4
[5,1,4,3,6,2]=>4
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>5
[5,1,6,4,2,3]=>5
[5,1,6,4,3,2]=>7
[5,2,1,3,4,6]=>1
[5,2,1,3,6,4]=>1
[5,2,1,4,3,6]=>2
[5,2,1,4,6,3]=>2
[5,2,1,6,3,4]=>2
[5,2,1,6,4,3]=>3
[5,2,3,1,4,6]=>2
[5,2,3,1,6,4]=>2
[5,2,3,4,1,6]=>3
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>3
[5,2,3,6,4,1]=>4
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>3
[5,2,4,3,1,6]=>5
[5,2,4,3,6,1]=>5
[5,2,4,6,1,3]=>5
[5,2,4,6,3,1]=>6
[5,2,6,1,3,4]=>4
[5,2,6,1,4,3]=>5
[5,2,6,3,1,4]=>5
[5,2,6,3,4,1]=>6
[5,2,6,4,1,3]=>6
[5,2,6,4,3,1]=>8
[5,3,1,2,4,6]=>2
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>3
[5,3,1,6,2,4]=>3
[5,3,1,6,4,2]=>4
[5,3,2,1,4,6]=>4
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>5
[5,3,2,4,6,1]=>5
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>6
[5,3,4,1,2,6]=>5
[5,3,4,1,6,2]=>5
[5,3,4,2,1,6]=>7
[5,3,4,2,6,1]=>7
[5,3,4,6,1,2]=>8
[5,3,4,6,2,1]=>8
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>7
[5,3,6,2,1,4]=>7
[5,3,6,2,4,1]=>8
[5,3,6,4,1,2]=>9
[5,3,6,4,2,1]=>10
[5,4,1,2,3,6]=>3
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>5
[5,4,1,3,6,2]=>5
[5,4,1,6,2,3]=>5
[5,4,1,6,3,2]=>6
[5,4,2,1,3,6]=>5
[5,4,2,1,6,3]=>5
[5,4,2,3,1,6]=>7
[5,4,2,3,6,1]=>7
[5,4,2,6,1,3]=>7
[5,4,2,6,3,1]=>8
[5,4,3,1,2,6]=>7
[5,4,3,1,6,2]=>7
[5,4,3,2,1,6]=>10
[5,4,3,2,6,1]=>10
[5,4,3,6,1,2]=>10
[5,4,3,6,2,1]=>11
[5,4,6,1,2,3]=>9
[5,4,6,1,3,2]=>10
[5,4,6,2,1,3]=>10
[5,4,6,2,3,1]=>11
[5,4,6,3,1,2]=>11
[5,4,6,3,2,1]=>13
[5,6,1,2,3,4]=>6
[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]=>8
[5,6,1,4,3,2]=>10
[5,6,2,1,3,4]=>7
[5,6,2,1,4,3]=>8
[5,6,2,3,1,4]=>8
[5,6,2,3,4,1]=>9
[5,6,2,4,1,3]=>9
[5,6,2,4,3,1]=>11
[5,6,3,1,2,4]=>8
[5,6,3,1,4,2]=>9
[5,6,3,2,1,4]=>10
[5,6,3,2,4,1]=>11
[5,6,3,4,1,2]=>11
[5,6,3,4,2,1]=>13
[5,6,4,1,2,3]=>9
[5,6,4,1,3,2]=>11
[5,6,4,2,1,3]=>11
[5,6,4,2,3,1]=>13
[5,6,4,3,1,2]=>13
[5,6,4,3,2,1]=>16
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>1
[6,1,2,4,3,5]=>1
[6,1,2,4,5,3]=>2
[6,1,2,5,3,4]=>2
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>2
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>5
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>3
[6,1,4,3,2,5]=>4
[6,1,4,3,5,2]=>5
[6,1,4,5,2,3]=>5
[6,1,4,5,3,2]=>7
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>5
[6,1,5,3,2,4]=>5
[6,1,5,3,4,2]=>7
[6,1,5,4,2,3]=>7
[6,1,5,4,3,2]=>10
[6,2,1,3,4,5]=>1
[6,2,1,3,5,4]=>2
[6,2,1,4,3,5]=>2
[6,2,1,4,5,3]=>3
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>5
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>3
[6,2,3,4,5,1]=>4
[6,2,3,5,1,4]=>4
[6,2,3,5,4,1]=>6
[6,2,4,1,3,5]=>3
[6,2,4,1,5,3]=>4
[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]=>8
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>6
[6,2,5,3,1,4]=>6
[6,2,5,3,4,1]=>8
[6,2,5,4,1,3]=>8
[6,2,5,4,3,1]=>11
[6,3,1,2,4,5]=>2
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>4
[6,3,1,5,2,4]=>4
[6,3,1,5,4,2]=>6
[6,3,2,1,4,5]=>4
[6,3,2,1,5,4]=>5
[6,3,2,4,1,5]=>5
[6,3,2,4,5,1]=>6
[6,3,2,5,1,4]=>6
[6,3,2,5,4,1]=>8
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>6
[6,3,4,2,1,5]=>7
[6,3,4,2,5,1]=>8
[6,3,4,5,1,2]=>9
[6,3,4,5,2,1]=>10
[6,3,5,1,2,4]=>6
[6,3,5,1,4,2]=>8
[6,3,5,2,1,4]=>8
[6,3,5,2,4,1]=>10
[6,3,5,4,1,2]=>11
[6,3,5,4,2,1]=>13
[6,4,1,2,3,5]=>3
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>5
[6,4,1,3,5,2]=>6
[6,4,1,5,2,3]=>6
[6,4,1,5,3,2]=>8
[6,4,2,1,3,5]=>5
[6,4,2,1,5,3]=>6
[6,4,2,3,1,5]=>7
[6,4,2,3,5,1]=>8
[6,4,2,5,1,3]=>8
[6,4,2,5,3,1]=>10
[6,4,3,1,2,5]=>7
[6,4,3,1,5,2]=>8
[6,4,3,2,1,5]=>10
[6,4,3,2,5,1]=>11
[6,4,3,5,1,2]=>11
[6,4,3,5,2,1]=>13
[6,4,5,1,2,3]=>9
[6,4,5,1,3,2]=>11
[6,4,5,2,1,3]=>11
[6,4,5,2,3,1]=>13
[6,4,5,3,1,2]=>13
[6,4,5,3,2,1]=>16
[6,5,1,2,3,4]=>4
[6,5,1,2,4,3]=>6
[6,5,1,3,2,4]=>6
[6,5,1,3,4,2]=>8
[6,5,1,4,2,3]=>8
[6,5,1,4,3,2]=>11
[6,5,2,1,3,4]=>6
[6,5,2,1,4,3]=>8
[6,5,2,3,1,4]=>8
[6,5,2,3,4,1]=>10
[6,5,2,4,1,3]=>10
[6,5,2,4,3,1]=>13
[6,5,3,1,2,4]=>8
[6,5,3,1,4,2]=>10
[6,5,3,2,1,4]=>11
[6,5,3,2,4,1]=>13
[6,5,3,4,1,2]=>13
[6,5,3,4,2,1]=>16
[6,5,4,1,2,3]=>10
[6,5,4,1,3,2]=>13
[6,5,4,2,1,3]=>13
[6,5,4,2,3,1]=>16
[6,5,4,3,1,2]=>16
[6,5,4,3,2,1]=>20
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>0
[1,2,3,4,6,5,7]=>0
[1,2,3,4,6,7,5]=>0
[1,2,3,4,7,5,6]=>0
[1,2,3,4,7,6,5]=>1
[1,2,3,5,4,6,7]=>0
[1,2,3,5,4,7,6]=>0
[1,2,3,5,6,4,7]=>0
[1,2,3,5,6,7,4]=>0
[1,2,3,5,7,4,6]=>0
[1,2,3,5,7,6,4]=>1
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,3,6,5,4,7]=>1
[1,2,3,6,5,7,4]=>1
[1,2,3,6,7,4,5]=>1
[1,2,3,6,7,5,4]=>2
[1,2,3,7,4,5,6]=>0
[1,2,3,7,4,6,5]=>1
[1,2,3,7,5,4,6]=>1
[1,2,3,7,5,6,4]=>2
[1,2,3,7,6,4,5]=>2
[1,2,3,7,6,5,4]=>4
[1,2,4,3,5,6,7]=>0
[1,2,4,3,5,7,6]=>0
[1,2,4,3,6,5,7]=>0
[1,2,4,3,6,7,5]=>0
[1,2,4,3,7,5,6]=>0
[1,2,4,3,7,6,5]=>1
[1,2,4,5,3,6,7]=>0
[1,2,4,5,3,7,6]=>0
[1,2,4,5,6,3,7]=>0
[1,2,4,5,6,7,3]=>0
[1,2,4,5,7,3,6]=>0
[1,2,4,5,7,6,3]=>1
[1,2,4,6,3,5,7]=>0
[1,2,4,6,3,7,5]=>0
[1,2,4,6,5,3,7]=>1
[1,2,4,6,5,7,3]=>1
[1,2,4,6,7,3,5]=>1
[1,2,4,6,7,5,3]=>2
[1,2,4,7,3,5,6]=>0
[1,2,4,7,3,6,5]=>1
[1,2,4,7,5,3,6]=>1
[1,2,4,7,5,6,3]=>2
[1,2,4,7,6,3,5]=>2
[1,2,4,7,6,5,3]=>4
[1,2,5,3,4,6,7]=>0
[1,2,5,3,4,7,6]=>0
[1,2,5,3,6,4,7]=>0
[1,2,5,3,6,7,4]=>0
[1,2,5,3,7,4,6]=>0
[1,2,5,3,7,6,4]=>1
[1,2,5,4,3,6,7]=>1
[1,2,5,4,3,7,6]=>1
[1,2,5,4,6,3,7]=>1
[1,2,5,4,6,7,3]=>1
[1,2,5,4,7,3,6]=>1
[1,2,5,4,7,6,3]=>2
[1,2,5,6,3,4,7]=>1
[1,2,5,6,3,7,4]=>1
[1,2,5,6,4,3,7]=>2
[1,2,5,6,4,7,3]=>2
[1,2,5,6,7,3,4]=>3
[1,2,5,6,7,4,3]=>3
[1,2,5,7,3,4,6]=>1
[1,2,5,7,3,6,4]=>2
[1,2,5,7,4,3,6]=>2
[1,2,5,7,4,6,3]=>3
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>5
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>0
[1,2,6,3,5,4,7]=>1
[1,2,6,3,5,7,4]=>1
[1,2,6,3,7,4,5]=>1
[1,2,6,3,7,5,4]=>2
[1,2,6,4,3,5,7]=>1
[1,2,6,4,3,7,5]=>1
[1,2,6,4,5,3,7]=>2
[1,2,6,4,5,7,3]=>2
[1,2,6,4,7,3,5]=>2
[1,2,6,4,7,5,3]=>3
[1,2,6,5,3,4,7]=>2
[1,2,6,5,3,7,4]=>2
[1,2,6,5,4,3,7]=>4
[1,2,6,5,4,7,3]=>4
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>5
[1,2,6,7,3,4,5]=>3
[1,2,6,7,3,5,4]=>4
[1,2,6,7,4,3,5]=>4
[1,2,6,7,4,5,3]=>5
[1,2,6,7,5,3,4]=>5
[1,2,6,7,5,4,3]=>7
[1,2,7,3,4,5,6]=>0
[1,2,7,3,4,6,5]=>1
[1,2,7,3,5,4,6]=>1
[1,2,7,3,5,6,4]=>2
[1,2,7,3,6,4,5]=>2
[1,2,7,3,6,5,4]=>4
[1,2,7,4,3,5,6]=>1
[1,2,7,4,3,6,5]=>2
[1,2,7,4,5,3,6]=>2
[1,2,7,4,5,6,3]=>3
[1,2,7,4,6,3,5]=>3
[1,2,7,4,6,5,3]=>5
[1,2,7,5,3,4,6]=>2
[1,2,7,5,3,6,4]=>3
[1,2,7,5,4,3,6]=>4
[1,2,7,5,4,6,3]=>5
[1,2,7,5,6,3,4]=>5
[1,2,7,5,6,4,3]=>7
[1,2,7,6,3,4,5]=>3
[1,2,7,6,3,5,4]=>5
[1,2,7,6,4,3,5]=>5
[1,2,7,6,4,5,3]=>7
[1,2,7,6,5,3,4]=>7
[1,2,7,6,5,4,3]=>10
[1,3,2,4,5,6,7]=>0
[1,3,2,4,5,7,6]=>0
[1,3,2,4,6,5,7]=>0
[1,3,2,4,6,7,5]=>0
[1,3,2,4,7,5,6]=>0
[1,3,2,4,7,6,5]=>1
[1,3,2,5,4,6,7]=>0
[1,3,2,5,4,7,6]=>0
[1,3,2,5,6,4,7]=>0
[1,3,2,5,6,7,4]=>0
[1,3,2,5,7,4,6]=>0
[1,3,2,5,7,6,4]=>1
[1,3,2,6,4,5,7]=>0
[1,3,2,6,4,7,5]=>0
[1,3,2,6,5,4,7]=>1
[1,3,2,6,5,7,4]=>1
[1,3,2,6,7,4,5]=>1
[1,3,2,6,7,5,4]=>2
[1,3,2,7,4,5,6]=>0
[1,3,2,7,4,6,5]=>1
[1,3,2,7,5,4,6]=>1
[1,3,2,7,5,6,4]=>2
[1,3,2,7,6,4,5]=>2
[1,3,2,7,6,5,4]=>4
[1,3,4,2,5,6,7]=>0
[1,3,4,2,5,7,6]=>0
[1,3,4,2,6,5,7]=>0
[1,3,4,2,6,7,5]=>0
[1,3,4,2,7,5,6]=>0
[1,3,4,2,7,6,5]=>1
[1,3,4,5,2,6,7]=>0
[1,3,4,5,2,7,6]=>0
[1,3,4,5,6,2,7]=>0
[1,3,4,5,6,7,2]=>0
[1,3,4,5,7,2,6]=>0
[1,3,4,5,7,6,2]=>1
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>0
[1,3,4,6,5,2,7]=>1
[1,3,4,6,5,7,2]=>1
[1,3,4,6,7,2,5]=>1
[1,3,4,6,7,5,2]=>2
[1,3,4,7,2,5,6]=>0
[1,3,4,7,2,6,5]=>1
[1,3,4,7,5,2,6]=>1
[1,3,4,7,5,6,2]=>2
[1,3,4,7,6,2,5]=>2
[1,3,4,7,6,5,2]=>4
[1,3,5,2,4,6,7]=>0
[1,3,5,2,4,7,6]=>0
[1,3,5,2,6,4,7]=>0
[1,3,5,2,6,7,4]=>0
[1,3,5,2,7,4,6]=>0
[1,3,5,2,7,6,4]=>1
[1,3,5,4,2,6,7]=>1
[1,3,5,4,2,7,6]=>1
[1,3,5,4,6,2,7]=>1
[1,3,5,4,6,7,2]=>1
[1,3,5,4,7,2,6]=>1
[1,3,5,4,7,6,2]=>2
[1,3,5,6,2,4,7]=>1
[1,3,5,6,2,7,4]=>1
[1,3,5,6,4,2,7]=>2
[1,3,5,6,4,7,2]=>2
[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]=>2
[1,3,5,7,4,2,6]=>2
[1,3,5,7,4,6,2]=>3
[1,3,5,7,6,2,4]=>4
[1,3,5,7,6,4,2]=>5
[1,3,6,2,4,5,7]=>0
[1,3,6,2,4,7,5]=>0
[1,3,6,2,5,4,7]=>1
[1,3,6,2,5,7,4]=>1
[1,3,6,2,7,4,5]=>1
[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]=>2
[1,3,6,4,5,7,2]=>2
[1,3,6,4,7,2,5]=>2
[1,3,6,4,7,5,2]=>3
[1,3,6,5,2,4,7]=>2
[1,3,6,5,2,7,4]=>2
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>4
[1,3,6,5,7,2,4]=>4
[1,3,6,5,7,4,2]=>5
[1,3,6,7,2,4,5]=>3
[1,3,6,7,2,5,4]=>4
[1,3,6,7,4,2,5]=>4
[1,3,6,7,4,5,2]=>5
[1,3,6,7,5,2,4]=>5
[1,3,6,7,5,4,2]=>7
[1,3,7,2,4,5,6]=>0
[1,3,7,2,4,6,5]=>1
[1,3,7,2,5,4,6]=>1
[1,3,7,2,5,6,4]=>2
[1,3,7,2,6,4,5]=>2
[1,3,7,2,6,5,4]=>4
[1,3,7,4,2,5,6]=>1
[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]=>3
[1,3,7,4,6,5,2]=>5
[1,3,7,5,2,4,6]=>2
[1,3,7,5,2,6,4]=>3
[1,3,7,5,4,2,6]=>4
[1,3,7,5,4,6,2]=>5
[1,3,7,5,6,2,4]=>5
[1,3,7,5,6,4,2]=>7
[1,3,7,6,2,4,5]=>3
[1,3,7,6,2,5,4]=>5
[1,3,7,6,4,2,5]=>5
[1,3,7,6,4,5,2]=>7
[1,3,7,6,5,2,4]=>7
[1,3,7,6,5,4,2]=>10
[1,4,2,3,5,6,7]=>0
[1,4,2,3,5,7,6]=>0
[1,4,2,3,6,5,7]=>0
[1,4,2,3,6,7,5]=>0
[1,4,2,3,7,5,6]=>0
[1,4,2,3,7,6,5]=>1
[1,4,2,5,3,6,7]=>0
[1,4,2,5,3,7,6]=>0
[1,4,2,5,6,3,7]=>0
[1,4,2,5,6,7,3]=>0
[1,4,2,5,7,3,6]=>0
[1,4,2,5,7,6,3]=>1
[1,4,2,6,3,5,7]=>0
[1,4,2,6,3,7,5]=>0
[1,4,2,6,5,3,7]=>1
[1,4,2,6,5,7,3]=>1
[1,4,2,6,7,3,5]=>1
[1,4,2,6,7,5,3]=>2
[1,4,2,7,3,5,6]=>0
[1,4,2,7,3,6,5]=>1
[1,4,2,7,5,3,6]=>1
[1,4,2,7,5,6,3]=>2
[1,4,2,7,6,3,5]=>2
[1,4,2,7,6,5,3]=>4
[1,4,3,2,5,6,7]=>1
[1,4,3,2,5,7,6]=>1
[1,4,3,2,6,5,7]=>1
[1,4,3,2,6,7,5]=>1
[1,4,3,2,7,5,6]=>1
[1,4,3,2,7,6,5]=>2
[1,4,3,5,2,6,7]=>1
[1,4,3,5,2,7,6]=>1
[1,4,3,5,6,2,7]=>1
[1,4,3,5,6,7,2]=>1
[1,4,3,5,7,2,6]=>1
[1,4,3,5,7,6,2]=>2
[1,4,3,6,2,5,7]=>1
[1,4,3,6,2,7,5]=>1
[1,4,3,6,5,2,7]=>2
[1,4,3,6,5,7,2]=>2
[1,4,3,6,7,2,5]=>2
[1,4,3,6,7,5,2]=>3
[1,4,3,7,2,5,6]=>1
[1,4,3,7,2,6,5]=>2
[1,4,3,7,5,2,6]=>2
[1,4,3,7,5,6,2]=>3
[1,4,3,7,6,2,5]=>3
[1,4,3,7,6,5,2]=>5
[1,4,5,2,3,6,7]=>1
[1,4,5,2,3,7,6]=>1
[1,4,5,2,6,3,7]=>1
[1,4,5,2,6,7,3]=>1
[1,4,5,2,7,3,6]=>1
[1,4,5,2,7,6,3]=>2
[1,4,5,3,2,6,7]=>2
[1,4,5,3,2,7,6]=>2
[1,4,5,3,6,2,7]=>2
[1,4,5,3,6,7,2]=>2
[1,4,5,3,7,2,6]=>2
[1,4,5,3,7,6,2]=>3
[1,4,5,6,2,3,7]=>3
[1,4,5,6,2,7,3]=>3
[1,4,5,6,3,2,7]=>3
[1,4,5,6,3,7,2]=>3
[1,4,5,6,7,2,3]=>6
[1,4,5,6,7,3,2]=>4
[1,4,5,7,2,3,6]=>3
[1,4,5,7,2,6,3]=>4
[1,4,5,7,3,2,6]=>3
[1,4,5,7,3,6,2]=>4
[1,4,5,7,6,2,3]=>7
[1,4,5,7,6,3,2]=>6
[1,4,6,2,3,5,7]=>1
[1,4,6,2,3,7,5]=>1
[1,4,6,2,5,3,7]=>2
[1,4,6,2,5,7,3]=>2
[1,4,6,2,7,3,5]=>2
[1,4,6,2,7,5,3]=>3
[1,4,6,3,2,5,7]=>2
[1,4,6,3,2,7,5]=>2
[1,4,6,3,5,2,7]=>3
[1,4,6,3,5,7,2]=>3
[1,4,6,3,7,2,5]=>3
[1,4,6,3,7,5,2]=>4
[1,4,6,5,2,3,7]=>4
[1,4,6,5,2,7,3]=>4
[1,4,6,5,3,2,7]=>5
                    

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Description

The number of patterns 321 or 3412 in a permutation.
A permutation is boolean if its principal order ideal in the (strong) Bruhat order is boolean.
It is shown in [1, Theorem 5.3] that a permutation is boolean if and only if it avoids the two patterns 321 and 3412.

References

[1] Tenner, B. E. Pattern avoidance and the Bruhat order MathSciNet:2333139 arXiv:math/0604322

Code

def statistic(sigma):
    return len(sigma.pattern_positions([3,2,1]) + sigma.pattern_positions([3,4,1,2]))

Created

Jun 06, 2019 at 10:07 by Christian Stump

Updated

Jun 06, 2019 at 10:07 by Christian Stump