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]=>1 [3,4,2,1]=>3 [4,1,2,3]=>1 [4,1,3,2]=>2 [4,2,1,3]=>2 [4,2,3,1]=>3 [4,3,1,2]=>3 [4,3,2,1]=>8 [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]=>1 [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]=>3 [1,5,4,2,3]=>3 [1,5,4,3,2]=>8 [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]=>1 [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]=>3 [2,5,4,1,3]=>3 [2,5,4,3,1]=>8 [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]=>1 [3,4,1,5,2]=>1 [3,4,2,1,5]=>3 [3,4,2,5,1]=>3 [3,4,5,1,2]=>1 [3,4,5,2,1]=>4 [3,5,1,2,4]=>1 [3,5,1,4,2]=>2 [3,5,2,1,4]=>3 [3,5,2,4,1]=>5 [3,5,4,1,2]=>3 [3,5,4,2,1]=>11 [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]=>1 [4,1,5,3,2]=>3 [4,2,1,3,5]=>2 [4,2,1,5,3]=>2 [4,2,3,1,5]=>3 [4,2,3,5,1]=>3 [4,2,5,1,3]=>2 [4,2,5,3,1]=>5 [4,3,1,2,5]=>3 [4,3,1,5,2]=>3 [4,3,2,1,5]=>8 [4,3,2,5,1]=>8 [4,3,5,1,2]=>3 [4,3,5,2,1]=>11 [4,5,1,2,3]=>1 [4,5,1,3,2]=>3 [4,5,2,1,3]=>3 [4,5,2,3,1]=>6 [4,5,3,1,2]=>6 [4,5,3,2,1]=>20 [5,1,2,3,4]=>1 [5,1,2,4,3]=>2 [5,1,3,2,4]=>2 [5,1,3,4,2]=>3 [5,1,4,2,3]=>3 [5,1,4,3,2]=>8 [5,2,1,3,4]=>2 [5,2,1,4,3]=>4 [5,2,3,1,4]=>3 [5,2,3,4,1]=>4 [5,2,4,1,3]=>5 [5,2,4,3,1]=>11 [5,3,1,2,4]=>3 [5,3,1,4,2]=>5 [5,3,2,1,4]=>8 [5,3,2,4,1]=>11 [5,3,4,1,2]=>6 [5,3,4,2,1]=>20 [5,4,1,2,3]=>4 [5,4,1,3,2]=>11 [5,4,2,1,3]=>11 [5,4,2,3,1]=>20 [5,4,3,1,2]=>20 [5,4,3,2,1]=>62 [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]=>1 [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]=>3 [1,2,6,5,3,4]=>3 [1,2,6,5,4,3]=>8 [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]=>1 [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]=>3 [1,3,6,5,2,4]=>3 [1,3,6,5,4,2]=>8 [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]=>1 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>3 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>1 [1,4,5,6,3,2]=>4 [1,4,6,2,3,5]=>1 [1,4,6,2,5,3]=>2 [1,4,6,3,2,5]=>3 [1,4,6,3,5,2]=>5 [1,4,6,5,2,3]=>3 [1,4,6,5,3,2]=>11 [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]=>1 [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]=>3 [1,5,3,4,6,2]=>3 [1,5,3,6,2,4]=>2 [1,5,3,6,4,2]=>5 [1,5,4,2,3,6]=>3 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>8 [1,5,4,3,6,2]=>8 [1,5,4,6,2,3]=>3 [1,5,4,6,3,2]=>11 [1,5,6,2,3,4]=>1 [1,5,6,2,4,3]=>3 [1,5,6,3,2,4]=>3 [1,5,6,3,4,2]=>6 [1,5,6,4,2,3]=>6 [1,5,6,4,3,2]=>20 [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]=>3 [1,6,2,5,3,4]=>3 [1,6,2,5,4,3]=>8 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>4 [1,6,3,4,2,5]=>3 [1,6,3,4,5,2]=>4 [1,6,3,5,2,4]=>5 [1,6,3,5,4,2]=>11 [1,6,4,2,3,5]=>3 [1,6,4,2,5,3]=>5 [1,6,4,3,2,5]=>8 [1,6,4,3,5,2]=>11 [1,6,4,5,2,3]=>6 [1,6,4,5,3,2]=>20 [1,6,5,2,3,4]=>4 [1,6,5,2,4,3]=>11 [1,6,5,3,2,4]=>11 [1,6,5,3,4,2]=>20 [1,6,5,4,2,3]=>20 [1,6,5,4,3,2]=>62 [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]=>1 [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]=>3 [2,1,6,5,3,4]=>3 [2,1,6,5,4,3]=>8 [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]=>1 [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]=>3 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>8 [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]=>1 [2,4,5,1,6,3]=>1 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>1 [2,4,5,6,3,1]=>4 [2,4,6,1,3,5]=>1 [2,4,6,1,5,3]=>2 [2,4,6,3,1,5]=>3 [2,4,6,3,5,1]=>5 [2,4,6,5,1,3]=>3 [2,4,6,5,3,1]=>11 [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]=>1 [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]=>3 [2,5,3,4,6,1]=>3 [2,5,3,6,1,4]=>2 [2,5,3,6,4,1]=>5 [2,5,4,1,3,6]=>3 [2,5,4,1,6,3]=>3 [2,5,4,3,1,6]=>8 [2,5,4,3,6,1]=>8 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>11 [2,5,6,1,3,4]=>1 [2,5,6,1,4,3]=>3 [2,5,6,3,1,4]=>3 [2,5,6,3,4,1]=>6 [2,5,6,4,1,3]=>6 [2,5,6,4,3,1]=>20 [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]=>3 [2,6,1,5,3,4]=>3 [2,6,1,5,4,3]=>8 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>4 [2,6,3,4,1,5]=>3 [2,6,3,4,5,1]=>4 [2,6,3,5,1,4]=>5 [2,6,3,5,4,1]=>11 [2,6,4,1,3,5]=>3 [2,6,4,1,5,3]=>5 [2,6,4,3,1,5]=>8 [2,6,4,3,5,1]=>11 [2,6,4,5,1,3]=>6 [2,6,4,5,3,1]=>20 [2,6,5,1,3,4]=>4 [2,6,5,1,4,3]=>11 [2,6,5,3,1,4]=>11 [2,6,5,3,4,1]=>20 [2,6,5,4,1,3]=>20 [2,6,5,4,3,1]=>62 [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]=>1 [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]=>3 [3,1,6,5,2,4]=>3 [3,1,6,5,4,2]=>8 [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]=>2 [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]=>6 [3,2,6,5,1,4]=>6 [3,2,6,5,4,1]=>16 [3,4,1,2,5,6]=>1 [3,4,1,2,6,5]=>1 [3,4,1,5,2,6]=>1 [3,4,1,5,6,2]=>1 [3,4,1,6,2,5]=>1 [3,4,1,6,5,2]=>2 [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]=>1 [3,4,5,1,6,2]=>1 [3,4,5,2,1,6]=>4 [3,4,5,2,6,1]=>4 [3,4,5,6,1,2]=>1 [3,4,5,6,2,1]=>5 [3,4,6,1,2,5]=>1 [3,4,6,1,5,2]=>2 [3,4,6,2,1,5]=>4 [3,4,6,2,5,1]=>7 [3,4,6,5,1,2]=>3 [3,4,6,5,2,1]=>14 [3,5,1,2,4,6]=>1 [3,5,1,2,6,4]=>1 [3,5,1,4,2,6]=>2 [3,5,1,4,6,2]=>2 [3,5,1,6,2,4]=>1 [3,5,1,6,4,2]=>3 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>3 [3,5,2,4,1,6]=>5 [3,5,2,4,6,1]=>5 [3,5,2,6,1,4]=>3 [3,5,2,6,4,1]=>8 [3,5,4,1,2,6]=>3 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>11 [3,5,4,2,6,1]=>11 [3,5,4,6,1,2]=>3 [3,5,4,6,2,1]=>14 [3,5,6,1,2,4]=>1 [3,5,6,1,4,2]=>3 [3,5,6,2,1,4]=>4 [3,5,6,2,4,1]=>9 [3,5,6,4,1,2]=>6 [3,5,6,4,2,1]=>26 [3,6,1,2,4,5]=>1 [3,6,1,2,5,4]=>2 [3,6,1,4,2,5]=>2 [3,6,1,4,5,2]=>3 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>8 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>6 [3,6,2,4,1,5]=>5 [3,6,2,4,5,1]=>7 [3,6,2,5,1,4]=>8 [3,6,2,5,4,1]=>19 [3,6,4,1,2,5]=>3 [3,6,4,1,5,2]=>5 [3,6,4,2,1,5]=>11 [3,6,4,2,5,1]=>16 [3,6,4,5,1,2]=>6 [3,6,4,5,2,1]=>26 [3,6,5,1,2,4]=>4 [3,6,5,1,4,2]=>11 [3,6,5,2,1,4]=>15 [3,6,5,2,4,1]=>31 [3,6,5,4,1,2]=>20 [3,6,5,4,2,1]=>82 [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]=>1 [4,1,5,2,6,3]=>1 [4,1,5,3,2,6]=>3 [4,1,5,3,6,2]=>3 [4,1,5,6,2,3]=>1 [4,1,5,6,3,2]=>4 [4,1,6,2,3,5]=>1 [4,1,6,2,5,3]=>2 [4,1,6,3,2,5]=>3 [4,1,6,3,5,2]=>5 [4,1,6,5,2,3]=>3 [4,1,6,5,3,2]=>11 [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]=>3 [4,2,3,1,6,5]=>3 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>3 [4,2,3,6,1,5]=>3 [4,2,3,6,5,1]=>6 [4,2,5,1,3,6]=>2 [4,2,5,1,6,3]=>2 [4,2,5,3,1,6]=>5 [4,2,5,3,6,1]=>5 [4,2,5,6,1,3]=>2 [4,2,5,6,3,1]=>7 [4,2,6,1,3,5]=>2 [4,2,6,1,5,3]=>4 [4,2,6,3,1,5]=>5 [4,2,6,3,5,1]=>8 [4,2,6,5,1,3]=>6 [4,2,6,5,3,1]=>19 [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]=>8 [4,3,2,1,6,5]=>8 [4,3,2,5,1,6]=>8 [4,3,2,5,6,1]=>8 [4,3,2,6,1,5]=>8 [4,3,2,6,5,1]=>16 [4,3,5,1,2,6]=>3 [4,3,5,1,6,2]=>3 [4,3,5,2,1,6]=>11 [4,3,5,2,6,1]=>11 [4,3,5,6,1,2]=>3 [4,3,5,6,2,1]=>14 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>6 [4,3,6,2,1,5]=>11 [4,3,6,2,5,1]=>19 [4,3,6,5,1,2]=>9 [4,3,6,5,2,1]=>39 [4,5,1,2,3,6]=>1 [4,5,1,2,6,3]=>1 [4,5,1,3,2,6]=>3 [4,5,1,3,6,2]=>3 [4,5,1,6,2,3]=>1 [4,5,1,6,3,2]=>4 [4,5,2,1,3,6]=>3 [4,5,2,1,6,3]=>3 [4,5,2,3,1,6]=>6 [4,5,2,3,6,1]=>6 [4,5,2,6,1,3]=>3 [4,5,2,6,3,1]=>9 [4,5,3,1,2,6]=>6 [4,5,3,1,6,2]=>6 [4,5,3,2,1,6]=>20 [4,5,3,2,6,1]=>20 [4,5,3,6,1,2]=>6 [4,5,3,6,2,1]=>26 [4,5,6,1,2,3]=>1 [4,5,6,1,3,2]=>4 [4,5,6,2,1,3]=>4 [4,5,6,2,3,1]=>10 [4,5,6,3,1,2]=>10 [4,5,6,3,2,1]=>40 [4,6,1,2,3,5]=>1 [4,6,1,2,5,3]=>2 [4,6,1,3,5,2]=>5 [4,6,1,5,2,3]=>3 [4,6,1,5,3,2]=>11 [4,6,2,1,3,5]=>3 [4,6,2,1,5,3]=>6 [4,6,2,3,1,5]=>6 [4,6,2,3,5,1]=>9 [4,6,2,5,1,3]=>8 [4,6,2,5,3,1]=>22 [4,6,3,1,2,5]=>6 [4,6,3,1,5,2]=>11 [4,6,3,2,1,5]=>20 [4,6,3,2,5,1]=>31 [6,2,1,4,3,5]=>4 [6,4,2,1,3,5]=>11
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Description
The number of connected components of short braid edges in the graph of braid moves of a permutation.
Given a permutation $\pi$, let $\operatorname{Red}(\pi)$ denote the set of reduced words for $\pi$ in terms of simple transpositions $s_i = (i,i+1)$. We now say that two reduced words are connected by a short braid move if they are obtained from each other by a modification of the form $s_i s_j \leftrightarrow s_j s_i$ for $|i-j| > 1$ as a consecutive subword of a reduced word.
For example, the two reduced words $s_1s_3s_2$ and $s_3s_1s_2$ for
$$(1243) = (12)(34)(23) = (34)(12)(23)$$
share an edge because they are obtained from each other by interchanging $s_1s_3 \leftrightarrow s_3s_1$.
This statistic counts the number connected components of such short braid moves among all reduced words.
Code
def short_braid_move_graph(pi):
    V = [ tuple(w) for w in pi.reduced_words() ]
    is_edge = lambda w1,w2: w1 != w2 and any( w1[:i] == w2[:i] and w1[i+2:] == w2[i+2:] for i in range(len(w1)-1) )
    return Graph([V,is_edge])

def statistic(pi):
    return len( short_braid_move_graph(pi).connected_components() )
Created
Jul 03, 2017 at 16:58 by Christian Stump
Updated
Dec 25, 2017 at 17:32 by Martin Rubey