edit this statistic or download as text // json
Identifier
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]=>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]=>4 [3,2,1,4]=>2 [3,2,4,1]=>4 [3,4,1,2]=>3 [3,4,2,1]=>3 [4,1,2,3]=>3 [4,1,3,2]=>4 [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]=>4 [1,4,3,2,5]=>2 [1,4,3,5,2]=>4 [1,4,5,2,3]=>3 [1,4,5,3,2]=>3 [1,5,2,3,4]=>3 [1,5,2,4,3]=>4 [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]=>5 [2,4,3,1,5]=>3 [2,4,3,5,1]=>5 [2,4,5,1,3]=>4 [2,4,5,3,1]=>4 [2,5,1,3,4]=>4 [2,5,1,4,3]=>5 [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]=>4 [3,1,4,5,2]=>5 [3,1,5,2,4]=>5 [3,1,5,4,2]=>5 [3,2,1,4,5]=>2 [3,2,1,5,4]=>3 [3,2,4,1,5]=>4 [3,2,4,5,1]=>5 [3,2,5,1,4]=>5 [3,2,5,4,1]=>5 [3,4,1,2,5]=>3 [3,4,1,5,2]=>6 [3,4,2,1,5]=>3 [3,4,2,5,1]=>6 [3,4,5,1,2]=>4 [3,4,5,2,1]=>4 [3,5,1,2,4]=>4 [3,5,1,4,2]=>6 [3,5,2,1,4]=>4 [3,5,2,4,1]=>6 [3,5,4,1,2]=>4 [3,5,4,2,1]=>4 [4,1,2,3,5]=>3 [4,1,2,5,3]=>5 [4,1,3,2,5]=>4 [4,1,3,5,2]=>6 [4,1,5,2,3]=>6 [4,1,5,3,2]=>6 [4,2,1,3,5]=>3 [4,2,1,5,3]=>5 [4,2,3,1,5]=>4 [4,2,3,5,1]=>6 [4,2,5,1,3]=>6 [4,2,5,3,1]=>6 [4,3,1,2,5]=>3 [4,3,1,5,2]=>6 [4,3,2,1,5]=>3 [4,3,2,5,1]=>6 [4,3,5,1,2]=>5 [4,3,5,2,1]=>5 [4,5,1,2,3]=>4 [4,5,1,3,2]=>5 [4,5,2,1,3]=>4 [4,5,2,3,1]=>5 [4,5,3,1,2]=>4 [4,5,3,2,1]=>4 [5,1,2,3,4]=>4 [5,1,2,4,3]=>5 [5,1,3,2,4]=>5 [5,1,3,4,2]=>6 [5,1,4,2,3]=>6 [5,1,4,3,2]=>6 [5,2,1,3,4]=>4 [5,2,1,4,3]=>5 [5,2,3,1,4]=>5 [5,2,3,4,1]=>6 [5,2,4,1,3]=>6 [5,2,4,3,1]=>6 [5,3,1,2,4]=>4 [5,3,1,4,2]=>6 [5,3,2,1,4]=>4 [5,3,2,4,1]=>6 [5,3,4,1,2]=>5 [5,3,4,2,1]=>5 [5,4,1,2,3]=>4 [5,4,1,3,2]=>5 [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]=>4 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>4 [1,2,5,6,3,4]=>3 [1,2,5,6,4,3]=>3 [1,2,6,3,4,5]=>3 [1,2,6,3,5,4]=>4 [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]=>5 [1,3,5,4,2,6]=>3 [1,3,5,4,6,2]=>5 [1,3,5,6,2,4]=>4 [1,3,5,6,4,2]=>4 [1,3,6,2,4,5]=>4 [1,3,6,2,5,4]=>5 [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]=>4 [1,4,2,5,6,3]=>5 [1,4,2,6,3,5]=>5 [1,4,2,6,5,3]=>5 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>3 [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]=>5 [1,4,5,2,3,6]=>3 [1,4,5,2,6,3]=>6 [1,4,5,3,2,6]=>3 [1,4,5,3,6,2]=>6 [1,4,5,6,2,3]=>4 [1,4,5,6,3,2]=>4 [1,4,6,2,3,5]=>4 [1,4,6,2,5,3]=>6 [1,4,6,3,2,5]=>4 [1,4,6,3,5,2]=>6 [1,4,6,5,2,3]=>4 [1,4,6,5,3,2]=>4 [1,5,2,3,4,6]=>3 [1,5,2,3,6,4]=>5 [1,5,2,4,3,6]=>4 [1,5,2,4,6,3]=>6 [1,5,2,6,3,4]=>6 [1,5,2,6,4,3]=>6 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>5 [1,5,3,4,2,6]=>4 [1,5,3,4,6,2]=>6 [1,5,3,6,2,4]=>6 [1,5,3,6,4,2]=>6 [1,5,4,2,3,6]=>3 [1,5,4,2,6,3]=>6 [1,5,4,3,2,6]=>3 [1,5,4,3,6,2]=>6 [1,5,4,6,2,3]=>5 [1,5,4,6,3,2]=>5 [1,5,6,2,3,4]=>4 [1,5,6,2,4,3]=>5 [1,5,6,3,2,4]=>4 [1,5,6,3,4,2]=>5 [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]=>5 [1,6,2,4,3,5]=>5 [1,6,2,4,5,3]=>6 [1,6,2,5,3,4]=>6 [1,6,2,5,4,3]=>6 [1,6,3,2,4,5]=>4 [1,6,3,2,5,4]=>5 [1,6,3,4,2,5]=>5 [1,6,3,4,5,2]=>6 [1,6,3,5,2,4]=>6 [1,6,3,5,4,2]=>6 [1,6,4,2,3,5]=>4 [1,6,4,2,5,3]=>6 [1,6,4,3,2,5]=>4 [1,6,4,3,5,2]=>6 [1,6,4,5,2,3]=>5 [1,6,4,5,3,2]=>5 [1,6,5,2,3,4]=>4 [1,6,5,2,4,3]=>5 [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]=>5 [2,1,5,4,3,6]=>3 [2,1,5,4,6,3]=>5 [2,1,5,6,3,4]=>4 [2,1,5,6,4,3]=>4 [2,1,6,3,4,5]=>4 [2,1,6,3,5,4]=>5 [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]=>6 [2,3,5,4,1,6]=>4 [2,3,5,4,6,1]=>6 [2,3,5,6,1,4]=>5 [2,3,5,6,4,1]=>5 [2,3,6,1,4,5]=>5 [2,3,6,1,5,4]=>6 [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]=>5 [2,4,1,5,6,3]=>6 [2,4,1,6,3,5]=>6 [2,4,1,6,5,3]=>6 [2,4,3,1,5,6]=>3 [2,4,3,1,6,5]=>4 [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]=>6 [2,4,5,1,3,6]=>4 [2,4,5,1,6,3]=>7 [2,4,5,3,1,6]=>4 [2,4,5,3,6,1]=>7 [2,4,5,6,1,3]=>5 [2,4,5,6,3,1]=>5 [2,4,6,1,3,5]=>5 [2,4,6,1,5,3]=>7 [2,4,6,3,1,5]=>5 [2,4,6,3,5,1]=>7 [2,4,6,5,1,3]=>5 [2,4,6,5,3,1]=>5 [2,5,1,3,4,6]=>4 [2,5,1,3,6,4]=>6 [2,5,1,4,3,6]=>5 [2,5,1,4,6,3]=>7 [2,5,1,6,3,4]=>7 [2,5,1,6,4,3]=>7 [2,5,3,1,4,6]=>4 [2,5,3,1,6,4]=>6 [2,5,3,4,1,6]=>5 [2,5,3,4,6,1]=>7 [2,5,3,6,1,4]=>7 [2,5,3,6,4,1]=>7 [2,5,4,1,3,6]=>4 [2,5,4,1,6,3]=>7 [2,5,4,3,1,6]=>4 [2,5,4,3,6,1]=>7 [2,5,4,6,1,3]=>6 [2,5,4,6,3,1]=>6 [2,5,6,1,3,4]=>5 [2,5,6,1,4,3]=>6 [2,5,6,3,1,4]=>5 [2,5,6,3,4,1]=>6 [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]=>6 [2,6,1,4,3,5]=>6 [2,6,1,4,5,3]=>7 [2,6,1,5,3,4]=>7 [2,6,1,5,4,3]=>7 [2,6,3,1,4,5]=>5 [2,6,3,1,5,4]=>6 [2,6,3,4,1,5]=>6 [2,6,3,4,5,1]=>7 [2,6,3,5,1,4]=>7 [2,6,3,5,4,1]=>7 [2,6,4,1,3,5]=>5 [2,6,4,1,5,3]=>7 [2,6,4,3,1,5]=>5 [2,6,4,3,5,1]=>7 [2,6,4,5,1,3]=>6 [2,6,4,5,3,1]=>6 [2,6,5,1,3,4]=>5 [2,6,5,1,4,3]=>6 [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]=>4 [3,1,4,2,6,5]=>5 [3,1,4,5,2,6]=>5 [3,1,4,5,6,2]=>6 [3,1,4,6,2,5]=>6 [3,1,4,6,5,2]=>6 [3,1,5,2,4,6]=>5 [3,1,5,2,6,4]=>7 [3,1,5,4,2,6]=>5 [3,1,5,4,6,2]=>7 [3,1,5,6,2,4]=>6 [3,1,5,6,4,2]=>6 [3,1,6,2,4,5]=>6 [3,1,6,2,5,4]=>7 [3,1,6,4,2,5]=>6 [3,1,6,4,5,2]=>7 [3,1,6,5,2,4]=>6 [3,1,6,5,4,2]=>6 [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]=>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]=>6 [3,2,5,1,4,6]=>5 [3,2,5,1,6,4]=>7 [3,2,5,4,1,6]=>5 [3,2,5,4,6,1]=>7 [3,2,5,6,1,4]=>6 [3,2,5,6,4,1]=>6 [3,2,6,1,4,5]=>6 [3,2,6,1,5,4]=>7 [3,2,6,4,1,5]=>6 [3,2,6,4,5,1]=>7 [3,2,6,5,1,4]=>6 [3,2,6,5,4,1]=>6 [3,4,1,2,5,6]=>3 [3,4,1,2,6,5]=>4 [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]=>7 [3,4,2,1,5,6]=>3 [3,4,2,1,6,5]=>4 [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]=>7 [3,4,5,1,2,6]=>4 [3,4,5,1,6,2]=>8 [3,4,5,2,1,6]=>4 [3,4,5,2,6,1]=>8 [3,4,5,6,1,2]=>5 [3,4,5,6,2,1]=>5 [3,4,6,1,2,5]=>5 [3,4,6,1,5,2]=>8 [3,4,6,2,1,5]=>5 [3,4,6,2,5,1]=>8 [3,4,6,5,1,2]=>5 [3,4,6,5,2,1]=>5 [3,5,1,2,4,6]=>4 [3,5,1,2,6,4]=>6 [3,5,1,4,2,6]=>6 [3,5,1,4,6,2]=>8 [3,5,1,6,2,4]=>8 [3,5,1,6,4,2]=>8 [3,5,2,1,4,6]=>4 [3,5,2,1,6,4]=>6 [3,5,2,4,1,6]=>6 [3,5,2,4,6,1]=>8 [3,5,2,6,1,4]=>8 [3,5,2,6,4,1]=>8 [3,5,4,1,2,6]=>4 [3,5,4,1,6,2]=>8 [3,5,4,2,1,6]=>4 [3,5,4,2,6,1]=>8 [3,5,4,6,1,2]=>6 [3,5,4,6,2,1]=>6 [3,5,6,1,2,4]=>5 [3,5,6,1,4,2]=>7 [3,5,6,2,1,4]=>5 [3,5,6,2,4,1]=>7 [3,5,6,4,1,2]=>5 [3,5,6,4,2,1]=>5 [3,6,1,2,4,5]=>5 [3,6,1,2,5,4]=>6 [3,6,1,4,2,5]=>7 [3,6,1,4,5,2]=>8 [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]=>6 [3,6,2,4,1,5]=>7 [3,6,2,4,5,1]=>8 [3,6,2,5,1,4]=>8 [3,6,2,5,4,1]=>8 [3,6,4,1,2,5]=>5 [3,6,4,1,5,2]=>8 [3,6,4,2,1,5]=>5 [3,6,4,2,5,1]=>8 [3,6,4,5,1,2]=>6 [3,6,4,5,2,1]=>6 [3,6,5,1,2,4]=>5 [3,6,5,1,4,2]=>7 [3,6,5,2,1,4]=>5 [3,6,5,2,4,1]=>7 [3,6,5,4,1,2]=>5 [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]=>5 [4,1,2,5,6,3]=>6 [4,1,2,6,3,5]=>6 [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]=>6 [4,1,3,5,6,2]=>7 [4,1,3,6,2,5]=>7 [4,1,3,6,5,2]=>7 [4,1,5,2,3,6]=>6 [4,1,5,2,6,3]=>9 [4,1,5,3,2,6]=>6 [4,1,5,3,6,2]=>9 [4,1,5,6,2,3]=>7 [4,1,5,6,3,2]=>7 [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]=>7 [4,1,6,5,3,2]=>7 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>4 [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]=>6 [4,2,3,1,5,6]=>4 [4,2,3,1,6,5]=>5 [4,2,3,5,1,6]=>6 [4,2,3,5,6,1]=>7 [4,2,3,6,1,5]=>7 [4,2,3,6,5,1]=>7 [4,2,5,1,3,6]=>6 [4,2,5,1,6,3]=>9 [4,2,5,3,1,6]=>6 [4,2,5,3,6,1]=>9 [4,2,5,6,1,3]=>7 [4,2,5,6,3,1]=>7 [4,2,6,1,3,5]=>7 [4,2,6,1,5,3]=>9 [4,2,6,3,1,5]=>7 [4,2,6,3,5,1]=>9 [4,2,6,5,1,3]=>7 [4,2,6,5,3,1]=>7 [4,3,1,2,5,6]=>3 [4,3,1,2,6,5]=>4 [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]=>7 [4,3,2,1,5,6]=>3 [4,3,2,1,6,5]=>4 [4,3,2,5,1,6]=>6 [4,3,2,5,6,1]=>7 [4,3,2,6,1,5]=>7 [4,3,2,6,5,1]=>7 [4,3,5,1,2,6]=>5 [4,3,5,1,6,2]=>9 [4,3,5,2,1,6]=>5 [4,3,5,2,6,1]=>9 [4,3,5,6,1,2]=>6 [4,3,5,6,2,1]=>6 [4,3,6,1,2,5]=>6 [4,3,6,1,5,2]=>9 [4,3,6,2,1,5]=>6 [4,3,6,2,5,1]=>9 [4,3,6,5,1,2]=>6 [4,3,6,5,2,1]=>6 [4,5,1,2,3,6]=>4 [4,5,1,2,6,3]=>7 [4,5,1,3,2,6]=>5 [4,5,1,3,6,2]=>8 [4,5,1,6,2,3]=>8 [4,5,1,6,3,2]=>8 [4,5,2,1,3,6]=>4 [4,5,2,1,6,3]=>7 [4,5,2,3,1,6]=>5 [4,5,2,3,6,1]=>8 [4,5,2,6,1,3]=>8 [4,5,2,6,3,1]=>8 [4,5,3,1,2,6]=>4 [4,5,3,1,6,2]=>8 [4,5,3,2,1,6]=>4 [4,5,3,2,6,1]=>8 [4,5,3,6,1,2]=>7 [4,5,3,6,2,1]=>7 [4,5,6,1,2,3]=>5 [4,5,6,1,3,2]=>6 [4,5,6,2,1,3]=>5 [4,5,6,2,3,1]=>6 [4,5,6,3,1,2]=>5 [4,5,6,3,2,1]=>5 [4,6,1,2,3,5]=>5 [4,6,1,2,5,3]=>7 [4,6,1,3,2,5]=>6 [4,6,1,3,5,2]=>8 [4,6,1,5,2,3]=>8 [4,6,1,5,3,2]=>8 [4,6,2,1,3,5]=>5 [4,6,2,1,5,3]=>7 [4,6,2,3,1,5]=>6 [4,6,2,3,5,1]=>8 [4,6,2,5,1,3]=>8 [4,6,2,5,3,1]=>8 [4,6,3,1,2,5]=>5 [4,6,3,1,5,2]=>8 [4,6,3,2,1,5]=>5 [4,6,3,2,5,1]=>8 [4,6,3,5,1,2]=>7 [4,6,3,5,2,1]=>7 [4,6,5,1,2,3]=>5 [4,6,5,1,3,2]=>6 [4,6,5,2,1,3]=>5 [4,6,5,2,3,1]=>6 [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]=>6 [5,1,2,4,3,6]=>5 [5,1,2,4,6,3]=>7 [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]=>7 [5,1,3,4,2,6]=>6 [5,1,3,4,6,2]=>8 [5,1,3,6,2,4]=>8 [5,1,3,6,4,2]=>8 [5,1,4,2,3,6]=>6 [5,1,4,2,6,3]=>9 [5,1,4,3,2,6]=>6 [5,1,4,3,6,2]=>9 [5,1,4,6,2,3]=>8 [5,1,4,6,3,2]=>8 [5,1,6,2,3,4]=>8 [5,1,6,2,4,3]=>9 [5,1,6,3,2,4]=>8 [5,1,6,3,4,2]=>9 [5,1,6,4,2,3]=>8 [5,1,6,4,3,2]=>8 [5,2,1,3,4,6]=>4 [5,2,1,3,6,4]=>6 [5,2,1,4,3,6]=>5 [5,2,1,4,6,3]=>7 [5,2,1,6,3,4]=>7 [5,2,1,6,4,3]=>7 [5,2,3,1,4,6]=>5 [5,2,3,1,6,4]=>7 [5,2,3,4,1,6]=>6 [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]=>6 [5,2,4,1,6,3]=>9 [5,2,4,3,1,6]=>6 [5,2,4,3,6,1]=>9 [5,2,4,6,1,3]=>8 [5,2,4,6,3,1]=>8 [5,2,6,1,3,4]=>8 [5,2,6,1,4,3]=>9 [5,2,6,3,1,4]=>8 [5,2,6,3,4,1]=>9 [5,2,6,4,1,3]=>8 [5,2,6,4,3,1]=>8 [5,3,1,2,4,6]=>4 [5,3,1,2,6,4]=>6 [5,3,1,4,2,6]=>6 [5,3,1,4,6,2]=>8 [5,3,1,6,2,4]=>8 [5,3,1,6,4,2]=>8 [5,3,2,1,4,6]=>4 [5,3,2,1,6,4]=>6 [5,3,2,4,1,6]=>6 [5,3,2,4,6,1]=>8 [5,3,2,6,1,4]=>8 [5,3,2,6,4,1]=>8 [5,3,4,1,2,6]=>5 [5,3,4,1,6,2]=>9 [5,3,4,2,1,6]=>5 [5,3,4,2,6,1]=>9 [5,3,4,6,1,2]=>7 [5,3,4,6,2,1]=>7 [5,3,6,1,2,4]=>7 [5,3,6,1,4,2]=>9 [5,3,6,2,1,4]=>7 [5,3,6,2,4,1]=>9 [5,3,6,4,1,2]=>7 [5,3,6,4,2,1]=>7 [5,4,1,2,3,6]=>4 [5,4,1,2,6,3]=>7 [5,4,1,3,2,6]=>5 [5,4,1,3,6,2]=>8 [5,4,1,6,2,3]=>8 [5,4,1,6,3,2]=>8 [5,4,2,1,3,6]=>4 [5,4,2,1,6,3]=>7 [5,4,2,3,1,6]=>5 [5,4,2,3,6,1]=>8 [5,4,2,6,1,3]=>8 [5,4,2,6,3,1]=>8 [5,4,3,1,2,6]=>4 [5,4,3,1,6,2]=>8 [5,4,3,2,1,6]=>4 [5,4,3,2,6,1]=>8 [5,4,3,6,1,2]=>7 [5,4,3,6,2,1]=>7 [5,4,6,1,2,3]=>6 [5,4,6,1,3,2]=>7 [5,4,6,2,1,3]=>6 [5,4,6,2,3,1]=>7 [5,4,6,3,1,2]=>6 [5,4,6,3,2,1]=>6 [5,6,1,2,3,4]=>5 [5,6,1,2,4,3]=>6 [5,6,1,3,2,4]=>6 [5,6,1,3,4,2]=>7 [5,6,1,4,2,3]=>7 [5,6,1,4,3,2]=>7 [5,6,2,1,3,4]=>5 [5,6,2,1,4,3]=>6 [5,6,2,3,1,4]=>6 [5,6,2,3,4,1]=>7 [5,6,2,4,1,3]=>7 [5,6,2,4,3,1]=>7 [5,6,3,1,2,4]=>5 [5,6,3,1,4,2]=>7 [5,6,3,2,1,4]=>5 [5,6,3,2,4,1]=>7 [5,6,3,4,1,2]=>6 [5,6,3,4,2,1]=>6 [5,6,4,1,2,3]=>5 [5,6,4,1,3,2]=>6 [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]=>6 [6,1,2,4,3,5]=>6 [6,1,2,4,5,3]=>7 [6,1,2,5,3,4]=>7 [6,1,2,5,4,3]=>7 [6,1,3,2,4,5]=>6 [6,1,3,2,5,4]=>7 [6,1,3,4,2,5]=>7 [6,1,3,4,5,2]=>8 [6,1,3,5,2,4]=>8 [6,1,3,5,4,2]=>8 [6,1,4,2,3,5]=>7 [6,1,4,2,5,3]=>9 [6,1,4,3,2,5]=>7 [6,1,4,3,5,2]=>9 [6,1,4,5,2,3]=>8 [6,1,4,5,3,2]=>8 [6,1,5,2,3,4]=>8 [6,1,5,2,4,3]=>9 [6,1,5,3,2,4]=>8 [6,1,5,3,4,2]=>9 [6,1,5,4,2,3]=>8 [6,1,5,4,3,2]=>8 [6,2,1,3,4,5]=>5 [6,2,1,3,5,4]=>6 [6,2,1,4,3,5]=>6 [6,2,1,4,5,3]=>7 [6,2,1,5,3,4]=>7 [6,2,1,5,4,3]=>7 [6,2,3,1,4,5]=>6 [6,2,3,1,5,4]=>7 [6,2,3,4,1,5]=>7 [6,2,3,4,5,1]=>8 [6,2,3,5,1,4]=>8 [6,2,3,5,4,1]=>8 [6,2,4,1,3,5]=>7 [6,2,4,1,5,3]=>9 [6,2,4,3,1,5]=>7 [6,2,4,3,5,1]=>9 [6,2,4,5,1,3]=>8 [6,2,4,5,3,1]=>8 [6,2,5,1,3,4]=>8 [6,2,5,1,4,3]=>9 [6,2,5,3,1,4]=>8 [6,2,5,3,4,1]=>9 [6,2,5,4,1,3]=>8 [6,2,5,4,3,1]=>8 [6,3,1,2,4,5]=>5 [6,3,1,2,5,4]=>6 [6,3,1,4,2,5]=>7 [6,3,1,4,5,2]=>8 [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]=>6 [6,3,2,4,1,5]=>7 [6,3,2,4,5,1]=>8 [6,3,2,5,1,4]=>8 [6,3,2,5,4,1]=>8 [6,3,4,1,2,5]=>6 [6,3,4,1,5,2]=>9 [6,3,4,2,1,5]=>6 [6,3,4,2,5,1]=>9 [6,3,4,5,1,2]=>7 [6,3,4,5,2,1]=>7 [6,3,5,1,2,4]=>7 [6,3,5,1,4,2]=>9 [6,3,5,2,1,4]=>7 [6,3,5,2,4,1]=>9 [6,3,5,4,1,2]=>7 [6,3,5,4,2,1]=>7 [6,4,1,2,3,5]=>5 [6,4,1,2,5,3]=>7 [6,4,1,3,2,5]=>6 [6,4,1,3,5,2]=>8 [6,4,1,5,2,3]=>8 [6,4,1,5,3,2]=>8 [6,4,2,1,3,5]=>5 [6,4,2,1,5,3]=>7 [6,4,2,3,1,5]=>6 [6,4,2,3,5,1]=>8 [6,4,2,5,1,3]=>8 [6,4,2,5,3,1]=>8 [6,4,3,1,2,5]=>5 [6,4,3,1,5,2]=>8 [6,4,3,2,1,5]=>5 [6,4,3,2,5,1]=>8 [6,4,3,5,1,2]=>7 [6,4,3,5,2,1]=>7 [6,4,5,1,2,3]=>6 [6,4,5,1,3,2]=>7 [6,4,5,2,1,3]=>6 [6,4,5,2,3,1]=>7 [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]=>6 [6,5,1,3,2,4]=>6 [6,5,1,3,4,2]=>7 [6,5,1,4,2,3]=>7 [6,5,1,4,3,2]=>7 [6,5,2,1,3,4]=>5 [6,5,2,1,4,3]=>6 [6,5,2,3,1,4]=>6 [6,5,2,3,4,1]=>7 [6,5,2,4,1,3]=>7 [6,5,2,4,3,1]=>7 [6,5,3,1,2,4]=>5 [6,5,3,1,4,2]=>7 [6,5,3,2,1,4]=>5 [6,5,3,2,4,1]=>7 [6,5,3,4,1,2]=>6 [6,5,3,4,2,1]=>6 [6,5,4,1,2,3]=>5 [6,5,4,1,3,2]=>6 [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
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Description
The sum of the descent differences of a permutations.
This statistic is given by
$$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} (\pi_i-\pi_{i+1}).$$
See St000111The sum of the descent tops (or Genocchi descents) of a permutation. and St000154The sum of the descent bottoms of a permutation. for the sum of the descent tops and the descent bottoms, respectively. This statistic was studied in [1] and [2] where is was called the drop of a permutation.
References
[1] Babson, E., Steingr'─▒msson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
[2] Petersen, T. K., Tenner, B. E. The depth of a permutation arXiv:1202.4765
[3] Triangle read by rows: For n >= 1, k >= 0, T(n,k) = the number of permutations pi of n such that the total distance sum_i abs(i-pi(i)) = 2k. Equivalently, k = sum_i max(i-pi(i),0). OEIS:A062869
Code
def statistic(x):
    return sum(x[i]-x[i+1] for i in range(x.size()-1) if x[i]>x[i+1])
Created
Nov 30, 2012 at 21:30 by Chris Berg
Updated
May 29, 2015 at 16:16 by Martin Rubey