- FindStat

Identifier

St000304: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

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

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Description

The load of a permutation.
The definition of the load of a finite word in a totally ordered alphabet can be found in [1], for permutations, it is given by the major index St000004The major index of a permutation. of the reverse Mp00064reverse of the inverse Mp00066inverse permutation.

References

[1] Lascoux, A., Schützenberger, M.-P. A new statistics on words MathSciNet:0593537

Code

def statistic(pi):
    return pi.inverse().reverse().major_index()

Created

Dec 01, 2015 at 21:19 by Christian Stump

Updated

Nov 07, 2017 at 10:25 by Martin Rubey