edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>0 [2,1]=>2 [1,2,3]=>0 [1,3,2]=>3 [2,1,3]=>2 [2,3,1]=>3 [3,1,2]=>3 [3,2,1]=>5 [1,2,3,4]=>0 [1,2,4,3]=>4 [1,3,2,4]=>3 [1,3,4,2]=>4 [1,4,2,3]=>4 [1,4,3,2]=>7 [2,1,3,4]=>2 [2,1,4,3]=>6 [2,3,1,4]=>3 [2,3,4,1]=>4 [2,4,1,3]=>4 [2,4,3,1]=>7 [3,1,2,4]=>3 [3,1,4,2]=>7 [3,2,1,4]=>5 [3,2,4,1]=>7 [3,4,1,2]=>4 [3,4,2,1]=>6 [4,1,2,3]=>4 [4,1,3,2]=>7 [4,2,1,3]=>6 [4,2,3,1]=>7 [4,3,1,2]=>7 [4,3,2,1]=>9 [1,2,3,4,5]=>0 [1,2,3,5,4]=>5 [1,2,4,3,5]=>4 [1,2,4,5,3]=>5 [1,2,5,3,4]=>5 [1,2,5,4,3]=>9 [1,3,2,4,5]=>3 [1,3,2,5,4]=>8 [1,3,4,2,5]=>4 [1,3,4,5,2]=>5 [1,3,5,2,4]=>5 [1,3,5,4,2]=>9 [1,4,2,3,5]=>4 [1,4,2,5,3]=>9 [1,4,3,2,5]=>7 [1,4,3,5,2]=>9 [1,4,5,2,3]=>5 [1,4,5,3,2]=>8 [1,5,2,3,4]=>5 [1,5,2,4,3]=>9 [1,5,3,2,4]=>8 [1,5,3,4,2]=>9 [1,5,4,2,3]=>9 [1,5,4,3,2]=>12 [2,1,3,4,5]=>2 [2,1,3,5,4]=>7 [2,1,4,3,5]=>6 [2,1,4,5,3]=>7 [2,1,5,3,4]=>7 [2,1,5,4,3]=>11 [2,3,1,4,5]=>3 [2,3,1,5,4]=>8 [2,3,4,1,5]=>4 [2,3,4,5,1]=>5 [2,3,5,1,4]=>5 [2,3,5,4,1]=>9 [2,4,1,3,5]=>4 [2,4,1,5,3]=>9 [2,4,3,1,5]=>7 [2,4,3,5,1]=>9 [2,4,5,1,3]=>5 [2,4,5,3,1]=>8 [2,5,1,3,4]=>5 [2,5,1,4,3]=>9 [2,5,3,1,4]=>8 [2,5,3,4,1]=>9 [2,5,4,1,3]=>9 [2,5,4,3,1]=>12 [3,1,2,4,5]=>3 [3,1,2,5,4]=>8 [3,1,4,2,5]=>7 [3,1,4,5,2]=>8 [3,1,5,2,4]=>8 [3,1,5,4,2]=>12 [3,2,1,4,5]=>5 [3,2,1,5,4]=>10 [3,2,4,1,5]=>7 [3,2,4,5,1]=>8 [3,2,5,1,4]=>8 [3,2,5,4,1]=>12 [3,4,1,2,5]=>4 [3,4,1,5,2]=>9 [3,4,2,1,5]=>6 [3,4,2,5,1]=>9 [3,4,5,1,2]=>5 [3,4,5,2,1]=>7 [3,5,1,2,4]=>5 [3,5,1,4,2]=>9 [3,5,2,1,4]=>7 [3,5,2,4,1]=>9 [3,5,4,1,2]=>9 [3,5,4,2,1]=>11 [4,1,2,3,5]=>4 [4,1,2,5,3]=>9 [4,1,3,2,5]=>7 [4,1,3,5,2]=>9 [4,1,5,2,3]=>9 [4,1,5,3,2]=>12 [4,2,1,3,5]=>6 [4,2,1,5,3]=>11 [4,2,3,1,5]=>7 [4,2,3,5,1]=>9 [4,2,5,1,3]=>9 [4,2,5,3,1]=>12 [4,3,1,2,5]=>7 [4,3,1,5,2]=>12 [4,3,2,1,5]=>9 [4,3,2,5,1]=>12 [4,3,5,1,2]=>9 [4,3,5,2,1]=>11 [4,5,1,2,3]=>5 [4,5,1,3,2]=>8 [4,5,2,1,3]=>7 [4,5,2,3,1]=>8 [4,5,3,1,2]=>8 [4,5,3,2,1]=>10 [5,1,2,3,4]=>5 [5,1,2,4,3]=>9 [5,1,3,2,4]=>8 [5,1,3,4,2]=>9 [5,1,4,2,3]=>9 [5,1,4,3,2]=>12 [5,2,1,3,4]=>7 [5,2,1,4,3]=>11 [5,2,3,1,4]=>8 [5,2,3,4,1]=>9 [5,2,4,1,3]=>9 [5,2,4,3,1]=>12 [5,3,1,2,4]=>8 [5,3,1,4,2]=>12 [5,3,2,1,4]=>10 [5,3,2,4,1]=>12 [5,3,4,1,2]=>9 [5,3,4,2,1]=>11 [5,4,1,2,3]=>9 [5,4,1,3,2]=>12 [5,4,2,1,3]=>11 [5,4,2,3,1]=>12 [5,4,3,1,2]=>12 [5,4,3,2,1]=>14 [1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>6 [1,2,3,5,4,6]=>5 [1,2,3,5,6,4]=>6 [1,2,3,6,4,5]=>6 [1,2,3,6,5,4]=>11 [1,2,4,3,5,6]=>4 [1,2,4,3,6,5]=>10 [1,2,4,5,3,6]=>5 [1,2,4,5,6,3]=>6 [1,2,4,6,3,5]=>6 [1,2,4,6,5,3]=>11 [1,2,5,3,4,6]=>5 [1,2,5,3,6,4]=>11 [1,2,5,4,3,6]=>9 [1,2,5,4,6,3]=>11 [1,2,5,6,3,4]=>6 [1,2,5,6,4,3]=>10 [1,2,6,3,4,5]=>6 [1,2,6,3,5,4]=>11 [1,2,6,4,3,5]=>10 [1,2,6,4,5,3]=>11 [1,2,6,5,3,4]=>11 [1,2,6,5,4,3]=>15 [1,3,2,4,5,6]=>3 [1,3,2,4,6,5]=>9 [1,3,2,5,4,6]=>8 [1,3,2,5,6,4]=>9 [1,3,2,6,4,5]=>9 [1,3,2,6,5,4]=>14 [1,3,4,2,5,6]=>4 [1,3,4,2,6,5]=>10 [1,3,4,5,2,6]=>5 [1,3,4,5,6,2]=>6 [1,3,4,6,2,5]=>6 [1,3,4,6,5,2]=>11 [1,3,5,2,4,6]=>5 [1,3,5,2,6,4]=>11 [1,3,5,4,2,6]=>9 [1,3,5,4,6,2]=>11 [1,3,5,6,2,4]=>6 [1,3,5,6,4,2]=>10 [1,3,6,2,4,5]=>6 [1,3,6,2,5,4]=>11 [1,3,6,4,2,5]=>10 [1,3,6,4,5,2]=>11 [1,3,6,5,2,4]=>11 [1,3,6,5,4,2]=>15 [1,4,2,3,5,6]=>4 [1,4,2,3,6,5]=>10 [1,4,2,5,3,6]=>9 [1,4,2,5,6,3]=>10 [1,4,2,6,3,5]=>10 [1,4,2,6,5,3]=>15 [1,4,3,2,5,6]=>7 [1,4,3,2,6,5]=>13 [1,4,3,5,2,6]=>9 [1,4,3,5,6,2]=>10 [1,4,3,6,2,5]=>10 [1,4,3,6,5,2]=>15 [1,4,5,2,3,6]=>5 [1,4,5,2,6,3]=>11 [1,4,5,3,2,6]=>8 [1,4,5,3,6,2]=>11 [1,4,5,6,2,3]=>6 [1,4,5,6,3,2]=>9 [1,4,6,2,3,5]=>6 [1,4,6,2,5,3]=>11 [1,4,6,3,2,5]=>9 [1,4,6,3,5,2]=>11 [1,4,6,5,2,3]=>11 [1,4,6,5,3,2]=>14 [1,5,2,3,4,6]=>5 [1,5,2,3,6,4]=>11 [1,5,2,4,3,6]=>9 [1,5,2,4,6,3]=>11 [1,5,2,6,3,4]=>11 [1,5,2,6,4,3]=>15 [1,5,3,2,4,6]=>8 [1,5,3,2,6,4]=>14 [1,5,3,4,2,6]=>9 [1,5,3,4,6,2]=>11 [1,5,3,6,2,4]=>11 [1,5,3,6,4,2]=>15 [1,5,4,2,3,6]=>9 [1,5,4,2,6,3]=>15 [1,5,4,3,2,6]=>12 [1,5,4,3,6,2]=>15 [1,5,4,6,2,3]=>11 [1,5,4,6,3,2]=>14 [1,5,6,2,3,4]=>6 [1,5,6,2,4,3]=>10 [1,5,6,3,2,4]=>9 [1,5,6,3,4,2]=>10 [1,5,6,4,2,3]=>10 [1,5,6,4,3,2]=>13 [1,6,2,3,4,5]=>6 [1,6,2,3,5,4]=>11 [1,6,2,4,3,5]=>10 [1,6,2,4,5,3]=>11 [1,6,2,5,3,4]=>11 [1,6,2,5,4,3]=>15 [1,6,3,2,4,5]=>9 [1,6,3,2,5,4]=>14 [1,6,3,4,2,5]=>10 [1,6,3,4,5,2]=>11 [1,6,3,5,2,4]=>11 [1,6,3,5,4,2]=>15 [1,6,4,2,3,5]=>10 [1,6,4,2,5,3]=>15 [1,6,4,3,2,5]=>13 [1,6,4,3,5,2]=>15 [1,6,4,5,2,3]=>11 [1,6,4,5,3,2]=>14 [1,6,5,2,3,4]=>11 [1,6,5,2,4,3]=>15 [1,6,5,3,2,4]=>14 [1,6,5,3,4,2]=>15 [1,6,5,4,2,3]=>15 [1,6,5,4,3,2]=>18 [2,1,3,4,5,6]=>2 [2,1,3,4,6,5]=>8 [2,1,3,5,4,6]=>7 [2,1,3,5,6,4]=>8 [2,1,3,6,4,5]=>8 [2,1,3,6,5,4]=>13 [2,1,4,3,5,6]=>6 [2,1,4,3,6,5]=>12 [2,1,4,5,3,6]=>7 [2,1,4,5,6,3]=>8 [2,1,4,6,3,5]=>8 [2,1,4,6,5,3]=>13 [2,1,5,3,4,6]=>7 [2,1,5,3,6,4]=>13 [2,1,5,4,3,6]=>11 [2,1,5,4,6,3]=>13 [2,1,5,6,3,4]=>8 [2,1,5,6,4,3]=>12 [2,1,6,3,4,5]=>8 [2,1,6,3,5,4]=>13 [2,1,6,4,3,5]=>12 [2,1,6,4,5,3]=>13 [2,1,6,5,3,4]=>13 [2,1,6,5,4,3]=>17 [2,3,1,4,5,6]=>3 [2,3,1,4,6,5]=>9 [2,3,1,5,4,6]=>8 [2,3,1,5,6,4]=>9 [2,3,1,6,4,5]=>9 [2,3,1,6,5,4]=>14 [2,3,4,1,5,6]=>4 [2,3,4,1,6,5]=>10 [2,3,4,5,1,6]=>5 [2,3,4,5,6,1]=>6 [2,3,4,6,1,5]=>6 [2,3,4,6,5,1]=>11 [2,3,5,1,4,6]=>5 [2,3,5,1,6,4]=>11 [2,3,5,4,1,6]=>9 [2,3,5,4,6,1]=>11 [2,3,5,6,1,4]=>6 [2,3,5,6,4,1]=>10 [2,3,6,1,4,5]=>6 [2,3,6,1,5,4]=>11 [2,3,6,4,1,5]=>10 [2,3,6,4,5,1]=>11 [2,3,6,5,1,4]=>11 [2,3,6,5,4,1]=>15 [2,4,1,3,5,6]=>4 [2,4,1,3,6,5]=>10 [2,4,1,5,3,6]=>9 [2,4,1,5,6,3]=>10 [2,4,1,6,3,5]=>10 [2,4,1,6,5,3]=>15 [2,4,3,1,5,6]=>7 [2,4,3,1,6,5]=>13 [2,4,3,5,1,6]=>9 [2,4,3,5,6,1]=>10 [2,4,3,6,1,5]=>10 [2,4,3,6,5,1]=>15 [2,4,5,1,3,6]=>5 [2,4,5,1,6,3]=>11 [2,4,5,3,1,6]=>8 [2,4,5,3,6,1]=>11 [2,4,5,6,1,3]=>6 [2,4,5,6,3,1]=>9 [2,4,6,1,3,5]=>6 [2,4,6,1,5,3]=>11 [2,4,6,3,1,5]=>9 [2,4,6,3,5,1]=>11 [2,4,6,5,1,3]=>11 [2,4,6,5,3,1]=>14 [2,5,1,3,4,6]=>5 [2,5,1,3,6,4]=>11 [2,5,1,4,3,6]=>9 [2,5,1,4,6,3]=>11 [2,5,1,6,3,4]=>11 [2,5,1,6,4,3]=>15 [2,5,3,1,4,6]=>8 [2,5,3,1,6,4]=>14 [2,5,3,4,1,6]=>9 [2,5,3,4,6,1]=>11 [2,5,3,6,1,4]=>11 [2,5,3,6,4,1]=>15 [2,5,4,1,3,6]=>9 [2,5,4,1,6,3]=>15 [2,5,4,3,1,6]=>12 [2,5,4,3,6,1]=>15 [2,5,4,6,1,3]=>11 [2,5,4,6,3,1]=>14 [2,5,6,1,3,4]=>6 [2,5,6,1,4,3]=>10 [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]=>13 [2,6,1,3,4,5]=>6 [2,6,1,3,5,4]=>11 [2,6,1,4,3,5]=>10 [2,6,1,4,5,3]=>11 [2,6,1,5,3,4]=>11 [2,6,1,5,4,3]=>15 [2,6,3,1,4,5]=>9 [2,6,3,1,5,4]=>14 [2,6,3,4,1,5]=>10 [2,6,3,4,5,1]=>11 [2,6,3,5,1,4]=>11 [2,6,3,5,4,1]=>15 [2,6,4,1,3,5]=>10 [2,6,4,1,5,3]=>15 [2,6,4,3,1,5]=>13 [2,6,4,3,5,1]=>15 [2,6,4,5,1,3]=>11 [2,6,4,5,3,1]=>14 [2,6,5,1,3,4]=>11 [2,6,5,1,4,3]=>15 [2,6,5,3,1,4]=>14 [2,6,5,3,4,1]=>15 [2,6,5,4,1,3]=>15 [2,6,5,4,3,1]=>18 [3,1,2,4,5,6]=>3 [3,1,2,4,6,5]=>9 [3,1,2,5,4,6]=>8 [3,1,2,5,6,4]=>9 [3,1,2,6,4,5]=>9 [3,1,2,6,5,4]=>14 [3,1,4,2,5,6]=>7 [3,1,4,2,6,5]=>13 [3,1,4,5,2,6]=>8 [3,1,4,5,6,2]=>9 [3,1,4,6,2,5]=>9 [3,1,4,6,5,2]=>14 [3,1,5,2,4,6]=>8 [3,1,5,2,6,4]=>14 [3,1,5,4,2,6]=>12 [3,1,5,4,6,2]=>14 [3,1,5,6,2,4]=>9 [3,1,5,6,4,2]=>13 [3,1,6,2,4,5]=>9 [3,1,6,2,5,4]=>14 [3,1,6,4,2,5]=>13 [3,1,6,4,5,2]=>14 [3,1,6,5,2,4]=>14 [3,1,6,5,4,2]=>18 [3,2,1,4,5,6]=>5 [3,2,1,4,6,5]=>11 [3,2,1,5,4,6]=>10 [3,2,1,5,6,4]=>11 [3,2,1,6,4,5]=>11 [3,2,1,6,5,4]=>16 [3,2,4,1,5,6]=>7 [3,2,4,1,6,5]=>13 [3,2,4,5,1,6]=>8 [3,2,4,5,6,1]=>9 [3,2,4,6,1,5]=>9 [3,2,4,6,5,1]=>14 [3,2,5,1,4,6]=>8 [3,2,5,1,6,4]=>14 [3,2,5,4,1,6]=>12 [3,2,5,4,6,1]=>14 [3,2,5,6,1,4]=>9 [3,2,5,6,4,1]=>13 [3,2,6,1,4,5]=>9 [3,2,6,1,5,4]=>14 [3,2,6,4,1,5]=>13 [3,2,6,4,5,1]=>14 [3,2,6,5,1,4]=>14 [3,2,6,5,4,1]=>18 [3,4,1,2,5,6]=>4 [3,4,1,2,6,5]=>10 [3,4,1,5,2,6]=>9 [3,4,1,5,6,2]=>10 [3,4,1,6,2,5]=>10 [3,4,1,6,5,2]=>15 [3,4,2,1,5,6]=>6 [3,4,2,1,6,5]=>12 [3,4,2,5,1,6]=>9 [3,4,2,5,6,1]=>10 [3,4,2,6,1,5]=>10 [3,4,2,6,5,1]=>15 [3,4,5,1,2,6]=>5 [3,4,5,1,6,2]=>11 [3,4,5,2,1,6]=>7 [3,4,5,2,6,1]=>11 [3,4,5,6,1,2]=>6 [3,4,5,6,2,1]=>8 [3,4,6,1,2,5]=>6 [3,4,6,1,5,2]=>11 [3,4,6,2,1,5]=>8 [3,4,6,2,5,1]=>11 [3,4,6,5,1,2]=>11 [3,4,6,5,2,1]=>13 [3,5,1,2,4,6]=>5 [3,5,1,2,6,4]=>11 [3,5,1,4,2,6]=>9 [3,5,1,4,6,2]=>11 [3,5,1,6,2,4]=>11 [3,5,1,6,4,2]=>15 [3,5,2,1,4,6]=>7 [3,5,2,1,6,4]=>13 [3,5,2,4,1,6]=>9 [3,5,2,4,6,1]=>11 [3,5,2,6,1,4]=>11 [3,5,2,6,4,1]=>15 [3,5,4,1,2,6]=>9 [3,5,4,1,6,2]=>15 [3,5,4,2,1,6]=>11 [3,5,4,2,6,1]=>15 [3,5,4,6,1,2]=>11 [3,5,4,6,2,1]=>13 [3,5,6,1,2,4]=>6 [3,5,6,1,4,2]=>10 [3,5,6,2,1,4]=>8 [3,5,6,2,4,1]=>10 [3,5,6,4,1,2]=>10 [3,5,6,4,2,1]=>12 [3,6,1,2,4,5]=>6 [3,6,1,2,5,4]=>11 [3,6,1,4,2,5]=>10 [3,6,1,4,5,2]=>11 [3,6,1,5,2,4]=>11 [3,6,1,5,4,2]=>15 [3,6,2,1,4,5]=>8 [3,6,2,1,5,4]=>13 [3,6,2,4,1,5]=>10 [3,6,2,4,5,1]=>11 [3,6,2,5,1,4]=>11 [3,6,2,5,4,1]=>15 [3,6,4,1,2,5]=>10 [3,6,4,1,5,2]=>15 [3,6,4,2,1,5]=>12 [3,6,4,2,5,1]=>15 [3,6,4,5,1,2]=>11 [3,6,4,5,2,1]=>13 [3,6,5,1,2,4]=>11 [3,6,5,1,4,2]=>15 [3,6,5,2,1,4]=>13 [3,6,5,2,4,1]=>15 [3,6,5,4,1,2]=>15 [3,6,5,4,2,1]=>17 [4,1,2,3,5,6]=>4 [4,1,2,3,6,5]=>10 [4,1,2,5,3,6]=>9 [4,1,2,5,6,3]=>10 [4,1,2,6,3,5]=>10 [4,1,2,6,5,3]=>15 [4,1,3,2,5,6]=>7 [4,1,3,2,6,5]=>13 [4,1,3,5,2,6]=>9 [4,1,3,5,6,2]=>10 [4,1,3,6,2,5]=>10 [4,1,3,6,5,2]=>15 [4,1,5,2,3,6]=>9 [4,1,5,2,6,3]=>15 [4,1,5,3,2,6]=>12 [4,1,5,3,6,2]=>15 [4,1,5,6,2,3]=>10 [4,1,5,6,3,2]=>13 [4,1,6,2,3,5]=>10 [4,1,6,2,5,3]=>15 [4,1,6,3,2,5]=>13 [4,1,6,3,5,2]=>15 [4,1,6,5,2,3]=>15 [4,1,6,5,3,2]=>18 [4,2,1,3,5,6]=>6 [4,2,1,3,6,5]=>12 [4,2,1,5,3,6]=>11 [4,2,1,5,6,3]=>12 [4,2,1,6,3,5]=>12 [4,2,1,6,5,3]=>17 [4,2,3,1,5,6]=>7 [4,2,3,1,6,5]=>13 [4,2,3,5,1,6]=>9 [4,2,3,5,6,1]=>10 [4,2,3,6,1,5]=>10 [4,2,3,6,5,1]=>15 [4,2,5,1,3,6]=>9 [4,2,5,1,6,3]=>15 [4,2,5,3,1,6]=>12 [4,2,5,3,6,1]=>15 [4,2,5,6,1,3]=>10 [4,2,5,6,3,1]=>13 [4,2,6,1,3,5]=>10 [4,2,6,1,5,3]=>15 [4,2,6,3,1,5]=>13 [4,2,6,3,5,1]=>15 [4,2,6,5,1,3]=>15 [4,2,6,5,3,1]=>18 [4,3,1,2,5,6]=>7 [4,3,1,2,6,5]=>13 [4,3,1,5,2,6]=>12 [4,3,1,5,6,2]=>13 [4,3,1,6,2,5]=>13 [4,3,1,6,5,2]=>18 [4,3,2,1,5,6]=>9 [4,3,2,1,6,5]=>15 [4,3,2,5,1,6]=>12 [4,3,2,5,6,1]=>13 [4,3,2,6,1,5]=>13 [4,3,2,6,5,1]=>18 [4,3,5,1,2,6]=>9 [4,3,5,1,6,2]=>15 [4,3,5,2,1,6]=>11 [4,3,5,2,6,1]=>15 [4,3,5,6,1,2]=>10 [4,3,5,6,2,1]=>12 [4,3,6,1,2,5]=>10 [4,3,6,1,5,2]=>15 [4,3,6,2,1,5]=>12 [4,3,6,2,5,1]=>15 [4,3,6,5,1,2]=>15 [4,3,6,5,2,1]=>17 [4,5,1,2,3,6]=>5 [4,5,1,2,6,3]=>11 [4,5,1,3,2,6]=>8 [4,5,1,3,6,2]=>11 [4,5,1,6,2,3]=>11 [4,5,1,6,3,2]=>14 [4,5,2,1,3,6]=>7 [4,5,2,1,6,3]=>13 [4,5,2,3,1,6]=>8 [4,5,2,3,6,1]=>11 [4,5,2,6,1,3]=>11 [4,5,2,6,3,1]=>14 [4,5,3,1,2,6]=>8 [4,5,3,1,6,2]=>14 [4,5,3,2,1,6]=>10 [4,5,3,2,6,1]=>14 [4,5,3,6,1,2]=>11 [4,5,3,6,2,1]=>13 [4,5,6,1,2,3]=>6 [4,5,6,1,3,2]=>9 [4,5,6,2,1,3]=>8 [4,5,6,2,3,1]=>9 [4,5,6,3,1,2]=>9 [4,5,6,3,2,1]=>11 [4,6,1,2,3,5]=>6 [4,6,1,2,5,3]=>11 [4,6,1,3,2,5]=>9 [4,6,1,3,5,2]=>11 [4,6,1,5,2,3]=>11 [4,6,1,5,3,2]=>14 [4,6,2,1,3,5]=>8 [4,6,2,1,5,3]=>13 [4,6,2,3,1,5]=>9 [4,6,2,3,5,1]=>11 [4,6,2,5,1,3]=>11 [4,6,2,5,3,1]=>14 [4,6,3,1,2,5]=>9 [4,6,3,1,5,2]=>14 [4,6,3,2,1,5]=>11 [4,6,3,2,5,1]=>14 [4,6,3,5,1,2]=>11 [4,6,3,5,2,1]=>13 [4,6,5,1,2,3]=>11 [4,6,5,1,3,2]=>14 [4,6,5,2,1,3]=>13 [4,6,5,2,3,1]=>14 [4,6,5,3,1,2]=>14 [4,6,5,3,2,1]=>16 [5,1,2,3,4,6]=>5 [5,1,2,3,6,4]=>11 [5,1,2,4,3,6]=>9 [5,1,2,4,6,3]=>11 [5,1,2,6,3,4]=>11 [5,1,2,6,4,3]=>15 [5,1,3,2,4,6]=>8 [5,1,3,2,6,4]=>14 [5,1,3,4,2,6]=>9 [5,1,3,4,6,2]=>11 [5,1,3,6,2,4]=>11 [5,1,3,6,4,2]=>15 [5,1,4,2,3,6]=>9 [5,1,4,2,6,3]=>15 [5,1,4,3,2,6]=>12 [5,1,4,3,6,2]=>15 [5,1,4,6,2,3]=>11 [5,1,4,6,3,2]=>14 [5,1,6,2,3,4]=>11 [5,1,6,2,4,3]=>15 [5,1,6,3,2,4]=>14 [5,1,6,3,4,2]=>15 [5,1,6,4,2,3]=>15 [5,1,6,4,3,2]=>18 [5,2,1,3,4,6]=>7 [5,2,1,3,6,4]=>13 [5,2,1,4,3,6]=>11 [5,2,1,4,6,3]=>13 [5,2,1,6,3,4]=>13 [5,2,1,6,4,3]=>17 [5,2,3,1,4,6]=>8 [5,2,3,1,6,4]=>14 [5,2,3,4,1,6]=>9 [5,2,3,4,6,1]=>11 [5,2,3,6,1,4]=>11 [5,2,3,6,4,1]=>15 [5,2,4,1,3,6]=>9 [5,2,4,1,6,3]=>15 [5,2,4,3,1,6]=>12 [5,2,4,3,6,1]=>15 [5,2,4,6,1,3]=>11 [5,2,4,6,3,1]=>14 [5,2,6,1,3,4]=>11 [5,2,6,1,4,3]=>15 [5,2,6,3,1,4]=>14 [5,2,6,3,4,1]=>15 [5,2,6,4,1,3]=>15 [5,2,6,4,3,1]=>18 [5,3,1,2,4,6]=>8 [5,3,1,2,6,4]=>14 [5,3,1,4,2,6]=>12 [5,3,1,4,6,2]=>14 [5,3,1,6,2,4]=>14 [5,3,1,6,4,2]=>18 [5,3,2,1,4,6]=>10 [5,3,2,1,6,4]=>16 [5,3,2,4,1,6]=>12 [5,3,2,4,6,1]=>14 [5,3,2,6,1,4]=>14 [5,3,2,6,4,1]=>18 [5,3,4,1,2,6]=>9 [5,3,4,1,6,2]=>15 [5,3,4,2,1,6]=>11 [5,3,4,2,6,1]=>15 [5,3,4,6,1,2]=>11 [5,3,4,6,2,1]=>13 [5,3,6,1,2,4]=>11 [5,3,6,1,4,2]=>15 [5,3,6,2,1,4]=>13 [5,3,6,2,4,1]=>15 [5,3,6,4,1,2]=>15 [5,3,6,4,2,1]=>17 [5,4,1,2,3,6]=>9 [5,4,1,2,6,3]=>15 [5,4,1,3,2,6]=>12 [5,4,1,3,6,2]=>15 [5,4,1,6,2,3]=>15 [5,4,1,6,3,2]=>18 [5,4,2,1,3,6]=>11 [5,4,2,1,6,3]=>17 [5,4,2,3,1,6]=>12 [5,4,2,3,6,1]=>15 [5,4,2,6,1,3]=>15 [5,4,2,6,3,1]=>18 [5,4,3,1,2,6]=>12 [5,4,3,1,6,2]=>18 [5,4,3,2,1,6]=>14 [5,4,3,2,6,1]=>18 [5,4,3,6,1,2]=>15 [5,4,3,6,2,1]=>17 [5,4,6,1,2,3]=>11 [5,4,6,1,3,2]=>14 [5,4,6,2,1,3]=>13 [5,4,6,2,3,1]=>14 [5,4,6,3,1,2]=>14 [5,4,6,3,2,1]=>16 [5,6,1,2,3,4]=>6 [5,6,1,2,4,3]=>10 [5,6,1,3,2,4]=>9 [5,6,1,3,4,2]=>10 [5,6,1,4,2,3]=>10 [5,6,1,4,3,2]=>13 [5,6,2,1,3,4]=>8 [5,6,2,1,4,3]=>12 [5,6,2,3,1,4]=>9 [5,6,2,3,4,1]=>10 [5,6,2,4,1,3]=>10 [5,6,2,4,3,1]=>13 [5,6,3,1,2,4]=>9 [5,6,3,1,4,2]=>13 [5,6,3,2,1,4]=>11 [5,6,3,2,4,1]=>13 [5,6,3,4,1,2]=>10 [5,6,3,4,2,1]=>12 [5,6,4,1,2,3]=>10 [5,6,4,1,3,2]=>13 [5,6,4,2,1,3]=>12 [5,6,4,2,3,1]=>13 [5,6,4,3,1,2]=>13 [5,6,4,3,2,1]=>15 [6,1,2,3,4,5]=>6 [6,1,2,3,5,4]=>11 [6,1,2,4,3,5]=>10 [6,1,2,4,5,3]=>11 [6,1,2,5,3,4]=>11 [6,1,2,5,4,3]=>15 [6,1,3,2,4,5]=>9 [6,1,3,2,5,4]=>14 [6,1,3,4,2,5]=>10 [6,1,3,4,5,2]=>11 [6,1,3,5,2,4]=>11 [6,1,3,5,4,2]=>15 [6,1,4,2,3,5]=>10 [6,1,4,2,5,3]=>15 [6,1,4,3,2,5]=>13 [6,1,4,3,5,2]=>15 [6,1,4,5,2,3]=>11 [6,1,4,5,3,2]=>14 [6,1,5,2,3,4]=>11 [6,1,5,2,4,3]=>15 [6,1,5,3,2,4]=>14 [6,1,5,3,4,2]=>15 [6,1,5,4,2,3]=>15 [6,1,5,4,3,2]=>18 [6,2,1,3,4,5]=>8 [6,2,1,3,5,4]=>13 [6,2,1,4,3,5]=>12 [6,2,1,4,5,3]=>13 [6,2,1,5,3,4]=>13 [6,2,1,5,4,3]=>17 [6,2,3,1,4,5]=>9 [6,2,3,1,5,4]=>14 [6,2,3,4,1,5]=>10 [6,2,3,4,5,1]=>11 [6,2,3,5,1,4]=>11 [6,2,3,5,4,1]=>15 [6,2,4,1,3,5]=>10 [6,2,4,1,5,3]=>15 [6,2,4,3,1,5]=>13 [6,2,4,3,5,1]=>15 [6,2,4,5,1,3]=>11 [6,2,4,5,3,1]=>14 [6,2,5,1,3,4]=>11 [6,2,5,1,4,3]=>15 [6,2,5,3,1,4]=>14 [6,2,5,3,4,1]=>15 [6,2,5,4,1,3]=>15 [6,2,5,4,3,1]=>18 [6,3,1,2,4,5]=>9 [6,3,1,2,5,4]=>14 [6,3,1,4,2,5]=>13 [6,3,1,4,5,2]=>14 [6,3,1,5,2,4]=>14 [6,3,1,5,4,2]=>18 [6,3,2,1,4,5]=>11 [6,3,2,1,5,4]=>16 [6,3,2,4,1,5]=>13 [6,3,2,4,5,1]=>14 [6,3,2,5,1,4]=>14 [6,3,2,5,4,1]=>18 [6,3,4,1,2,5]=>10 [6,3,4,1,5,2]=>15 [6,3,4,2,1,5]=>12 [6,3,4,2,5,1]=>15 [6,3,4,5,1,2]=>11 [6,3,4,5,2,1]=>13 [6,3,5,1,2,4]=>11 [6,3,5,1,4,2]=>15 [6,3,5,2,1,4]=>13 [6,3,5,2,4,1]=>15 [6,3,5,4,1,2]=>15 [6,3,5,4,2,1]=>17 [6,4,1,2,3,5]=>10 [6,4,1,2,5,3]=>15 [6,4,1,3,2,5]=>13 [6,4,1,3,5,2]=>15 [6,4,1,5,2,3]=>15 [6,4,1,5,3,2]=>18 [6,4,2,1,3,5]=>12 [6,4,2,1,5,3]=>17 [6,4,2,3,1,5]=>13 [6,4,2,3,5,1]=>15 [6,4,2,5,1,3]=>15 [6,4,2,5,3,1]=>18 [6,4,3,1,2,5]=>13 [6,4,3,1,5,2]=>18 [6,4,3,2,1,5]=>15 [6,4,3,2,5,1]=>18 [6,4,3,5,1,2]=>15 [6,4,3,5,2,1]=>17 [6,4,5,1,2,3]=>11 [6,4,5,1,3,2]=>14 [6,4,5,2,1,3]=>13 [6,4,5,2,3,1]=>14 [6,4,5,3,1,2]=>14 [6,4,5,3,2,1]=>16 [6,5,1,2,3,4]=>11 [6,5,1,2,4,3]=>15 [6,5,1,3,2,4]=>14 [6,5,1,3,4,2]=>15 [6,5,1,4,2,3]=>15 [6,5,1,4,3,2]=>18 [6,5,2,1,3,4]=>13 [6,5,2,1,4,3]=>17 [6,5,2,3,1,4]=>14 [6,5,2,3,4,1]=>15 [6,5,2,4,1,3]=>15 [6,5,2,4,3,1]=>18 [6,5,3,1,2,4]=>14 [6,5,3,1,4,2]=>18 [6,5,3,2,1,4]=>16 [6,5,3,2,4,1]=>18 [6,5,3,4,1,2]=>15 [6,5,3,4,2,1]=>17 [6,5,4,1,2,3]=>15 [6,5,4,1,3,2]=>18 [6,5,4,2,1,3]=>17 [6,5,4,2,3,1]=>18 [6,5,4,3,1,2]=>18 [6,5,4,3,2,1]=>20
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Description
The sum of the descent tops (or Genocchi descents) of a permutation.
This statistic is given by
$$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} \pi_i.$$
References
[1] Babson, E., Steingr'─▒msson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
[2] Nunge, A. An equivalence of multistatistics on permutations arXiv:1601.02928
[3] Clarke, R. J., Steingr'─▒msson, E., Zeng, J. New Euler-Mahonian statistics on permutations and words MathSciNet:1436481
Code
def statistic(pi):
    return sum( pi[i] for i in range(pi.size()-1) if pi[i] > pi[i+1] )
Created
Jun 15, 2013 at 13:31 by Chris Berg
Updated
Apr 06, 2016 at 06:56 by Martin Rubey