edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>2 [1,2,3,4]=>1 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>1 [1,4,2,3]=>1 [1,4,3,2]=>2 [2,1,3,4]=>1 [2,1,4,3]=>1 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>1 [2,4,3,1]=>2 [3,1,2,4]=>1 [3,1,4,2]=>1 [3,2,1,4]=>2 [3,2,4,1]=>2 [3,4,1,2]=>2 [3,4,2,1]=>3 [4,1,2,3]=>1 [4,1,3,2]=>2 [4,2,1,3]=>2 [4,2,3,1]=>4 [4,3,1,2]=>3 [4,3,2,1]=>5 [1,2,3,4,5]=>1 [1,2,3,5,4]=>1 [1,2,4,3,5]=>1 [1,2,4,5,3]=>1 [1,2,5,3,4]=>1 [1,2,5,4,3]=>2 [1,3,2,4,5]=>1 [1,3,2,5,4]=>1 [1,3,4,2,5]=>1 [1,3,4,5,2]=>1 [1,3,5,2,4]=>1 [1,3,5,4,2]=>2 [1,4,2,3,5]=>1 [1,4,2,5,3]=>1 [1,4,3,2,5]=>2 [1,4,3,5,2]=>2 [1,4,5,2,3]=>2 [1,4,5,3,2]=>3 [1,5,2,3,4]=>1 [1,5,2,4,3]=>2 [1,5,3,2,4]=>2 [1,5,3,4,2]=>4 [1,5,4,2,3]=>3 [1,5,4,3,2]=>5 [2,1,3,4,5]=>1 [2,1,3,5,4]=>1 [2,1,4,3,5]=>1 [2,1,4,5,3]=>1 [2,1,5,3,4]=>1 [2,1,5,4,3]=>2 [2,3,1,4,5]=>1 [2,3,1,5,4]=>1 [2,3,4,1,5]=>1 [2,3,4,5,1]=>1 [2,3,5,1,4]=>1 [2,3,5,4,1]=>2 [2,4,1,3,5]=>1 [2,4,1,5,3]=>1 [2,4,3,1,5]=>2 [2,4,3,5,1]=>2 [2,4,5,1,3]=>2 [2,4,5,3,1]=>3 [2,5,1,3,4]=>1 [2,5,1,4,3]=>2 [2,5,3,1,4]=>2 [2,5,3,4,1]=>4 [2,5,4,1,3]=>3 [2,5,4,3,1]=>5 [3,1,2,4,5]=>1 [3,1,2,5,4]=>1 [3,1,4,2,5]=>1 [3,1,4,5,2]=>1 [3,1,5,2,4]=>1 [3,1,5,4,2]=>2 [3,2,1,4,5]=>2 [3,2,1,5,4]=>2 [3,2,4,1,5]=>2 [3,2,4,5,1]=>2 [3,2,5,1,4]=>2 [3,2,5,4,1]=>4 [3,4,1,2,5]=>2 [3,4,1,5,2]=>2 [3,4,2,1,5]=>3 [3,4,2,5,1]=>3 [3,4,5,1,2]=>3 [3,4,5,2,1]=>5 [3,5,1,2,4]=>2 [3,5,1,4,2]=>4 [3,5,2,1,4]=>3 [3,5,2,4,1]=>6 [3,5,4,1,2]=>5 [3,5,4,2,1]=>8 [4,1,2,3,5]=>1 [4,1,2,5,3]=>1 [4,1,3,2,5]=>2 [4,1,3,5,2]=>2 [4,1,5,2,3]=>2 [4,1,5,3,2]=>3 [4,2,1,3,5]=>2 [4,2,1,5,3]=>2 [4,2,3,1,5]=>4 [4,2,3,5,1]=>4 [4,2,5,1,3]=>4 [4,2,5,3,1]=>6 [4,3,1,2,5]=>3 [4,3,1,5,2]=>3 [4,3,2,1,5]=>5 [4,3,2,5,1]=>5 [4,3,5,1,2]=>5 [4,3,5,2,1]=>8 [4,5,1,2,3]=>3 [4,5,1,3,2]=>5 [4,5,2,1,3]=>5 [4,5,2,3,1]=>8 [4,5,3,1,2]=>9 [4,5,3,2,1]=>14 [5,1,2,3,4]=>1 [5,1,2,4,3]=>2 [5,1,3,2,4]=>2 [5,1,3,4,2]=>4 [5,1,4,2,3]=>3 [5,1,4,3,2]=>5 [5,2,1,3,4]=>2 [5,2,1,4,3]=>4 [5,2,3,1,4]=>4 [5,2,3,4,1]=>8 [5,2,4,1,3]=>6 [5,2,4,3,1]=>10 [5,3,1,2,4]=>3 [5,3,1,4,2]=>6 [5,3,2,1,4]=>5 [5,3,2,4,1]=>10 [5,3,4,1,2]=>8 [5,3,4,2,1]=>13 [5,4,1,2,3]=>5 [5,4,1,3,2]=>8 [5,4,2,1,3]=>8 [5,4,2,3,1]=>13 [5,4,3,1,2]=>14 [5,4,3,2,1]=>23 [1,2,3,4,5,6]=>1 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>1 [1,2,3,5,6,4]=>1 [1,2,3,6,4,5]=>1 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>1 [1,2,4,5,3,6]=>1 [1,2,4,5,6,3]=>1 [1,2,4,6,3,5]=>1 [1,2,4,6,5,3]=>2 [1,2,5,3,4,6]=>1 [1,2,5,3,6,4]=>1 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>2 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>3 [1,2,6,3,4,5]=>1 [1,2,6,3,5,4]=>2 [1,2,6,4,3,5]=>2 [1,2,6,4,5,3]=>4 [1,2,6,5,3,4]=>3 [1,2,6,5,4,3]=>5 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>1 [1,3,2,5,4,6]=>1 [1,3,2,5,6,4]=>1 [1,3,2,6,4,5]=>1 [1,3,2,6,5,4]=>2 [1,3,4,2,5,6]=>1 [1,3,4,2,6,5]=>1 [1,3,4,5,2,6]=>1 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>1 [1,3,4,6,5,2]=>2 [1,3,5,2,4,6]=>1 [1,3,5,2,6,4]=>1 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>2 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>3 [1,3,6,2,4,5]=>1 [1,3,6,2,5,4]=>2 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>4 [1,3,6,5,2,4]=>3 [1,3,6,5,4,2]=>5 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>1 [1,4,2,5,3,6]=>1 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>1 [1,4,2,6,5,3]=>2 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>2 [1,4,3,5,2,6]=>2 [1,4,3,5,6,2]=>2 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>4 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>2 [1,4,5,3,2,6]=>3 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>3 [1,4,5,6,3,2]=>5 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>4 [1,4,6,3,2,5]=>3 [1,4,6,3,5,2]=>6 [1,4,6,5,2,3]=>5 [1,4,6,5,3,2]=>8 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>1 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>2 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>3 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>2 [1,5,3,4,2,6]=>4 [1,5,3,4,6,2]=>4 [1,5,3,6,2,4]=>4 [1,5,3,6,4,2]=>6 [1,5,4,2,3,6]=>3 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>5 [1,5,4,3,6,2]=>5 [1,5,4,6,2,3]=>5 [1,5,4,6,3,2]=>8 [1,5,6,2,3,4]=>3 [1,5,6,2,4,3]=>5 [1,5,6,3,2,4]=>5 [1,5,6,3,4,2]=>8 [1,5,6,4,2,3]=>9 [1,5,6,4,3,2]=>14 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>2 [1,6,2,4,3,5]=>2 [1,6,2,4,5,3]=>4 [1,6,2,5,3,4]=>3 [1,6,2,5,4,3]=>5 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>4 [1,6,3,4,2,5]=>4 [1,6,3,4,5,2]=>8 [1,6,3,5,2,4]=>6 [1,6,3,5,4,2]=>10 [1,6,4,2,3,5]=>3 [1,6,4,2,5,3]=>6 [1,6,4,3,2,5]=>5 [1,6,4,3,5,2]=>10 [1,6,4,5,2,3]=>8 [1,6,4,5,3,2]=>13 [1,6,5,2,3,4]=>5 [1,6,5,2,4,3]=>8 [1,6,5,3,2,4]=>8 [1,6,5,3,4,2]=>13 [1,6,5,4,2,3]=>14 [1,6,5,4,3,2]=>23 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>1 [2,1,3,5,4,6]=>1 [2,1,3,5,6,4]=>1 [2,1,3,6,4,5]=>1 [2,1,3,6,5,4]=>2 [2,1,4,3,5,6]=>1 [2,1,4,3,6,5]=>1 [2,1,4,5,3,6]=>1 [2,1,4,5,6,3]=>1 [2,1,4,6,3,5]=>1 [2,1,4,6,5,3]=>2 [2,1,5,3,4,6]=>1 [2,1,5,3,6,4]=>1 [2,1,5,4,3,6]=>2 [2,1,5,4,6,3]=>2 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>3 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>2 [2,1,6,4,3,5]=>2 [2,1,6,4,5,3]=>4 [2,1,6,5,3,4]=>3 [2,1,6,5,4,3]=>5 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>1 [2,3,1,5,4,6]=>1 [2,3,1,5,6,4]=>1 [2,3,1,6,4,5]=>1 [2,3,1,6,5,4]=>2 [2,3,4,1,5,6]=>1 [2,3,4,1,6,5]=>1 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>1 [2,3,4,6,5,1]=>2 [2,3,5,1,4,6]=>1 [2,3,5,1,6,4]=>1 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>2 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>3 [2,3,6,1,4,5]=>1 [2,3,6,1,5,4]=>2 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>4 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>5 [2,4,1,3,5,6]=>1 [2,4,1,3,6,5]=>1 [2,4,1,5,3,6]=>1 [2,4,1,5,6,3]=>1 [2,4,1,6,3,5]=>1 [2,4,1,6,5,3]=>2 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>2 [2,4,3,5,1,6]=>2 [2,4,3,5,6,1]=>2 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>4 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>2 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>3 [2,4,5,6,3,1]=>5 [2,4,6,1,3,5]=>2 [2,4,6,1,5,3]=>4 [2,4,6,3,1,5]=>3 [2,4,6,3,5,1]=>6 [2,4,6,5,1,3]=>5 [2,4,6,5,3,1]=>8 [2,5,1,3,4,6]=>1 [2,5,1,3,6,4]=>1 [2,5,1,4,3,6]=>2 [2,5,1,4,6,3]=>2 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>3 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>2 [2,5,3,4,1,6]=>4 [2,5,3,4,6,1]=>4 [2,5,3,6,1,4]=>4 [2,5,3,6,4,1]=>6 [2,5,4,1,3,6]=>3 [2,5,4,1,6,3]=>3 [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]=>8 [2,5,6,1,3,4]=>3 [2,5,6,1,4,3]=>5 [2,5,6,3,1,4]=>5 [2,5,6,3,4,1]=>8 [2,5,6,4,1,3]=>9 [2,5,6,4,3,1]=>14 [2,6,1,3,4,5]=>1 [2,6,1,3,5,4]=>2 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>4 [2,6,1,5,3,4]=>3 [2,6,1,5,4,3]=>5 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>4 [2,6,3,4,1,5]=>4 [2,6,3,4,5,1]=>8 [2,6,3,5,1,4]=>6 [2,6,3,5,4,1]=>10 [2,6,4,1,3,5]=>3 [2,6,4,1,5,3]=>6 [2,6,4,3,1,5]=>5 [2,6,4,3,5,1]=>10 [2,6,4,5,1,3]=>8 [2,6,4,5,3,1]=>13 [2,6,5,1,3,4]=>5 [2,6,5,1,4,3]=>8 [2,6,5,3,1,4]=>8 [2,6,5,3,4,1]=>13 [2,6,5,4,1,3]=>14 [2,6,5,4,3,1]=>23 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>1 [3,1,2,5,4,6]=>1 [3,1,2,5,6,4]=>1 [3,1,2,6,4,5]=>1 [3,1,2,6,5,4]=>2 [3,1,4,2,5,6]=>1 [3,1,4,2,6,5]=>1 [3,1,4,5,2,6]=>1 [3,1,4,5,6,2]=>1 [3,1,4,6,2,5]=>1 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>1 [3,1,5,2,6,4]=>1 [3,1,5,4,2,6]=>2 [3,1,5,4,6,2]=>2 [3,1,5,6,2,4]=>2 [3,1,5,6,4,2]=>3 [3,1,6,2,4,5]=>1 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>4 [3,1,6,5,2,4]=>3 [3,1,6,5,4,2]=>5 [3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>2 [3,2,1,5,4,6]=>2 [3,2,1,5,6,4]=>2 [3,2,1,6,4,5]=>2 [3,2,1,6,5,4]=>4 [3,2,4,1,5,6]=>2 [3,2,4,1,6,5]=>2 [3,2,4,5,1,6]=>2 [3,2,4,5,6,1]=>2 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>4 [3,2,5,1,4,6]=>2 [3,2,5,1,6,4]=>2 [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]=>6 [3,2,6,1,4,5]=>2 [3,2,6,1,5,4]=>4 [3,2,6,4,1,5]=>4 [3,2,6,4,5,1]=>8 [3,2,6,5,1,4]=>6 [3,2,6,5,4,1]=>10 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>2 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>2 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>4 [3,4,2,1,5,6]=>3 [3,4,2,1,6,5]=>3 [3,4,2,5,1,6]=>3 [3,4,2,5,6,1]=>3 [3,4,2,6,1,5]=>3 [3,4,2,6,5,1]=>6 [3,4,5,1,2,6]=>3 [3,4,5,1,6,2]=>3 [3,4,5,2,1,6]=>5 [3,4,5,2,6,1]=>5 [3,4,5,6,1,2]=>5 [3,4,5,6,2,1]=>8 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>6 [3,4,6,2,1,5]=>5 [3,4,6,2,5,1]=>10 [3,4,6,5,1,2]=>8 [3,4,6,5,2,1]=>13 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>2 [3,5,1,4,2,6]=>4 [3,5,1,4,6,2]=>4 [3,5,1,6,2,4]=>4 [3,5,1,6,4,2]=>6 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>3 [3,5,2,4,1,6]=>6 [3,5,2,4,6,1]=>6 [3,5,2,6,1,4]=>6 [3,5,2,6,4,1]=>9 [3,5,4,1,2,6]=>5 [3,5,4,1,6,2]=>5 [3,5,4,2,1,6]=>8 [3,5,4,2,6,1]=>8 [3,5,4,6,1,2]=>8 [3,5,4,6,2,1]=>13 [3,5,6,1,2,4]=>5 [3,5,6,1,4,2]=>8 [3,5,6,2,1,4]=>8 [3,5,6,2,4,1]=>13 [3,5,6,4,1,2]=>14 [3,5,6,4,2,1]=>23 [3,6,1,2,4,5]=>2 [3,6,1,2,5,4]=>4 [3,6,1,4,2,5]=>4 [3,6,1,4,5,2]=>8 [3,6,1,5,2,4]=>6 [3,6,1,5,4,2]=>10 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>6 [3,6,2,4,1,5]=>6 [3,6,2,4,5,1]=>12 [3,6,2,5,1,4]=>9 [3,6,2,5,4,1]=>15 [3,6,4,1,2,5]=>5 [3,6,4,1,5,2]=>10 [3,6,4,2,1,5]=>8 [3,6,4,2,5,1]=>16 [3,6,4,5,1,2]=>13 [3,6,4,5,2,1]=>21 [3,6,5,1,2,4]=>8 [3,6,5,1,4,2]=>13 [3,6,5,2,1,4]=>13 [3,6,5,2,4,1]=>21 [3,6,5,4,1,2]=>23 [3,6,5,4,2,1]=>37 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>1 [4,1,2,5,3,6]=>1 [4,1,2,5,6,3]=>1 [4,1,2,6,3,5]=>1 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>2 [4,1,3,5,2,6]=>2 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>4 [4,1,5,2,3,6]=>2 [4,1,5,2,6,3]=>2 [4,1,5,3,2,6]=>3 [4,1,5,3,6,2]=>3 [4,1,5,6,2,3]=>3 [4,1,5,6,3,2]=>5 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>4 [4,1,6,3,2,5]=>3 [4,1,6,3,5,2]=>6 [4,1,6,5,2,3]=>5 [4,1,6,5,3,2]=>8 [4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>2 [4,2,1,5,3,6]=>2 [4,2,1,5,6,3]=>2 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>4 [4,2,3,1,5,6]=>4 [4,2,3,1,6,5]=>4 [4,2,3,5,1,6]=>4 [4,2,3,5,6,1]=>4 [4,2,3,6,1,5]=>4 [4,2,3,6,5,1]=>8 [4,2,5,1,3,6]=>4 [4,2,5,1,6,3]=>4 [4,2,5,3,1,6]=>6 [4,2,5,3,6,1]=>6 [4,2,5,6,1,3]=>6 [4,2,5,6,3,1]=>10 [4,2,6,1,3,5]=>4 [4,2,6,1,5,3]=>8 [4,2,6,3,1,5]=>6 [4,2,6,3,5,1]=>12 [4,2,6,5,1,3]=>10 [4,2,6,5,3,1]=>16 [4,3,1,2,5,6]=>3 [4,3,1,2,6,5]=>3 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>3 [4,3,1,6,2,5]=>3 [4,3,1,6,5,2]=>6 [4,3,2,1,5,6]=>5 [4,3,2,1,6,5]=>5 [4,3,2,5,1,6]=>5 [4,3,2,5,6,1]=>5 [4,3,2,6,1,5]=>5 [4,3,2,6,5,1]=>10 [4,3,5,1,2,6]=>5 [4,3,5,1,6,2]=>5 [4,3,5,2,1,6]=>8 [4,3,5,2,6,1]=>8 [4,3,5,6,1,2]=>8 [4,3,5,6,2,1]=>13 [4,3,6,1,2,5]=>5 [4,3,6,1,5,2]=>10 [4,3,6,2,1,5]=>8 [4,3,6,2,5,1]=>16 [4,3,6,5,1,2]=>13 [4,3,6,5,2,1]=>21 [4,5,1,2,3,6]=>3 [4,5,1,2,6,3]=>3 [4,5,1,3,2,6]=>5 [4,5,1,3,6,2]=>5 [4,5,1,6,2,3]=>5 [4,5,1,6,3,2]=>8 [4,5,2,1,3,6]=>5 [4,5,2,1,6,3]=>5 [4,5,2,3,1,6]=>8 [4,5,2,3,6,1]=>8 [4,5,2,6,1,3]=>8 [4,5,2,6,3,1]=>13 [4,5,3,1,2,6]=>9 [4,5,3,1,6,2]=>9 [4,5,3,2,1,6]=>14 [4,5,3,2,6,1]=>14 [4,5,3,6,1,2]=>14 [4,5,3,6,2,1]=>23 [4,5,6,1,2,3]=>9 [4,5,6,1,3,2]=>14 [4,5,6,2,1,3]=>14 [4,5,6,2,3,1]=>22 [4,5,6,3,1,2]=>22 [4,5,6,3,2,1]=>36 [4,6,1,2,3,5]=>3 [4,6,1,2,5,3]=>6 [4,6,1,3,2,5]=>5 [4,6,1,3,5,2]=>10 [4,6,1,5,2,3]=>8 [4,6,1,5,3,2]=>13 [4,6,2,1,3,5]=>5 [4,6,2,1,5,3]=>10 [4,6,2,3,1,5]=>8 [4,6,2,3,5,1]=>16 [4,6,2,5,1,3]=>13 [4,6,2,5,3,1]=>21 [4,6,3,1,2,5]=>9 [4,6,3,1,5,2]=>18 [4,6,3,2,1,5]=>14 [4,6,3,2,5,1]=>28 [4,6,3,5,1,2]=>23 [4,6,3,5,2,1]=>37 [4,6,5,1,2,3]=>14 [4,6,5,1,3,2]=>23 [4,6,5,2,1,3]=>22 [4,6,5,2,3,1]=>36 [4,6,5,3,1,2]=>36 [4,6,5,3,2,1]=>58 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>1 [5,1,2,4,3,6]=>2 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>2 [5,1,2,6,4,3]=>3 [5,1,3,2,4,6]=>2 [5,1,3,2,6,4]=>2 [5,1,3,4,2,6]=>4 [5,1,3,4,6,2]=>4 [5,1,3,6,2,4]=>4 [5,1,3,6,4,2]=>6 [5,1,4,2,3,6]=>3 [5,1,4,2,6,3]=>3 [5,1,4,3,2,6]=>5 [5,1,4,3,6,2]=>5 [5,1,4,6,2,3]=>5 [5,1,4,6,3,2]=>8 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>5 [5,1,6,3,2,4]=>5 [5,1,6,3,4,2]=>8 [5,1,6,4,2,3]=>9 [5,1,6,4,3,2]=>14 [5,2,1,3,4,6]=>2 [5,2,1,3,6,4]=>2 [5,2,1,4,3,6]=>4 [5,2,1,4,6,3]=>4 [5,2,1,6,3,4]=>4 [5,2,1,6,4,3]=>6 [5,2,3,1,4,6]=>4 [5,2,3,1,6,4]=>4 [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]=>12 [5,2,4,1,3,6]=>6 [5,2,4,1,6,3]=>6 [5,2,4,3,1,6]=>10 [5,2,4,3,6,1]=>10 [5,2,4,6,1,3]=>10 [5,2,4,6,3,1]=>16 [5,2,6,1,3,4]=>6 [5,2,6,1,4,3]=>10 [5,2,6,3,1,4]=>10 [5,2,6,3,4,1]=>16 [5,2,6,4,1,3]=>18 [5,2,6,4,3,1]=>28 [5,3,1,2,4,6]=>3 [5,3,1,2,6,4]=>3 [5,3,1,4,2,6]=>6 [5,3,1,4,6,2]=>6 [5,3,1,6,2,4]=>6 [5,3,1,6,4,2]=>9 [5,3,2,1,4,6]=>5 [5,3,2,1,6,4]=>5 [5,3,2,4,1,6]=>10 [5,3,2,4,6,1]=>10 [5,3,2,6,1,4]=>10 [5,3,2,6,4,1]=>15 [5,3,4,1,2,6]=>8 [5,3,4,1,6,2]=>8 [5,3,4,2,1,6]=>13 [5,3,4,2,6,1]=>13 [5,3,4,6,1,2]=>13 [5,3,4,6,2,1]=>21 [5,3,6,1,2,4]=>8 [5,3,6,1,4,2]=>13 [5,3,6,2,1,4]=>13 [5,3,6,2,4,1]=>21 [5,3,6,4,1,2]=>23 [5,3,6,4,2,1]=>37 [5,4,1,2,3,6]=>5 [5,4,1,2,6,3]=>5 [5,4,1,3,2,6]=>8 [5,4,1,3,6,2]=>8 [5,4,1,6,2,3]=>8 [5,4,1,6,3,2]=>13 [5,4,2,1,3,6]=>8 [5,4,2,1,6,3]=>8 [5,4,2,3,1,6]=>13 [5,4,2,3,6,1]=>13 [5,4,2,6,1,3]=>13 [5,4,2,6,3,1]=>21 [5,4,3,1,2,6]=>14 [5,4,3,1,6,2]=>14 [5,4,3,2,1,6]=>23 [5,4,3,2,6,1]=>23 [5,4,3,6,1,2]=>23 [5,4,3,6,2,1]=>37 [5,4,6,1,2,3]=>14 [5,4,6,1,3,2]=>22 [5,4,6,2,1,3]=>23 [5,4,6,2,3,1]=>36 [5,4,6,3,1,2]=>36 [5,4,6,3,2,1]=>58 [5,6,1,2,3,4]=>5 [5,6,1,2,4,3]=>8 [5,6,1,3,2,4]=>8 [5,6,1,3,4,2]=>13 [5,6,1,4,2,3]=>14 [5,6,1,4,3,2]=>23 [5,6,2,1,3,4]=>8 [5,6,2,1,4,3]=>13 [5,6,2,3,1,4]=>13 [5,6,2,3,4,1]=>21 [5,6,2,4,1,3]=>23 [5,6,2,4,3,1]=>37 [5,6,3,1,2,4]=>14 [5,6,3,1,4,2]=>23 [5,6,3,2,1,4]=>23 [5,6,3,2,4,1]=>37 [5,6,3,4,1,2]=>41 [5,6,3,4,2,1]=>65 [5,6,4,1,2,3]=>22 [5,6,4,1,3,2]=>36 [5,6,4,2,1,3]=>36 [5,6,4,2,3,1]=>58 [5,6,4,3,1,2]=>59 [5,6,4,3,2,1]=>94 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>2 [6,1,2,4,3,5]=>2 [6,1,2,4,5,3]=>4 [6,1,2,5,3,4]=>3 [6,1,2,5,4,3]=>5 [6,1,3,2,4,5]=>2 [6,1,3,2,5,4]=>4 [6,1,3,4,2,5]=>4 [6,1,3,4,5,2]=>8 [6,1,3,5,2,4]=>6 [6,1,3,5,4,2]=>10 [6,1,4,2,3,5]=>3 [6,1,4,2,5,3]=>6 [6,1,4,3,2,5]=>5 [6,1,4,3,5,2]=>10 [6,1,4,5,2,3]=>8 [6,1,4,5,3,2]=>13 [6,1,5,2,3,4]=>5 [6,1,5,2,4,3]=>8 [6,1,5,3,2,4]=>8 [6,1,5,3,4,2]=>13 [6,1,5,4,2,3]=>14 [6,1,5,4,3,2]=>23 [6,2,1,3,4,5]=>2 [6,2,1,3,5,4]=>4 [6,2,1,4,3,5]=>4 [6,2,1,4,5,3]=>8 [6,2,1,5,3,4]=>6 [6,2,1,5,4,3]=>10 [6,2,3,1,4,5]=>4 [6,2,3,1,5,4]=>8 [6,2,3,4,1,5]=>8 [6,2,3,4,5,1]=>16 [6,2,3,5,1,4]=>12 [6,2,3,5,4,1]=>20 [6,2,4,1,3,5]=>6 [6,2,4,1,5,3]=>12 [6,2,4,3,1,5]=>10 [6,2,4,3,5,1]=>20 [6,2,4,5,1,3]=>16 [6,2,4,5,3,1]=>26 [6,2,5,1,3,4]=>10 [6,2,5,1,4,3]=>16 [6,2,5,3,1,4]=>16 [6,2,5,3,4,1]=>26 [6,2,5,4,1,3]=>28 [6,2,5,4,3,1]=>46 [6,3,1,2,4,5]=>3 [6,3,1,2,5,4]=>6 [6,3,1,4,2,5]=>6 [6,3,1,4,5,2]=>12 [6,3,1,5,2,4]=>9 [6,3,1,5,4,2]=>15 [6,3,2,1,4,5]=>5 [6,3,2,1,5,4]=>10 [6,3,2,4,1,5]=>10 [6,3,2,4,5,1]=>20 [6,3,2,5,1,4]=>15 [6,3,2,5,4,1]=>25 [6,3,4,1,2,5]=>8 [6,3,4,1,5,2]=>16 [6,3,4,2,1,5]=>13 [6,3,4,2,5,1]=>26 [6,3,4,5,1,2]=>21 [6,3,4,5,2,1]=>34 [6,3,5,1,2,4]=>13 [6,3,5,1,4,2]=>21 [6,3,5,2,1,4]=>21 [6,3,5,2,4,1]=>34 [6,3,5,4,1,2]=>37 [6,3,5,4,2,1]=>60 [6,4,1,2,3,5]=>5 [6,4,1,2,5,3]=>10 [6,4,1,3,2,5]=>8 [6,4,1,3,5,2]=>16 [6,4,1,5,2,3]=>13 [6,4,1,5,3,2]=>21 [6,4,2,1,3,5]=>8 [6,4,2,1,5,3]=>16 [6,4,2,3,1,5]=>13 [6,4,2,3,5,1]=>26 [6,4,2,5,1,3]=>21 [6,4,2,5,3,1]=>34 [6,4,3,1,2,5]=>14 [6,4,3,1,5,2]=>28 [6,4,3,2,1,5]=>23 [6,4,3,2,5,1]=>46 [6,4,3,5,1,2]=>37 [6,4,3,5,2,1]=>60 [6,4,5,1,2,3]=>22 [6,4,5,1,3,2]=>36 [6,4,5,2,1,3]=>36 [6,4,5,2,3,1]=>59 [6,4,5,3,1,2]=>58 [6,4,5,3,2,1]=>94 [6,5,1,2,3,4]=>8 [6,5,1,2,4,3]=>13 [6,5,1,3,2,4]=>13 [6,5,1,3,4,2]=>21 [6,5,1,4,2,3]=>23 [6,5,1,4,3,2]=>37 [6,5,2,1,3,4]=>13 [6,5,2,1,4,3]=>21 [6,5,2,3,1,4]=>21 [6,5,2,3,4,1]=>34 [6,5,2,4,1,3]=>37 [6,5,2,4,3,1]=>60 [6,5,3,1,2,4]=>23 [6,5,3,1,4,2]=>37 [6,5,3,2,1,4]=>37 [6,5,3,2,4,1]=>60 [6,5,3,4,1,2]=>65 [6,5,3,4,2,1]=>106 [6,5,4,1,2,3]=>36 [6,5,4,1,3,2]=>58 [6,5,4,2,1,3]=>58 [6,5,4,2,3,1]=>94 [6,5,4,3,1,2]=>94 [6,5,4,3,2,1]=>153
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Description
The evaluation at 1 of the modified Kazhdan--Lusztig R polynomial (as in [1, Section 5.3]) with parameters given by the identity and the permutation.
Also the number of paths in the Bruhat order from the identity to the permutation that are increasing with respect to a given reflection ordering as defined in Björner and Brenti [1, Section 5.2].
References
[1] Björner, A., Brenti, F. Combinatorics of Coxeter groups MathSciNet:2133266
Code
def statistic(w):
    R.=QQ[]
    W = SymmetricGroup(n)
    KL = KazhdanLusztigPolynomial(W,q)
    return KL.R_tilde(W.one(),W(w)).subs(q=1)
Created
Jan 31, 2024 at 16:32 by Joel Lewis, Alejandro Morales
Updated
Jan 31, 2024 at 17:22 by Joel Lewis, Alejandro Morales