- FindStat

edit this statistic or download as text // json

Identifier

St001558: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>0
[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]=>3
[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]=>3
[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]=>4
[3,1,2,4]=>2
[3,1,4,2]=>3
[3,2,1,4]=>3
[3,2,4,1]=>4
[3,4,1,2]=>5
[3,4,2,1]=>5
[4,1,2,3]=>3
[4,1,3,2]=>4
[4,2,1,3]=>4
[4,2,3,1]=>6
[4,3,1,2]=>5
[4,3,2,1]=>6
[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]=>3
[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]=>4
[1,4,2,3,5]=>2
[1,4,2,5,3]=>3
[1,4,3,2,5]=>3
[1,4,3,5,2]=>4
[1,4,5,2,3]=>5
[1,4,5,3,2]=>5
[1,5,2,3,4]=>3
[1,5,2,4,3]=>4
[1,5,3,2,4]=>4
[1,5,3,4,2]=>6
[1,5,4,2,3]=>5
[1,5,4,3,2]=>6
[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]=>4
[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]=>5
[2,4,1,3,5]=>3
[2,4,1,5,3]=>4
[2,4,3,1,5]=>4
[2,4,3,5,1]=>5
[2,4,5,1,3]=>6
[2,4,5,3,1]=>6
[2,5,1,3,4]=>4
[2,5,1,4,3]=>5
[2,5,3,1,4]=>5
[2,5,3,4,1]=>7
[2,5,4,1,3]=>6
[2,5,4,3,1]=>7
[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]=>5
[3,2,1,4,5]=>3
[3,2,1,5,4]=>4
[3,2,4,1,5]=>4
[3,2,4,5,1]=>5
[3,2,5,1,4]=>5
[3,2,5,4,1]=>6
[3,4,1,2,5]=>5
[3,4,1,5,2]=>6
[3,4,2,1,5]=>5
[3,4,2,5,1]=>6
[3,4,5,1,2]=>7
[3,4,5,2,1]=>7
[3,5,1,2,4]=>6
[3,5,1,4,2]=>8
[3,5,2,1,4]=>6
[3,5,2,4,1]=>8
[3,5,4,1,2]=>8
[3,5,4,2,1]=>8
[4,1,2,3,5]=>3
[4,1,2,5,3]=>4
[4,1,3,2,5]=>4
[4,1,3,5,2]=>5
[4,1,5,2,3]=>6
[4,1,5,3,2]=>6
[4,2,1,3,5]=>4
[4,2,1,5,3]=>5
[4,2,3,1,5]=>6
[4,2,3,5,1]=>7
[4,2,5,1,3]=>8
[4,2,5,3,1]=>8
[4,3,1,2,5]=>5
[4,3,1,5,2]=>6
[4,3,2,1,5]=>6
[4,3,2,5,1]=>7
[4,3,5,1,2]=>8
[4,3,5,2,1]=>8
[4,5,1,2,3]=>7
[4,5,1,3,2]=>8
[4,5,2,1,3]=>8
[4,5,2,3,1]=>9
[4,5,3,1,2]=>9
[4,5,3,2,1]=>9
[5,1,2,3,4]=>4
[5,1,2,4,3]=>5
[5,1,3,2,4]=>5
[5,1,3,4,2]=>7
[5,1,4,2,3]=>6
[5,1,4,3,2]=>7
[5,2,1,3,4]=>5
[5,2,1,4,3]=>6
[5,2,3,1,4]=>7
[5,2,3,4,1]=>10
[5,2,4,1,3]=>8
[5,2,4,3,1]=>10
[5,3,1,2,4]=>6
[5,3,1,4,2]=>8
[5,3,2,1,4]=>7
[5,3,2,4,1]=>10
[5,3,4,1,2]=>9
[5,3,4,2,1]=>10
[5,4,1,2,3]=>7
[5,4,1,3,2]=>8
[5,4,2,1,3]=>8
[5,4,2,3,1]=>10
[5,4,3,1,2]=>9
[5,4,3,2,1]=>10
[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]=>3
[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]=>4
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>5
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>4
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>6
[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]=>4
[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]=>5
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>6
[1,3,5,6,4,2]=>6
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>5
[1,3,6,4,5,2]=>7
[1,3,6,5,2,4]=>6
[1,3,6,5,4,2]=>7
[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]=>5
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>6
[1,4,5,2,3,6]=>5
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>7
[1,4,5,6,3,2]=>7
[1,4,6,2,3,5]=>6
[1,4,6,2,5,3]=>8
[1,4,6,3,2,5]=>6
[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]=>3
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>5
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>6
[1,5,3,2,4,6]=>4
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>7
[1,5,3,6,2,4]=>8
[1,5,3,6,4,2]=>8
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>6
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>7
[1,5,4,6,2,3]=>8
[1,5,4,6,3,2]=>8
[1,5,6,2,3,4]=>7
[1,5,6,2,4,3]=>8
[1,5,6,3,2,4]=>8
[1,5,6,3,4,2]=>9
[1,5,6,4,2,3]=>9
[1,5,6,4,3,2]=>9
[1,6,2,3,4,5]=>4
[1,6,2,3,5,4]=>5
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>7
[1,6,2,5,3,4]=>6
[1,6,2,5,4,3]=>7
[1,6,3,2,4,5]=>5
[1,6,3,2,5,4]=>6
[1,6,3,4,2,5]=>7
[1,6,3,4,5,2]=>10
[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>10
[1,6,4,2,3,5]=>6
[1,6,4,2,5,3]=>8
[1,6,4,3,2,5]=>7
[1,6,4,3,5,2]=>10
[1,6,4,5,2,3]=>9
[1,6,4,5,3,2]=>10
[1,6,5,2,3,4]=>7
[1,6,5,2,4,3]=>8
[1,6,5,3,2,4]=>8
[1,6,5,3,4,2]=>10
[1,6,5,4,2,3]=>9
[1,6,5,4,3,2]=>10
[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]=>4
[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]=>5
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>5
[2,1,5,6,3,4]=>6
[2,1,5,6,4,3]=>6
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>5
[2,1,6,4,3,5]=>5
[2,1,6,4,5,3]=>7
[2,1,6,5,3,4]=>6
[2,1,6,5,4,3]=>7
[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]=>5
[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]=>6
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>5
[2,3,5,4,6,1]=>6
[2,3,5,6,1,4]=>7
[2,3,5,6,4,1]=>7
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>8
[2,3,6,5,1,4]=>7
[2,3,6,5,4,1]=>8
[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]=>6
[2,4,3,1,5,6]=>4
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>6
[2,4,3,6,1,5]=>6
[2,4,3,6,5,1]=>7
[2,4,5,1,3,6]=>6
[2,4,5,1,6,3]=>7
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>7
[2,4,5,6,1,3]=>8
[2,4,5,6,3,1]=>8
[2,4,6,1,3,5]=>7
[2,4,6,1,5,3]=>9
[2,4,6,3,1,5]=>7
[2,4,6,3,5,1]=>9
[2,4,6,5,1,3]=>9
[2,4,6,5,3,1]=>9
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>6
[2,5,1,6,3,4]=>7
[2,5,1,6,4,3]=>7
[2,5,3,1,4,6]=>5
[2,5,3,1,6,4]=>6
[2,5,3,4,1,6]=>7
[2,5,3,4,6,1]=>8
[2,5,3,6,1,4]=>9
[2,5,3,6,4,1]=>9
[2,5,4,1,3,6]=>6
[2,5,4,1,6,3]=>7
[2,5,4,3,1,6]=>7
[2,5,4,3,6,1]=>8
[2,5,4,6,1,3]=>9
[2,5,4,6,3,1]=>9
[2,5,6,1,3,4]=>8
[2,5,6,1,4,3]=>9
[2,5,6,3,1,4]=>9
[2,5,6,3,4,1]=>10
[2,5,6,4,1,3]=>10
[2,5,6,4,3,1]=>10
[2,6,1,3,4,5]=>5
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>6
[2,6,1,4,5,3]=>8
[2,6,1,5,3,4]=>7
[2,6,1,5,4,3]=>8
[2,6,3,1,4,5]=>6
[2,6,3,1,5,4]=>7
[2,6,3,4,1,5]=>8
[2,6,3,4,5,1]=>11
[2,6,3,5,1,4]=>9
[2,6,3,5,4,1]=>11
[2,6,4,1,3,5]=>7
[2,6,4,1,5,3]=>9
[2,6,4,3,1,5]=>8
[2,6,4,3,5,1]=>11
[2,6,4,5,1,3]=>10
[2,6,4,5,3,1]=>11
[2,6,5,1,3,4]=>8
[2,6,5,1,4,3]=>9
[2,6,5,3,1,4]=>9
[2,6,5,3,4,1]=>11
[2,6,5,4,1,3]=>10
[2,6,5,4,3,1]=>11
[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]=>5
[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]=>6
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>5
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>6
[3,1,5,6,2,4]=>7
[3,1,5,6,4,2]=>7
[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]=>8
[3,1,6,5,2,4]=>7
[3,1,6,5,4,2]=>8
[3,2,1,4,5,6]=>3
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>5
[3,2,1,6,4,5]=>5
[3,2,1,6,5,4]=>6
[3,2,4,1,5,6]=>4
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>5
[3,2,4,5,6,1]=>6
[3,2,4,6,1,5]=>6
[3,2,4,6,5,1]=>7
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>6
[3,2,5,4,1,6]=>6
[3,2,5,4,6,1]=>7
[3,2,5,6,1,4]=>8
[3,2,5,6,4,1]=>8
[3,2,6,1,4,5]=>6
[3,2,6,1,5,4]=>7
[3,2,6,4,1,5]=>7
[3,2,6,4,5,1]=>9
[3,2,6,5,1,4]=>8
[3,2,6,5,4,1]=>9
[3,4,1,2,5,6]=>5
[3,4,1,2,6,5]=>6
[3,4,1,5,2,6]=>6
[3,4,1,5,6,2]=>7
[3,4,1,6,2,5]=>7
[3,4,1,6,5,2]=>8
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>6
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>7
[3,4,2,6,1,5]=>7
[3,4,2,6,5,1]=>8
[3,4,5,1,2,6]=>7
[3,4,5,1,6,2]=>8
[3,4,5,2,1,6]=>7
[3,4,5,2,6,1]=>8
[3,4,5,6,1,2]=>9
[3,4,5,6,2,1]=>9
[3,4,6,1,2,5]=>8
[3,4,6,1,5,2]=>10
[3,4,6,2,1,5]=>8
[3,4,6,2,5,1]=>10
[3,4,6,5,1,2]=>10
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>6
[3,5,1,2,6,4]=>7
[3,5,1,4,2,6]=>8
[3,5,1,4,6,2]=>9
[3,5,1,6,2,4]=>10
[3,5,1,6,4,2]=>10
[3,5,2,1,4,6]=>6
[3,5,2,1,6,4]=>7
[3,5,2,4,1,6]=>8
[3,5,2,4,6,1]=>9
[3,5,2,6,1,4]=>10
[3,5,2,6,4,1]=>10
[3,5,4,1,2,6]=>8
[3,5,4,1,6,2]=>9
[3,5,4,2,1,6]=>8
[3,5,4,2,6,1]=>9
[3,5,4,6,1,2]=>10
[3,5,4,6,2,1]=>10
[3,5,6,1,2,4]=>10
[3,5,6,1,4,2]=>11
[3,5,6,2,1,4]=>10
[3,5,6,2,4,1]=>11
[3,5,6,4,1,2]=>11
[3,5,6,4,2,1]=>11
[3,6,1,2,4,5]=>7
[3,6,1,2,5,4]=>8
[3,6,1,4,2,5]=>9
[3,6,1,4,5,2]=>12
[3,6,1,5,2,4]=>10
[3,6,1,5,4,2]=>12
[3,6,2,1,4,5]=>7
[3,6,2,1,5,4]=>8
[3,6,2,4,1,5]=>9
[3,6,2,4,5,1]=>12
[3,6,2,5,1,4]=>10
[3,6,2,5,4,1]=>12
[3,6,4,1,2,5]=>9
[3,6,4,1,5,2]=>12
[3,6,4,2,1,5]=>9
[3,6,4,2,5,1]=>12
[3,6,4,5,1,2]=>12
[3,6,4,5,2,1]=>12
[3,6,5,1,2,4]=>10
[3,6,5,1,4,2]=>12
[3,6,5,2,1,4]=>10
[3,6,5,2,4,1]=>12
[3,6,5,4,1,2]=>12
[3,6,5,4,2,1]=>12
[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]=>6
[4,1,3,2,5,6]=>4
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>6
[4,1,3,6,2,5]=>6
[4,1,3,6,5,2]=>7
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>7
[4,1,5,3,2,6]=>6
[4,1,5,3,6,2]=>7
[4,1,5,6,2,3]=>8
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>7
[4,1,6,2,5,3]=>9
[4,1,6,3,2,5]=>7
[4,1,6,3,5,2]=>9
[4,1,6,5,2,3]=>9
[4,1,6,5,3,2]=>9
[4,2,1,3,5,6]=>4
[4,2,1,3,6,5]=>5
[4,2,1,5,3,6]=>5
[4,2,1,5,6,3]=>6
[4,2,1,6,3,5]=>6
[4,2,1,6,5,3]=>7
[4,2,3,1,5,6]=>6
[4,2,3,1,6,5]=>7
[4,2,3,5,1,6]=>7
[4,2,3,5,6,1]=>8
[4,2,3,6,1,5]=>8
[4,2,3,6,5,1]=>9
[4,2,5,1,3,6]=>8
[4,2,5,1,6,3]=>9
[4,2,5,3,1,6]=>8
[4,2,5,3,6,1]=>9
[4,2,5,6,1,3]=>10
[4,2,5,6,3,1]=>10
[4,2,6,1,3,5]=>9
[4,2,6,1,5,3]=>11
[4,2,6,3,1,5]=>9
[4,2,6,3,5,1]=>11
[4,2,6,5,1,3]=>11
[4,2,6,5,3,1]=>11
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>6
[4,3,1,5,2,6]=>6
[4,3,1,5,6,2]=>7
[4,3,1,6,2,5]=>7
[4,3,1,6,5,2]=>8
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>7
[4,3,2,5,1,6]=>7
[4,3,2,5,6,1]=>8
[4,3,2,6,1,5]=>8
[4,3,2,6,5,1]=>9
[4,3,5,1,2,6]=>8
[4,3,5,1,6,2]=>9
[4,3,5,2,1,6]=>8
[4,3,5,2,6,1]=>9
[4,3,5,6,1,2]=>10
[4,3,5,6,2,1]=>10
[4,3,6,1,2,5]=>9
[4,3,6,1,5,2]=>11
[4,3,6,2,1,5]=>9
[4,3,6,2,5,1]=>11
[4,3,6,5,1,2]=>11
[4,3,6,5,2,1]=>11
[4,5,1,2,3,6]=>7
[4,5,1,2,6,3]=>8
[4,5,1,3,2,6]=>8
[4,5,1,3,6,2]=>9
[4,5,1,6,2,3]=>10
[4,5,1,6,3,2]=>10
[4,5,2,1,3,6]=>8
[4,5,2,1,6,3]=>9
[4,5,2,3,1,6]=>9
[4,5,2,3,6,1]=>10
[4,5,2,6,1,3]=>11
[4,5,2,6,3,1]=>11
[4,5,3,1,2,6]=>9
[4,5,3,1,6,2]=>10
[4,5,3,2,1,6]=>9
[4,5,3,2,6,1]=>10
[4,5,3,6,1,2]=>11
[4,5,3,6,2,1]=>11
[4,5,6,1,2,3]=>12
[4,5,6,1,3,2]=>12
[4,5,6,2,1,3]=>12
[4,5,6,2,3,1]=>12
[4,5,6,3,1,2]=>12
[4,5,6,3,2,1]=>12
[4,6,1,2,3,5]=>8
[4,6,1,2,5,3]=>10
[4,6,1,3,2,5]=>9
[4,6,1,3,5,2]=>12
[4,6,1,5,2,3]=>11
[4,6,1,5,3,2]=>12
[4,6,2,1,3,5]=>9
[4,6,2,1,5,3]=>11
[4,6,2,3,1,5]=>10
[4,6,2,3,5,1]=>13
[4,6,2,5,1,3]=>12
[4,6,2,5,3,1]=>13
[4,6,3,1,2,5]=>10
[4,6,3,1,5,2]=>13
[4,6,3,2,1,5]=>10
[4,6,3,2,5,1]=>13
[4,6,3,5,1,2]=>13
[4,6,3,5,2,1]=>13
[4,6,5,1,2,3]=>12
[4,6,5,1,3,2]=>13
[4,6,5,2,1,3]=>12
[4,6,5,2,3,1]=>13
[4,6,5,3,1,2]=>13
[4,6,5,3,2,1]=>13
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>5
[5,1,2,4,3,6]=>5
[5,1,2,4,6,3]=>6
[5,1,2,6,3,4]=>7
[5,1,2,6,4,3]=>7
[5,1,3,2,4,6]=>5
[5,1,3,2,6,4]=>6
[5,1,3,4,2,6]=>7
[5,1,3,4,6,2]=>8
[5,1,3,6,2,4]=>9
[5,1,3,6,4,2]=>9
[5,1,4,2,3,6]=>6
[5,1,4,2,6,3]=>7
[5,1,4,3,2,6]=>7
[5,1,4,3,6,2]=>8
[5,1,4,6,2,3]=>9
[5,1,4,6,3,2]=>9
[5,1,6,2,3,4]=>8
[5,1,6,2,4,3]=>9
[5,1,6,3,2,4]=>9
[5,1,6,3,4,2]=>10
[5,1,6,4,2,3]=>10
[5,1,6,4,3,2]=>10
[5,2,1,3,4,6]=>5
[5,2,1,3,6,4]=>6
[5,2,1,4,3,6]=>6
[5,2,1,4,6,3]=>7
[5,2,1,6,3,4]=>8
[5,2,1,6,4,3]=>8
[5,2,3,1,4,6]=>7
[5,2,3,1,6,4]=>8
[5,2,3,4,1,6]=>10
[5,2,3,4,6,1]=>11
[5,2,3,6,1,4]=>12
[5,2,3,6,4,1]=>12
[5,2,4,1,3,6]=>8
[5,2,4,1,6,3]=>9
[5,2,4,3,1,6]=>10
[5,2,4,3,6,1]=>11
[5,2,4,6,1,3]=>12
[5,2,4,6,3,1]=>12
[5,2,6,1,3,4]=>10
[5,2,6,1,4,3]=>11
[5,2,6,3,1,4]=>12
[5,2,6,3,4,1]=>13
[5,2,6,4,1,3]=>13
[5,2,6,4,3,1]=>13
[5,3,1,2,4,6]=>6
[5,3,1,2,6,4]=>7
[5,3,1,4,2,6]=>8
[5,3,1,4,6,2]=>9
[5,3,1,6,2,4]=>10
[5,3,1,6,4,2]=>10
[5,3,2,1,4,6]=>7
[5,3,2,1,6,4]=>8
[5,3,2,4,1,6]=>10
[5,3,2,4,6,1]=>11
[5,3,2,6,1,4]=>12
[5,3,2,6,4,1]=>12
[5,3,4,1,2,6]=>9
[5,3,4,1,6,2]=>10
[5,3,4,2,1,6]=>10
[5,3,4,2,6,1]=>11
[5,3,4,6,1,2]=>12
[5,3,4,6,2,1]=>12
[5,3,6,1,2,4]=>11
[5,3,6,1,4,2]=>12
[5,3,6,2,1,4]=>12
[5,3,6,2,4,1]=>13
[5,3,6,4,1,2]=>13
[5,3,6,4,2,1]=>13
[5,4,1,2,3,6]=>7
[5,4,1,2,6,3]=>8
[5,4,1,3,2,6]=>8
[5,4,1,3,6,2]=>9
[5,4,1,6,2,3]=>10
[5,4,1,6,3,2]=>10
[5,4,2,1,3,6]=>8
[5,4,2,1,6,3]=>9
[5,4,2,3,1,6]=>10
[5,4,2,3,6,1]=>11
[5,4,2,6,1,3]=>12
[5,4,2,6,3,1]=>12
[5,4,3,1,2,6]=>9
[5,4,3,1,6,2]=>10
[5,4,3,2,1,6]=>10
[5,4,3,2,6,1]=>11
[5,4,3,6,1,2]=>12
[5,4,3,6,2,1]=>12
[5,4,6,1,2,3]=>12
[5,4,6,1,3,2]=>12
[5,4,6,2,1,3]=>13
[5,4,6,2,3,1]=>13
[5,4,6,3,1,2]=>13
[5,4,6,3,2,1]=>13
[5,6,1,2,3,4]=>9
[5,6,1,2,4,3]=>10
[5,6,1,3,2,4]=>10
[5,6,1,3,4,2]=>12
[5,6,1,4,2,3]=>11
[5,6,1,4,3,2]=>12
[5,6,2,1,3,4]=>10
[5,6,2,1,4,3]=>11
[5,6,2,3,1,4]=>12
[5,6,2,3,4,1]=>14
[5,6,2,4,1,3]=>13
[5,6,2,4,3,1]=>14
[5,6,3,1,2,4]=>11
[5,6,3,1,4,2]=>13
[5,6,3,2,1,4]=>12
[5,6,3,2,4,1]=>14
[5,6,3,4,1,2]=>14
[5,6,3,4,2,1]=>14
[5,6,4,1,2,3]=>12
[5,6,4,1,3,2]=>13
[5,6,4,2,1,3]=>13
[5,6,4,2,3,1]=>14
[5,6,4,3,1,2]=>14
[5,6,4,3,2,1]=>14
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>6
[6,1,2,4,3,5]=>6
[6,1,2,4,5,3]=>8
[6,1,2,5,3,4]=>7
[6,1,2,5,4,3]=>8
[6,1,3,2,4,5]=>6
[6,1,3,2,5,4]=>7
[6,1,3,4,2,5]=>8
[6,1,3,4,5,2]=>11
[6,1,3,5,2,4]=>9
[6,1,3,5,4,2]=>11
[6,1,4,2,3,5]=>7
[6,1,4,2,5,3]=>9
[6,1,4,3,2,5]=>8
[6,1,4,3,5,2]=>11
[6,1,4,5,2,3]=>10
[6,1,4,5,3,2]=>11
[6,1,5,2,3,4]=>8
[6,1,5,2,4,3]=>9
[6,1,5,3,2,4]=>9
[6,1,5,3,4,2]=>11
[6,1,5,4,2,3]=>10
[6,1,5,4,3,2]=>11
[6,2,1,3,4,5]=>6
[6,2,1,3,5,4]=>7
[6,2,1,4,3,5]=>7
[6,2,1,4,5,3]=>9
[6,2,1,5,3,4]=>8
[6,2,1,5,4,3]=>9
[6,2,3,1,4,5]=>8
[6,2,3,1,5,4]=>9
[6,2,3,4,1,5]=>11
[6,2,3,4,5,1]=>15
[6,2,3,5,1,4]=>12
[6,2,3,5,4,1]=>15
[6,2,4,1,3,5]=>9
[6,2,4,1,5,3]=>11
[6,2,4,3,1,5]=>11
[6,2,4,3,5,1]=>15
[6,2,4,5,1,3]=>13
[6,2,4,5,3,1]=>15
[6,2,5,1,3,4]=>10
[6,2,5,1,4,3]=>11
[6,2,5,3,1,4]=>12
[6,2,5,3,4,1]=>15
[6,2,5,4,1,3]=>13
[6,2,5,4,3,1]=>15
[6,3,1,2,4,5]=>7
[6,3,1,2,5,4]=>8
[6,3,1,4,2,5]=>9
[6,3,1,4,5,2]=>12
[6,3,1,5,2,4]=>10
[6,3,1,5,4,2]=>12
[6,3,2,1,4,5]=>8
[6,3,2,1,5,4]=>9
[6,3,2,4,1,5]=>11
[6,3,2,4,5,1]=>15
[6,3,2,5,1,4]=>12
[6,3,2,5,4,1]=>15
[6,3,4,1,2,5]=>10
[6,3,4,1,5,2]=>13
[6,3,4,2,1,5]=>11
[6,3,4,2,5,1]=>15
[6,3,4,5,1,2]=>14
[6,3,4,5,2,1]=>15
[6,3,5,1,2,4]=>11
[6,3,5,1,4,2]=>13
[6,3,5,2,1,4]=>12
[6,3,5,2,4,1]=>15
[6,3,5,4,1,2]=>14
[6,3,5,4,2,1]=>15
[6,4,1,2,3,5]=>8
[6,4,1,2,5,3]=>10
[6,4,1,3,2,5]=>9
[6,4,1,3,5,2]=>12
[6,4,1,5,2,3]=>11
[6,4,1,5,3,2]=>12
[6,4,2,1,3,5]=>9
[6,4,2,1,5,3]=>11
[6,4,2,3,1,5]=>11
[6,4,2,3,5,1]=>15
[6,4,2,5,1,3]=>13
[6,4,2,5,3,1]=>15
[6,4,3,1,2,5]=>10
[6,4,3,1,5,2]=>13
[6,4,3,2,1,5]=>11
[6,4,3,2,5,1]=>15
[6,4,3,5,1,2]=>14
[6,4,3,5,2,1]=>15
[6,4,5,1,2,3]=>12
[6,4,5,1,3,2]=>13
[6,4,5,2,1,3]=>13
[6,4,5,2,3,1]=>15
[6,4,5,3,1,2]=>14
[6,4,5,3,2,1]=>15
[6,5,1,2,3,4]=>9
[6,5,1,2,4,3]=>10
[6,5,1,3,2,4]=>10
[6,5,1,3,4,2]=>12
[6,5,1,4,2,3]=>11
[6,5,1,4,3,2]=>12
[6,5,2,1,3,4]=>10
[6,5,2,1,4,3]=>11
[6,5,2,3,1,4]=>12
[6,5,2,3,4,1]=>15
[6,5,2,4,1,3]=>13
[6,5,2,4,3,1]=>15
[6,5,3,1,2,4]=>11
[6,5,3,1,4,2]=>13
[6,5,3,2,1,4]=>12
[6,5,3,2,4,1]=>15
[6,5,3,4,1,2]=>14
[6,5,3,4,2,1]=>15
[6,5,4,1,2,3]=>12
[6,5,4,1,3,2]=>13
[6,5,4,2,1,3]=>13
[6,5,4,2,3,1]=>15
[6,5,4,3,1,2]=>14
[6,5,4,3,2,1]=>15
[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]=>3
[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]=>4
[1,2,3,6,4,5,7]=>2
[1,2,3,6,4,7,5]=>3
[1,2,3,6,5,4,7]=>3
[1,2,3,6,5,7,4]=>4
[1,2,3,6,7,4,5]=>5
[1,2,3,6,7,5,4]=>5
[1,2,3,7,4,5,6]=>3
[1,2,3,7,4,6,5]=>4
[1,2,3,7,5,4,6]=>4
[1,2,3,7,5,6,4]=>6
[1,2,3,7,6,4,5]=>5
[1,2,3,7,6,5,4]=>6
[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]=>4
[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]=>5
[1,2,4,6,3,5,7]=>3
[1,2,4,6,3,7,5]=>4
[1,2,4,6,5,3,7]=>4
[1,2,4,6,5,7,3]=>5
[1,2,4,6,7,3,5]=>6
[1,2,4,6,7,5,3]=>6
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>5
[1,2,4,7,5,3,6]=>5
[1,2,4,7,5,6,3]=>7
[1,2,4,7,6,3,5]=>6
[1,2,4,7,6,5,3]=>7
[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]=>5
[1,2,5,4,3,6,7]=>3
[1,2,5,4,3,7,6]=>4
[1,2,5,4,6,3,7]=>4
[1,2,5,4,6,7,3]=>5
[1,2,5,4,7,3,6]=>5
[1,2,5,4,7,6,3]=>6
[1,2,5,6,3,4,7]=>5
[1,2,5,6,3,7,4]=>6
[1,2,5,6,4,3,7]=>5
[1,2,5,6,4,7,3]=>6
[1,2,5,6,7,3,4]=>7
[1,2,5,6,7,4,3]=>7
[1,2,5,7,3,4,6]=>6
[1,2,5,7,3,6,4]=>8
[1,2,5,7,4,3,6]=>6
[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]=>3
[1,2,6,3,4,7,5]=>4
[1,2,6,3,5,4,7]=>4
[1,2,6,3,5,7,4]=>5
[1,2,6,3,7,4,5]=>6
[1,2,6,3,7,5,4]=>6
[1,2,6,4,3,5,7]=>4
[1,2,6,4,3,7,5]=>5
[1,2,6,4,5,3,7]=>6
[1,2,6,4,5,7,3]=>7
[1,2,6,4,7,3,5]=>8
[1,2,6,4,7,5,3]=>8
[1,2,6,5,3,4,7]=>5
[1,2,6,5,3,7,4]=>6
[1,2,6,5,4,3,7]=>6
[1,2,6,5,4,7,3]=>7
[1,2,6,5,7,3,4]=>8
[1,2,6,5,7,4,3]=>8
[1,2,6,7,3,4,5]=>7
[1,2,6,7,3,5,4]=>8
[1,2,6,7,4,3,5]=>8
[1,2,6,7,4,5,3]=>9
[1,2,6,7,5,3,4]=>9
[1,2,6,7,5,4,3]=>9
[1,2,7,3,4,5,6]=>4
[1,2,7,3,4,6,5]=>5
[1,2,7,3,5,4,6]=>5
[1,2,7,3,5,6,4]=>7
[1,2,7,3,6,4,5]=>6
[1,2,7,3,6,5,4]=>7
[1,2,7,4,3,5,6]=>5
[1,2,7,4,3,6,5]=>6
[1,2,7,4,5,3,6]=>7
[1,2,7,4,5,6,3]=>10
[1,2,7,4,6,3,5]=>8
[1,2,7,4,6,5,3]=>10
[1,2,7,5,3,4,6]=>6
[1,2,7,5,3,6,4]=>8
[1,2,7,5,4,3,6]=>7
[1,2,7,5,4,6,3]=>10
[1,2,7,5,6,3,4]=>9
[1,2,7,5,6,4,3]=>10
[1,2,7,6,3,4,5]=>7
[1,2,7,6,3,5,4]=>8
[1,2,7,6,4,3,5]=>8
[1,2,7,6,4,5,3]=>10
[1,2,7,6,5,3,4]=>9
[1,2,7,6,5,4,3]=>10
[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]=>4
[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]=>5
[1,3,2,6,4,5,7]=>3
[1,3,2,6,4,7,5]=>4
[1,3,2,6,5,4,7]=>4
[1,3,2,6,5,7,4]=>5
[1,3,2,6,7,4,5]=>6
[1,3,2,6,7,5,4]=>6
[1,3,2,7,4,5,6]=>4
[1,3,2,7,4,6,5]=>5
[1,3,2,7,5,4,6]=>5
[1,3,2,7,5,6,4]=>7
[1,3,2,7,6,4,5]=>6
[1,3,2,7,6,5,4]=>7
[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]=>5
[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]=>6
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>5
[1,3,4,6,5,2,7]=>5
[1,3,4,6,5,7,2]=>6
[1,3,4,6,7,2,5]=>7
[1,3,4,6,7,5,2]=>7
[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]=>8
[1,3,4,7,6,2,5]=>7
[1,3,4,7,6,5,2]=>8
[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]=>6
[1,3,5,4,2,6,7]=>4
[1,3,5,4,2,7,6]=>5
[1,3,5,4,6,2,7]=>5
[1,3,5,4,6,7,2]=>6
[1,3,5,4,7,2,6]=>6
[1,3,5,4,7,6,2]=>7
[1,3,5,6,2,4,7]=>6
[1,3,5,6,2,7,4]=>7
[1,3,5,6,4,2,7]=>6
[1,3,5,6,4,7,2]=>7
[1,3,5,6,7,2,4]=>8
[1,3,5,6,7,4,2]=>8
[1,3,5,7,2,4,6]=>7
[1,3,5,7,2,6,4]=>9
[1,3,5,7,4,2,6]=>7
[1,3,5,7,4,6,2]=>9
[1,3,5,7,6,2,4]=>9
[1,3,5,7,6,4,2]=>9
[1,3,6,2,4,5,7]=>4
[1,3,6,2,4,7,5]=>5
[1,3,6,2,5,4,7]=>5
[1,3,6,2,5,7,4]=>6
[1,3,6,2,7,4,5]=>7
[1,3,6,2,7,5,4]=>7
[1,3,6,4,2,5,7]=>5
[1,3,6,4,2,7,5]=>6
[1,3,6,4,5,2,7]=>7
[1,3,6,4,5,7,2]=>8
[1,3,6,4,7,2,5]=>9
[1,3,6,4,7,5,2]=>9
[1,3,6,5,2,4,7]=>6
[1,3,6,5,2,7,4]=>7
[1,3,6,5,4,2,7]=>7
[1,3,6,5,4,7,2]=>8
[1,3,6,5,7,2,4]=>9
[1,3,6,5,7,4,2]=>9
[1,3,6,7,2,4,5]=>8
[1,3,6,7,2,5,4]=>9
[1,3,6,7,4,2,5]=>9
[1,3,6,7,4,5,2]=>10
[1,3,6,7,5,2,4]=>10
[1,3,6,7,5,4,2]=>10
[1,3,7,2,4,5,6]=>5
[1,3,7,2,4,6,5]=>6
[1,3,7,2,5,4,6]=>6
[1,3,7,2,5,6,4]=>8
[1,3,7,2,6,4,5]=>7
[1,3,7,2,6,5,4]=>8
[1,3,7,4,2,5,6]=>6
[1,3,7,4,2,6,5]=>7
[1,3,7,4,5,2,6]=>8
[1,3,7,4,5,6,2]=>11
[1,3,7,4,6,2,5]=>9
[1,3,7,4,6,5,2]=>11
[1,3,7,5,2,4,6]=>7
[1,3,7,5,2,6,4]=>9
[1,3,7,5,4,2,6]=>8
[1,3,7,5,4,6,2]=>11
[1,3,7,5,6,2,4]=>10
[1,3,7,5,6,4,2]=>11
[1,3,7,6,2,4,5]=>8
[1,3,7,6,2,5,4]=>9
[1,3,7,6,4,2,5]=>9
[1,3,7,6,4,5,2]=>11
[1,3,7,6,5,2,4]=>10
[1,3,7,6,5,4,2]=>11
[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]=>5
[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]=>6
[1,4,2,6,3,5,7]=>4
[1,4,2,6,3,7,5]=>5
[1,4,2,6,5,3,7]=>5
[1,4,2,6,5,7,3]=>6
[1,4,2,6,7,3,5]=>7
[1,4,2,6,7,5,3]=>7
[1,4,2,7,3,5,6]=>5
[1,4,2,7,3,6,5]=>6
[1,4,2,7,5,3,6]=>6
[1,4,2,7,5,6,3]=>8
[1,4,2,7,6,3,5]=>7
[1,4,2,7,6,5,3]=>8
[1,4,3,2,5,6,7]=>3
[1,4,3,2,5,7,6]=>4
[1,4,3,2,6,5,7]=>4
[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]=>4
[1,4,3,5,2,7,6]=>5
[1,4,3,5,6,2,7]=>5
[1,4,3,5,6,7,2]=>6
[1,4,3,5,7,2,6]=>6
[1,4,3,5,7,6,2]=>7
[1,4,3,6,2,5,7]=>5
[1,4,3,6,2,7,5]=>6
[1,4,3,6,5,2,7]=>6
[1,4,3,6,5,7,2]=>7
[1,4,3,6,7,2,5]=>8
[1,4,3,6,7,5,2]=>8
[1,4,3,7,2,5,6]=>6
[1,4,3,7,2,6,5]=>7
[1,4,3,7,5,2,6]=>7
[1,4,3,7,5,6,2]=>9
[1,4,3,7,6,2,5]=>8
[1,4,3,7,6,5,2]=>9
[1,4,5,2,3,6,7]=>5
[1,4,5,2,3,7,6]=>6
[1,4,5,2,6,3,7]=>6
[1,4,5,2,6,7,3]=>7
[1,4,5,2,7,3,6]=>7
[1,4,5,2,7,6,3]=>8
[1,4,5,3,2,6,7]=>5
[1,4,5,3,2,7,6]=>6
[1,4,5,3,6,2,7]=>6
[1,4,5,3,6,7,2]=>7
[1,4,5,3,7,2,6]=>7
[1,4,5,3,7,6,2]=>8
[1,4,5,6,2,3,7]=>7
[1,4,5,6,2,7,3]=>8
[1,4,5,6,3,2,7]=>7
[1,4,5,6,3,7,2]=>8
[1,4,5,6,7,2,3]=>9
[1,4,5,6,7,3,2]=>9
[1,4,5,7,2,3,6]=>8
[1,4,5,7,2,6,3]=>10
[1,4,5,7,3,2,6]=>8
[1,4,5,7,3,6,2]=>10
[1,4,5,7,6,2,3]=>10
[1,4,5,7,6,3,2]=>10
[1,4,6,2,3,5,7]=>6
[1,4,6,2,3,7,5]=>7
[1,4,6,2,5,3,7]=>8
[1,4,6,2,5,7,3]=>9
[1,4,6,2,7,3,5]=>10
[1,4,6,2,7,5,3]=>10
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>7
[1,4,6,3,5,2,7]=>8
[1,4,6,3,5,7,2]=>9
[1,4,6,3,7,2,5]=>10
[1,4,6,3,7,5,2]=>10
[1,4,6,5,2,3,7]=>8
[1,4,6,5,2,7,3]=>9
[1,4,6,5,3,2,7]=>8
                    

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Description

The number of transpositions that are smaller or equal to a permutation in Bruhat order.
A statistic is known to be smooth if and only if this number coincides with the number of inversions. This is also equivalent for a permutation to avoid the two pattern $4231$ and $3412$.

Code

def statistic(pi):
    n = len(pi)
    B = Permutations(n).bruhat_poset(facade=True)
    return sum(Integer(1) for tau in B.principal_order_ideal(pi) if len(tau.fixed_points()) == n-2)

Created

Jul 07, 2020 at 09:53 by Christian Stump

Updated

Jul 07, 2020 at 09:53 by Christian Stump