edit this statistic or download as text // json
Identifier
Values
=>
[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]=>1 [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]=>1 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>1 [2,4,3,1]=>1 [3,1,2,4]=>1 [3,1,4,2]=>1 [3,2,1,4]=>1 [3,2,4,1]=>1 [3,4,1,2]=>1 [3,4,2,1]=>1 [4,1,2,3]=>1 [4,1,3,2]=>1 [4,2,1,3]=>1 [4,2,3,1]=>1 [4,3,1,2]=>1 [4,3,2,1]=>1 [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]=>1 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [1,3,4,2,5]=>1 [1,3,4,5,2]=>1 [1,3,5,2,4]=>1 [1,3,5,4,2]=>1 [1,4,2,3,5]=>1 [1,4,2,5,3]=>1 [1,4,3,2,5]=>1 [1,4,3,5,2]=>1 [1,4,5,2,3]=>1 [1,4,5,3,2]=>1 [1,5,2,3,4]=>1 [1,5,2,4,3]=>1 [1,5,3,2,4]=>1 [1,5,3,4,2]=>1 [1,5,4,2,3]=>1 [1,5,4,3,2]=>1 [2,1,3,4,5]=>1 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>2 [2,1,5,3,4]=>2 [2,1,5,4,3]=>3 [2,3,1,4,5]=>1 [2,3,1,5,4]=>2 [2,3,4,1,5]=>1 [2,3,4,5,1]=>1 [2,3,5,1,4]=>1 [2,3,5,4,1]=>1 [2,4,1,3,5]=>1 [2,4,1,5,3]=>2 [2,4,3,1,5]=>1 [2,4,3,5,1]=>1 [2,4,5,1,3]=>1 [2,4,5,3,1]=>1 [2,5,1,3,4]=>1 [2,5,1,4,3]=>2 [2,5,3,1,4]=>1 [2,5,3,4,1]=>1 [2,5,4,1,3]=>1 [2,5,4,3,1]=>1 [3,1,2,4,5]=>1 [3,1,2,5,4]=>2 [3,1,4,2,5]=>1 [3,1,4,5,2]=>1 [3,1,5,2,4]=>2 [3,1,5,4,2]=>2 [3,2,1,4,5]=>1 [3,2,1,5,4]=>3 [3,2,4,1,5]=>1 [3,2,4,5,1]=>1 [3,2,5,1,4]=>2 [3,2,5,4,1]=>2 [3,4,1,2,5]=>1 [3,4,1,5,2]=>1 [3,4,2,1,5]=>1 [3,4,2,5,1]=>1 [3,4,5,1,2]=>1 [3,4,5,2,1]=>1 [3,5,1,2,4]=>1 [3,5,1,4,2]=>1 [3,5,2,1,4]=>1 [3,5,2,4,1]=>1 [3,5,4,1,2]=>1 [3,5,4,2,1]=>1 [4,1,2,3,5]=>1 [4,1,2,5,3]=>1 [4,1,3,2,5]=>1 [4,1,3,5,2]=>1 [4,1,5,2,3]=>1 [4,1,5,3,2]=>1 [4,2,1,3,5]=>1 [4,2,1,5,3]=>2 [4,2,3,1,5]=>1 [4,2,3,5,1]=>1 [4,2,5,1,3]=>1 [4,2,5,3,1]=>1 [4,3,1,2,5]=>1 [4,3,1,5,2]=>1 [4,3,2,1,5]=>1 [4,3,2,5,1]=>1 [4,3,5,1,2]=>1 [4,3,5,2,1]=>1 [4,5,1,2,3]=>1 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>1 [4,5,3,1,2]=>1 [4,5,3,2,1]=>1 [5,1,2,3,4]=>1 [5,1,2,4,3]=>1 [5,1,3,2,4]=>1 [5,1,3,4,2]=>1 [5,1,4,2,3]=>1 [5,1,4,3,2]=>1 [5,2,1,3,4]=>1 [5,2,1,4,3]=>2 [5,2,3,1,4]=>1 [5,2,3,4,1]=>1 [5,2,4,1,3]=>1 [5,2,4,3,1]=>1 [5,3,1,2,4]=>1 [5,3,1,4,2]=>1 [5,3,2,1,4]=>1 [5,3,2,4,1]=>1 [5,3,4,1,2]=>1 [5,3,4,2,1]=>1 [5,4,1,2,3]=>1 [5,4,1,3,2]=>1 [5,4,2,1,3]=>1 [5,4,2,3,1]=>1 [5,4,3,1,2]=>1 [5,4,3,2,1]=>1 [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]=>1 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>2 [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]=>1 [1,2,5,3,4,6]=>1 [1,2,5,3,6,4]=>1 [1,2,5,4,3,6]=>1 [1,2,5,4,6,3]=>1 [1,2,5,6,3,4]=>1 [1,2,5,6,4,3]=>1 [1,2,6,3,4,5]=>1 [1,2,6,3,5,4]=>1 [1,2,6,4,3,5]=>1 [1,2,6,4,5,3]=>1 [1,2,6,5,3,4]=>1 [1,2,6,5,4,3]=>1 [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]=>2 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>3 [1,3,4,2,5,6]=>1 [1,3,4,2,6,5]=>2 [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]=>1 [1,3,5,2,4,6]=>1 [1,3,5,2,6,4]=>2 [1,3,5,4,2,6]=>1 [1,3,5,4,6,2]=>1 [1,3,5,6,2,4]=>1 [1,3,5,6,4,2]=>1 [1,3,6,2,4,5]=>1 [1,3,6,2,5,4]=>2 [1,3,6,4,2,5]=>1 [1,3,6,4,5,2]=>1 [1,3,6,5,2,4]=>1 [1,3,6,5,4,2]=>1 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>2 [1,4,2,5,3,6]=>1 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>2 [1,4,3,2,5,6]=>1 [1,4,3,2,6,5]=>3 [1,4,3,5,2,6]=>1 [1,4,3,5,6,2]=>1 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>2 [1,4,5,2,3,6]=>1 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>1 [1,4,5,3,6,2]=>1 [1,4,5,6,2,3]=>1 [1,4,5,6,3,2]=>1 [1,4,6,2,3,5]=>1 [1,4,6,2,5,3]=>1 [1,4,6,3,2,5]=>1 [1,4,6,3,5,2]=>1 [1,4,6,5,2,3]=>1 [1,4,6,5,3,2]=>1 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>1 [1,5,2,4,3,6]=>1 [1,5,2,4,6,3]=>1 [1,5,2,6,3,4]=>1 [1,5,2,6,4,3]=>1 [1,5,3,2,4,6]=>1 [1,5,3,2,6,4]=>2 [1,5,3,4,2,6]=>1 [1,5,3,4,6,2]=>1 [1,5,3,6,2,4]=>1 [1,5,3,6,4,2]=>1 [1,5,4,2,3,6]=>1 [1,5,4,2,6,3]=>1 [1,5,4,3,2,6]=>1 [1,5,4,3,6,2]=>1 [1,5,4,6,2,3]=>1 [1,5,4,6,3,2]=>1 [1,5,6,2,3,4]=>1 [1,5,6,2,4,3]=>1 [1,5,6,3,2,4]=>1 [1,5,6,3,4,2]=>1 [1,5,6,4,2,3]=>1 [1,5,6,4,3,2]=>1 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>1 [1,6,2,4,3,5]=>1 [1,6,2,4,5,3]=>1 [1,6,2,5,3,4]=>1 [1,6,2,5,4,3]=>1 [1,6,3,2,4,5]=>1 [1,6,3,2,5,4]=>2 [1,6,3,4,2,5]=>1 [1,6,3,4,5,2]=>1 [1,6,3,5,2,4]=>1 [1,6,3,5,4,2]=>1 [1,6,4,2,3,5]=>1 [1,6,4,2,5,3]=>1 [1,6,4,3,2,5]=>1 [1,6,4,3,5,2]=>1 [1,6,4,5,2,3]=>1 [1,6,4,5,3,2]=>1 [1,6,5,2,3,4]=>1 [1,6,5,2,4,3]=>1 [1,6,5,3,2,4]=>1 [1,6,5,3,4,2]=>1 [1,6,5,4,2,3]=>1 [1,6,5,4,3,2]=>1 [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]=>2 [2,1,3,6,4,5]=>2 [2,1,3,6,5,4]=>3 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>4 [2,1,4,5,3,6]=>2 [2,1,4,5,6,3]=>2 [2,1,4,6,3,5]=>3 [2,1,4,6,5,3]=>3 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>3 [2,1,5,4,3,6]=>3 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>3 [2,1,6,3,4,5]=>2 [2,1,6,3,5,4]=>3 [2,1,6,4,3,5]=>3 [2,1,6,4,5,3]=>3 [2,1,6,5,3,4]=>3 [2,1,6,5,4,3]=>4 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>2 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>3 [2,3,1,6,4,5]=>2 [2,3,1,6,5,4]=>4 [2,3,4,1,5,6]=>1 [2,3,4,1,6,5]=>2 [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]=>1 [2,3,5,1,4,6]=>1 [2,3,5,1,6,4]=>2 [2,3,5,4,1,6]=>1 [2,3,5,4,6,1]=>1 [2,3,5,6,1,4]=>1 [2,3,5,6,4,1]=>1 [2,3,6,1,4,5]=>1 [2,3,6,1,5,4]=>2 [2,3,6,4,1,5]=>1 [2,3,6,4,5,1]=>1 [2,3,6,5,1,4]=>1 [2,3,6,5,4,1]=>1 [2,4,1,3,5,6]=>1 [2,4,1,3,6,5]=>3 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>2 [2,4,1,6,3,5]=>3 [2,4,1,6,5,3]=>4 [2,4,3,1,5,6]=>1 [2,4,3,1,6,5]=>3 [2,4,3,5,1,6]=>1 [2,4,3,5,6,1]=>1 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>2 [2,4,5,1,3,6]=>1 [2,4,5,1,6,3]=>2 [2,4,5,3,1,6]=>1 [2,4,5,3,6,1]=>1 [2,4,5,6,1,3]=>1 [2,4,5,6,3,1]=>1 [2,4,6,1,3,5]=>1 [2,4,6,1,5,3]=>2 [2,4,6,3,1,5]=>1 [2,4,6,3,5,1]=>1 [2,4,6,5,1,3]=>1 [2,4,6,5,3,1]=>1 [2,5,1,3,4,6]=>1 [2,5,1,3,6,4]=>2 [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]=>1 [2,5,3,1,6,4]=>2 [2,5,3,4,1,6]=>1 [2,5,3,4,6,1]=>1 [2,5,3,6,1,4]=>1 [2,5,3,6,4,1]=>1 [2,5,4,1,3,6]=>1 [2,5,4,1,6,3]=>2 [2,5,4,3,1,6]=>1 [2,5,4,3,6,1]=>1 [2,5,4,6,1,3]=>1 [2,5,4,6,3,1]=>1 [2,5,6,1,3,4]=>1 [2,5,6,1,4,3]=>2 [2,5,6,3,1,4]=>1 [2,5,6,3,4,1]=>1 [2,5,6,4,1,3]=>1 [2,5,6,4,3,1]=>1 [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]=>2 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>3 [2,6,3,1,4,5]=>1 [2,6,3,1,5,4]=>2 [2,6,3,4,1,5]=>1 [2,6,3,4,5,1]=>1 [2,6,3,5,1,4]=>1 [2,6,3,5,4,1]=>1 [2,6,4,1,3,5]=>1 [2,6,4,1,5,3]=>2 [2,6,4,3,1,5]=>1 [2,6,4,3,5,1]=>1 [2,6,4,5,1,3]=>1 [2,6,4,5,3,1]=>1 [2,6,5,1,3,4]=>1 [2,6,5,1,4,3]=>2 [2,6,5,3,1,4]=>1 [2,6,5,3,4,1]=>1 [2,6,5,4,1,3]=>1 [2,6,5,4,3,1]=>1 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>2 [3,1,2,5,4,6]=>2 [3,1,2,5,6,4]=>2 [3,1,2,6,4,5]=>3 [3,1,2,6,5,4]=>4 [3,1,4,2,5,6]=>1 [3,1,4,2,6,5]=>3 [3,1,4,5,2,6]=>1 [3,1,4,5,6,2]=>1 [3,1,4,6,2,5]=>2 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>2 [3,1,5,2,6,4]=>3 [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]=>2 [3,1,6,2,4,5]=>2 [3,1,6,2,5,4]=>4 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>2 [3,1,6,5,2,4]=>3 [3,1,6,5,4,2]=>3 [3,2,1,4,5,6]=>1 [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]=>8 [3,2,4,1,5,6]=>1 [3,2,4,1,6,5]=>3 [3,2,4,5,1,6]=>1 [3,2,4,5,6,1]=>1 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>2 [3,2,5,1,4,6]=>2 [3,2,5,1,6,4]=>4 [3,2,5,4,1,6]=>2 [3,2,5,4,6,1]=>2 [3,2,5,6,1,4]=>2 [3,2,5,6,4,1]=>2 [3,2,6,1,4,5]=>2 [3,2,6,1,5,4]=>5 [3,2,6,4,1,5]=>2 [3,2,6,4,5,1]=>2 [3,2,6,5,1,4]=>3 [3,2,6,5,4,1]=>3 [3,4,1,2,5,6]=>1 [3,4,1,2,6,5]=>2 [3,4,1,5,2,6]=>1 [3,4,1,5,6,2]=>1 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>2 [3,4,2,1,5,6]=>1 [3,4,2,1,6,5]=>3 [3,4,2,5,1,6]=>1 [3,4,2,5,6,1]=>1 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>2 [3,4,5,1,2,6]=>1 [3,4,5,1,6,2]=>1 [3,4,5,2,1,6]=>1 [3,4,5,2,6,1]=>1 [3,4,5,6,1,2]=>1 [3,4,5,6,2,1]=>1 [3,4,6,1,2,5]=>1 [3,4,6,1,5,2]=>1 [3,4,6,2,1,5]=>1 [3,4,6,2,5,1]=>1 [3,4,6,5,1,2]=>1 [3,4,6,5,2,1]=>1 [3,5,1,2,4,6]=>1 [3,5,1,2,6,4]=>2 [3,5,1,4,2,6]=>1 [3,5,1,4,6,2]=>1 [3,5,1,6,2,4]=>2 [3,5,1,6,4,2]=>2 [3,5,2,1,4,6]=>1 [3,5,2,1,6,4]=>3 [3,5,2,4,1,6]=>1 [3,5,2,4,6,1]=>1 [3,5,2,6,1,4]=>2 [3,5,2,6,4,1]=>2 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>1 [3,5,4,2,1,6]=>1 [3,5,4,2,6,1]=>1 [3,5,4,6,1,2]=>1 [3,5,4,6,2,1]=>1 [3,5,6,1,2,4]=>1 [3,5,6,1,4,2]=>1 [3,5,6,2,1,4]=>1 [3,5,6,2,4,1]=>1 [3,5,6,4,1,2]=>1 [3,5,6,4,2,1]=>1 [3,6,1,2,4,5]=>1 [3,6,1,2,5,4]=>2 [3,6,1,4,2,5]=>1 [3,6,1,4,5,2]=>1 [3,6,1,5,2,4]=>2 [3,6,1,5,4,2]=>2 [3,6,2,1,4,5]=>1 [3,6,2,1,5,4]=>3 [3,6,2,4,1,5]=>1 [3,6,2,4,5,1]=>1 [3,6,2,5,1,4]=>2 [3,6,2,5,4,1]=>2 [3,6,4,1,2,5]=>1 [3,6,4,1,5,2]=>1 [3,6,4,2,1,5]=>1 [3,6,4,2,5,1]=>1 [3,6,4,5,1,2]=>1 [3,6,4,5,2,1]=>1 [3,6,5,1,2,4]=>1 [3,6,5,1,4,2]=>1 [3,6,5,2,1,4]=>1 [3,6,5,2,4,1]=>1 [3,6,5,4,1,2]=>1 [3,6,5,4,2,1]=>1 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>2 [4,1,2,5,3,6]=>1 [4,1,2,5,6,3]=>1 [4,1,2,6,3,5]=>2 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>3 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>1 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>2 [4,1,5,2,3,6]=>1 [4,1,5,2,6,3]=>1 [4,1,5,3,2,6]=>1 [4,1,5,3,6,2]=>1 [4,1,5,6,2,3]=>1 [4,1,5,6,3,2]=>1 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>2 [4,1,6,3,2,5]=>2 [4,1,6,3,5,2]=>2 [4,1,6,5,2,3]=>2 [4,1,6,5,3,2]=>2 [4,2,1,3,5,6]=>1 [4,2,1,3,6,5]=>3 [4,2,1,5,3,6]=>2 [4,2,1,5,6,3]=>2 [4,2,1,6,3,5]=>4 [4,2,1,6,5,3]=>5 [4,2,3,1,5,6]=>1 [4,2,3,1,6,5]=>3 [4,2,3,5,1,6]=>1 [4,2,3,5,6,1]=>1 [4,2,3,6,1,5]=>2 [4,2,3,6,5,1]=>2 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>2 [4,2,5,3,1,6]=>1 [4,2,5,3,6,1]=>1 [4,2,5,6,1,3]=>1 [4,2,5,6,3,1]=>1 [4,2,6,1,3,5]=>2 [4,2,6,1,5,3]=>4 [4,2,6,3,1,5]=>2 [4,2,6,3,5,1]=>2 [4,2,6,5,1,3]=>2 [4,2,6,5,3,1]=>2 [4,3,1,2,5,6]=>1 [4,3,1,2,6,5]=>3 [4,3,1,5,2,6]=>1 [4,3,1,5,6,2]=>1 [4,3,1,6,2,5]=>3 [4,3,1,6,5,2]=>3 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>4 [4,3,2,5,1,6]=>1 [4,3,2,5,6,1]=>1 [4,3,2,6,1,5]=>3 [4,3,2,6,5,1]=>3 [4,3,5,1,2,6]=>1 [4,3,5,1,6,2]=>1 [4,3,5,2,1,6]=>1 [4,3,5,2,6,1]=>1 [4,3,5,6,1,2]=>1 [4,3,5,6,2,1]=>1 [4,3,6,1,2,5]=>2 [4,3,6,1,5,2]=>2 [4,3,6,2,1,5]=>2 [4,3,6,2,5,1]=>2 [4,3,6,5,1,2]=>2 [4,3,6,5,2,1]=>2 [4,5,1,2,3,6]=>1 [4,5,1,2,6,3]=>1 [4,5,1,3,2,6]=>1 [4,5,1,3,6,2]=>1 [4,5,1,6,2,3]=>1 [4,5,1,6,3,2]=>1 [4,5,2,1,3,6]=>1 [4,5,2,1,6,3]=>2 [4,5,2,3,1,6]=>1 [4,5,2,3,6,1]=>1 [4,5,2,6,1,3]=>1 [4,5,2,6,3,1]=>1 [4,5,3,1,2,6]=>1 [4,5,3,1,6,2]=>1 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>1 [4,5,3,6,1,2]=>1 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>1 [4,5,6,1,3,2]=>1 [4,5,6,2,1,3]=>1 [4,5,6,2,3,1]=>1 [4,5,6,3,1,2]=>1 [4,5,6,3,2,1]=>1 [4,6,1,2,3,5]=>1 [4,6,1,2,5,3]=>1 [4,6,1,3,2,5]=>1 [4,6,1,3,5,2]=>1 [4,6,1,5,2,3]=>1 [4,6,1,5,3,2]=>1 [4,6,2,1,3,5]=>1 [4,6,2,1,5,3]=>2 [4,6,2,3,1,5]=>1 [4,6,2,3,5,1]=>1 [4,6,2,5,1,3]=>1 [4,6,2,5,3,1]=>1 [4,6,3,1,2,5]=>1 [4,6,3,1,5,2]=>1 [4,6,3,2,1,5]=>1 [4,6,3,2,5,1]=>1 [4,6,3,5,1,2]=>1 [4,6,3,5,2,1]=>1 [4,6,5,1,2,3]=>1 [4,6,5,1,3,2]=>1 [4,6,5,2,1,3]=>1 [4,6,5,2,3,1]=>1 [4,6,5,3,1,2]=>1 [4,6,5,3,2,1]=>1 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>1 [5,1,2,4,3,6]=>1 [5,1,2,4,6,3]=>1 [5,1,2,6,3,4]=>1 [5,1,2,6,4,3]=>1 [5,1,3,2,4,6]=>1 [5,1,3,2,6,4]=>2 [5,1,3,4,2,6]=>1 [5,1,3,4,6,2]=>1 [5,1,3,6,2,4]=>1 [5,1,3,6,4,2]=>1 [5,1,4,2,3,6]=>1 [5,1,4,2,6,3]=>1 [5,1,4,3,2,6]=>1 [5,1,4,3,6,2]=>1 [5,1,4,6,2,3]=>1 [5,1,4,6,3,2]=>1 [5,1,6,2,3,4]=>1 [5,1,6,2,4,3]=>1 [5,1,6,3,2,4]=>1 [5,1,6,3,4,2]=>1 [5,1,6,4,2,3]=>1 [5,1,6,4,3,2]=>1 [5,2,1,3,4,6]=>1 [5,2,1,3,6,4]=>2 [5,2,1,4,3,6]=>2 [5,2,1,4,6,3]=>2 [5,2,1,6,3,4]=>2 [5,2,1,6,4,3]=>3 [5,2,3,1,4,6]=>1 [5,2,3,1,6,4]=>2 [5,2,3,4,1,6]=>1 [5,2,3,4,6,1]=>1 [5,2,3,6,1,4]=>1 [5,2,3,6,4,1]=>1 [5,2,4,1,3,6]=>1 [5,2,4,1,6,3]=>2 [5,2,4,3,1,6]=>1 [5,2,4,3,6,1]=>1 [5,2,4,6,1,3]=>1 [5,2,4,6,3,1]=>1 [5,2,6,1,3,4]=>1 [5,2,6,1,4,3]=>2 [5,2,6,3,1,4]=>1 [5,2,6,3,4,1]=>1 [5,2,6,4,1,3]=>1 [5,2,6,4,3,1]=>1 [5,3,1,2,4,6]=>1 [5,3,1,2,6,4]=>2 [5,3,1,4,2,6]=>1 [5,3,1,4,6,2]=>1 [5,3,1,6,2,4]=>2 [5,3,1,6,4,2]=>2 [5,3,2,1,4,6]=>1 [5,3,2,1,6,4]=>3 [5,3,2,4,1,6]=>1 [5,3,2,4,6,1]=>1 [5,3,2,6,1,4]=>2 [5,3,2,6,4,1]=>2 [5,3,4,1,2,6]=>1 [5,3,4,1,6,2]=>1 [5,3,4,2,1,6]=>1 [5,3,4,2,6,1]=>1 [5,3,4,6,1,2]=>1 [5,3,4,6,2,1]=>1 [5,3,6,1,2,4]=>1 [5,3,6,1,4,2]=>1 [5,3,6,2,1,4]=>1 [5,3,6,2,4,1]=>1 [5,3,6,4,1,2]=>1 [5,3,6,4,2,1]=>1 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>1 [5,4,1,3,2,6]=>1 [5,4,1,3,6,2]=>1 [5,4,1,6,2,3]=>1 [5,4,1,6,3,2]=>1 [5,4,2,1,3,6]=>1 [5,4,2,1,6,3]=>2 [5,4,2,3,1,6]=>1 [5,4,2,3,6,1]=>1 [5,4,2,6,1,3]=>1 [5,4,2,6,3,1]=>1 [5,4,3,1,2,6]=>1 [5,4,3,1,6,2]=>1 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>1 [5,4,3,6,1,2]=>1 [5,4,3,6,2,1]=>1 [5,4,6,1,2,3]=>1 [5,4,6,1,3,2]=>1 [5,4,6,2,1,3]=>1 [5,4,6,2,3,1]=>1 [5,4,6,3,1,2]=>1 [5,4,6,3,2,1]=>1 [5,6,1,2,3,4]=>1 [5,6,1,2,4,3]=>1 [5,6,1,3,2,4]=>1 [5,6,1,3,4,2]=>1 [5,6,1,4,2,3]=>1 [5,6,1,4,3,2]=>1 [5,6,2,1,3,4]=>1 [5,6,2,1,4,3]=>2 [5,6,2,3,1,4]=>1 [5,6,2,3,4,1]=>1 [5,6,2,4,1,3]=>1 [5,6,2,4,3,1]=>1 [5,6,3,1,2,4]=>1 [5,6,3,1,4,2]=>1 [5,6,3,2,1,4]=>1 [5,6,3,2,4,1]=>1 [5,6,3,4,1,2]=>1 [5,6,3,4,2,1]=>1 [5,6,4,1,2,3]=>1 [5,6,4,1,3,2]=>1 [5,6,4,2,1,3]=>1 [5,6,4,2,3,1]=>1 [5,6,4,3,1,2]=>1 [5,6,4,3,2,1]=>1 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>1 [6,1,2,4,3,5]=>1 [6,1,2,4,5,3]=>1 [6,1,2,5,3,4]=>1 [6,1,2,5,4,3]=>1 [6,1,3,2,4,5]=>1 [6,1,3,2,5,4]=>2 [6,1,3,4,2,5]=>1 [6,1,3,4,5,2]=>1 [6,1,3,5,2,4]=>1 [6,1,3,5,4,2]=>1 [6,1,4,2,3,5]=>1 [6,1,4,2,5,3]=>1 [6,1,4,3,2,5]=>1 [6,1,4,3,5,2]=>1 [6,1,4,5,2,3]=>1 [6,1,4,5,3,2]=>1 [6,1,5,2,3,4]=>1 [6,1,5,2,4,3]=>1 [6,1,5,3,2,4]=>1 [6,1,5,3,4,2]=>1 [6,1,5,4,2,3]=>1 [6,1,5,4,3,2]=>1 [6,2,1,3,4,5]=>1 [6,2,1,3,5,4]=>2 [6,2,1,4,3,5]=>2 [6,2,1,4,5,3]=>2 [6,2,1,5,3,4]=>2 [6,2,1,5,4,3]=>3 [6,2,3,1,4,5]=>1 [6,2,3,1,5,4]=>2 [6,2,3,4,1,5]=>1 [6,2,3,4,5,1]=>1 [6,2,3,5,1,4]=>1 [6,2,3,5,4,1]=>1 [6,2,4,1,3,5]=>1 [6,2,4,1,5,3]=>2 [6,2,4,3,1,5]=>1 [6,2,4,3,5,1]=>1 [6,2,4,5,1,3]=>1 [6,2,4,5,3,1]=>1 [6,2,5,1,3,4]=>1 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>1 [6,2,5,3,4,1]=>1 [6,2,5,4,1,3]=>1 [6,2,5,4,3,1]=>1 [6,3,1,2,4,5]=>1 [6,3,1,2,5,4]=>2 [6,3,1,4,2,5]=>1 [6,3,1,4,5,2]=>1 [6,3,1,5,2,4]=>2 [6,3,1,5,4,2]=>2 [6,3,2,1,4,5]=>1 [6,3,2,1,5,4]=>3 [6,3,2,4,1,5]=>1 [6,3,2,4,5,1]=>1 [6,3,2,5,1,4]=>2 [6,3,2,5,4,1]=>2 [6,3,4,1,2,5]=>1 [6,3,4,1,5,2]=>1 [6,3,4,2,1,5]=>1 [6,3,4,2,5,1]=>1 [6,3,4,5,1,2]=>1 [6,3,4,5,2,1]=>1 [6,3,5,1,2,4]=>1 [6,3,5,1,4,2]=>1 [6,3,5,2,1,4]=>1 [6,3,5,2,4,1]=>1 [6,3,5,4,1,2]=>1 [6,3,5,4,2,1]=>1 [6,4,1,2,3,5]=>1 [6,4,1,2,5,3]=>1 [6,4,1,3,2,5]=>1 [6,4,1,3,5,2]=>1 [6,4,1,5,2,3]=>1 [6,4,1,5,3,2]=>1 [6,4,2,1,3,5]=>1 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>1 [6,4,2,3,5,1]=>1 [6,4,2,5,1,3]=>1 [6,4,2,5,3,1]=>1 [6,4,3,1,2,5]=>1 [6,4,3,1,5,2]=>1 [6,4,3,2,1,5]=>1 [6,4,3,2,5,1]=>1 [6,4,3,5,1,2]=>1 [6,4,3,5,2,1]=>1 [6,4,5,1,2,3]=>1 [6,4,5,1,3,2]=>1 [6,4,5,2,1,3]=>1 [6,4,5,2,3,1]=>1 [6,4,5,3,1,2]=>1 [6,4,5,3,2,1]=>1 [6,5,1,2,3,4]=>1 [6,5,1,2,4,3]=>1 [6,5,1,3,2,4]=>1 [6,5,1,3,4,2]=>1 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>1 [6,5,2,1,3,4]=>1 [6,5,2,1,4,3]=>2 [6,5,2,3,1,4]=>1 [6,5,2,3,4,1]=>1 [6,5,2,4,1,3]=>1 [6,5,2,4,3,1]=>1 [6,5,3,1,2,4]=>1 [6,5,3,1,4,2]=>1 [6,5,3,2,1,4]=>1 [6,5,3,2,4,1]=>1 [6,5,3,4,1,2]=>1 [6,5,3,4,2,1]=>1 [6,5,4,1,2,3]=>1 [6,5,4,1,3,2]=>1 [6,5,4,2,1,3]=>1 [6,5,4,2,3,1]=>1 [6,5,4,3,1,2]=>1 [6,5,4,3,2,1]=>1 [1,4,3,2,7,6,5]=>8 [1,4,3,7,2,6,5]=>5 [1,5,3,2,7,6,4]=>5 [2,1,4,3,6,7,5]=>5 [2,1,4,3,7,5,6]=>5 [2,1,4,3,7,6,5]=>8 [2,1,4,5,3,7,6]=>5 [2,1,4,6,3,7,5]=>5 [2,1,4,7,3,6,5]=>6 [2,1,5,3,4,7,6]=>5 [2,1,5,3,7,4,6]=>5 [2,1,5,3,7,6,4]=>6 [2,1,5,4,3,7,6]=>8 [2,1,5,4,7,3,6]=>6 [2,1,5,4,7,6,3]=>6 [2,1,6,4,3,7,5]=>6 [2,1,7,4,3,6,5]=>6 [2,1,7,6,5,4,3]=>5 [2,3,1,5,4,7,6]=>5 [2,3,1,5,7,6,4]=>5 [2,3,1,6,5,7,4]=>5 [2,3,1,6,7,5,4]=>5 [2,3,1,7,5,6,4]=>5 [2,3,1,7,6,5,4]=>7 [2,3,5,1,7,6,4]=>5 [2,4,1,3,7,6,5]=>8 [2,4,1,5,3,7,6]=>5 [2,4,1,6,3,7,5]=>6 [2,4,1,6,7,5,3]=>5 [2,4,1,7,3,6,5]=>7 [2,4,1,7,6,3,5]=>6 [2,4,1,7,6,5,3]=>7 [2,4,3,1,6,7,5]=>5 [2,4,3,1,7,6,5]=>9 [2,4,3,7,1,6,5]=>5 [2,5,1,3,7,6,4]=>5 [2,5,1,4,3,7,6]=>6 [2,5,1,4,7,3,6]=>5 [2,5,1,4,7,6,3]=>5 [2,5,1,7,3,6,4]=>5 [2,5,1,7,4,3,6]=>5 [2,5,1,7,4,6,3]=>5 [2,5,1,7,6,4,3]=>6 [2,5,3,1,7,6,4]=>7 [2,5,4,1,7,3,6]=>5 [2,5,4,1,7,6,3]=>6 [3,1,2,5,4,7,6]=>5 [3,1,2,7,4,6,5]=>5 [3,1,2,7,5,4,6]=>5 [3,1,2,7,5,6,4]=>5 [3,1,2,7,6,4,5]=>5 [3,1,2,7,6,5,4]=>7 [3,1,4,2,7,6,5]=>8 [3,1,4,7,2,6,5]=>5 [3,1,5,2,4,7,6]=>5 [3,1,5,2,7,4,6]=>6 [3,1,5,2,7,6,4]=>7 [3,1,5,4,2,7,6]=>6 [3,1,5,7,2,6,4]=>5 [3,1,6,2,7,5,4]=>6 [3,1,6,4,2,7,5]=>5 [3,1,6,5,2,7,4]=>5 [3,1,7,2,6,4,5]=>5 [3,1,7,2,6,5,4]=>7 [3,1,7,4,2,6,5]=>5 [3,1,7,5,2,6,4]=>5 [3,1,7,6,2,5,4]=>6 [3,2,1,4,7,6,5]=>8 [3,2,1,5,4,7,6]=>8 [3,2,1,5,7,4,6]=>8 [3,2,1,5,7,6,4]=>9 [3,2,1,6,4,7,5]=>8 [3,2,1,6,5,4,7]=>8 [3,2,1,6,5,7,4]=>9 [3,2,1,6,7,4,5]=>6 [3,2,1,6,7,5,4]=>10 [3,2,1,7,4,6,5]=>9 [3,2,1,7,5,4,6]=>9 [3,2,1,7,5,6,4]=>11 [3,2,1,7,6,4,5]=>10 [3,2,1,7,6,5,4]=>17 [3,2,4,1,6,7,5]=>5 [3,2,4,1,7,6,5]=>9 [3,2,4,7,1,6,5]=>5 [3,2,5,1,4,7,6]=>6 [3,2,5,1,6,7,4]=>5 [3,2,5,1,7,4,6]=>7 [3,2,5,1,7,6,4]=>11 [3,2,5,4,1,7,6]=>6 [3,2,5,7,1,6,4]=>6 [3,2,6,1,4,7,5]=>5 [3,2,6,1,5,4,7]=>5 [3,2,6,1,5,7,4]=>7 [3,2,6,1,7,4,5]=>5 [3,2,6,1,7,5,4]=>10 [3,2,6,4,1,7,5]=>5 [3,2,6,5,1,7,4]=>6 [3,2,6,7,1,5,4]=>5 [3,2,7,1,4,6,5]=>5 [3,2,7,1,5,4,6]=>5 [3,2,7,1,5,6,4]=>7 [3,2,7,1,6,4,5]=>6 [3,2,7,1,6,5,4]=>12 [3,2,7,4,1,6,5]=>5 [3,2,7,5,1,6,4]=>6 [3,2,7,6,1,5,4]=>7 [3,4,1,2,7,6,5]=>6 [3,4,1,7,2,6,5]=>5 [3,4,2,1,6,7,5]=>5 [3,4,2,1,7,6,5]=>10 [3,4,2,6,1,7,5]=>5 [3,4,2,7,1,6,5]=>6 [3,5,1,2,7,6,4]=>5 [3,5,1,7,2,6,4]=>5 [3,5,2,1,7,4,6]=>6 [3,5,2,1,7,6,4]=>10 [3,5,2,7,1,6,4]=>7 [3,6,2,1,7,5,4]=>8 [3,6,2,7,1,5,4]=>5 [3,7,2,1,6,5,4]=>8 [3,7,2,6,1,5,4]=>5 [4,1,2,7,3,6,5]=>5 [4,1,3,2,7,5,6]=>5 [4,1,3,2,7,6,5]=>9 [4,1,3,7,2,6,5]=>7 [4,1,6,3,2,7,5]=>5 [4,1,7,3,2,6,5]=>6 [4,2,1,3,7,5,6]=>5 [4,2,1,3,7,6,5]=>9 [4,2,1,5,3,7,6]=>6 [4,2,1,5,7,3,6]=>5 [4,2,1,5,7,6,3]=>5 [4,2,1,6,3,7,5]=>7 [4,2,1,6,5,3,7]=>5 [4,2,1,6,5,7,3]=>5 [4,2,1,6,7,3,5]=>5 [4,2,1,6,7,5,3]=>6 [4,2,1,7,3,5,6]=>5 [4,2,1,7,3,6,5]=>11 [4,2,1,7,5,3,6]=>7 [4,2,1,7,5,6,3]=>7 [4,2,1,7,6,3,5]=>10 [4,2,1,7,6,5,3]=>12 [4,2,3,1,6,7,5]=>5 [4,2,3,1,7,5,6]=>5 [4,2,3,1,7,6,5]=>11 [4,2,3,7,1,6,5]=>7 [4,2,5,1,7,3,6]=>5 [4,2,5,1,7,6,3]=>6 [4,2,6,1,3,7,5]=>5 [4,2,6,1,7,3,5]=>5 [4,2,6,1,7,5,3]=>7 [4,2,6,3,1,7,5]=>5 [4,2,7,1,3,6,5]=>6 [4,2,7,1,6,3,5]=>7 [4,2,7,1,6,5,3]=>9 [4,2,7,3,1,6,5]=>6 [4,2,7,6,1,5,3]=>6 [4,3,1,2,7,5,6]=>5 [4,3,1,2,7,6,5]=>10 [4,3,1,6,2,7,5]=>6 [4,3,1,7,2,6,5]=>10 [4,3,1,7,6,2,5]=>8 [4,3,1,7,6,5,2]=>8 [4,3,2,1,6,7,5]=>7 [4,3,2,1,7,5,6]=>7 [4,3,2,1,7,6,5]=>17 [4,3,2,6,1,7,5]=>7 [4,3,2,7,1,6,5]=>12 [4,3,2,7,6,1,5]=>8 [4,3,2,7,6,5,1]=>8 [4,3,6,2,1,7,5]=>6 [4,3,7,1,2,6,5]=>5 [4,3,7,1,6,2,5]=>5 [4,3,7,1,6,5,2]=>5 [4,3,7,2,1,6,5]=>7 [4,3,7,2,6,1,5]=>5 [4,3,7,2,6,5,1]=>5 [4,5,2,1,7,6,3]=>5 [4,6,2,1,7,5,3]=>5 [4,7,2,1,6,5,3]=>5 [5,1,3,2,7,6,4]=>5 [5,2,1,3,7,6,4]=>5 [5,2,1,4,3,7,6]=>6 [5,2,1,4,7,3,6]=>5 [5,2,1,4,7,6,3]=>5 [5,2,1,7,3,6,4]=>6 [5,2,1,7,4,3,6]=>6 [5,2,1,7,4,6,3]=>6 [5,2,1,7,6,3,4]=>5 [5,2,1,7,6,4,3]=>7 [5,2,3,1,7,6,4]=>7 [5,2,4,1,7,3,6]=>5 [5,2,4,1,7,6,3]=>6 [5,2,7,1,6,4,3]=>6 [5,3,1,2,7,4,6]=>5 [5,3,1,2,7,6,4]=>6 [5,3,1,7,2,6,4]=>7 [5,3,1,7,6,2,4]=>5 [5,3,1,7,6,4,2]=>5 [5,3,2,1,7,4,6]=>7 [5,3,2,1,7,6,4]=>12 [5,3,2,7,1,6,4]=>9 [5,3,2,7,6,1,4]=>5 [5,3,2,7,6,4,1]=>5 [5,3,7,2,1,6,4]=>6 [5,4,2,1,7,3,6]=>6 [5,4,2,1,7,6,3]=>7 [5,4,2,7,1,6,3]=>6 [5,4,3,2,1,7,6]=>5 [6,3,2,1,7,5,4]=>8 [6,3,2,7,1,5,4]=>5 [6,4,2,1,7,5,3]=>5 [7,3,2,1,6,5,4]=>8 [7,3,2,6,1,5,4]=>5 [7,4,2,1,6,5,3]=>5
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Description
The Edelman-Greene number of a permutation.
This is the sum of the coefficients of the expansion of the Stanley symmetric function $F_\omega$ in Schur functions. Equivalently, this is the number of semistandard tableaux whose column words - obtained by reading up columns starting with the leftmost - are reduced words for $\omega$.
References
[1] Billey, S., Pawlowski, B. Permutation patterns, Stanley symmetric functions, and generalized Specht modules MathSciNet:3252657
Code
# very slow
def statistic(pi):
    if pi.avoids([2,1,4,3]):
        return 1
    s = SymmetricFunctions(QQ).s()    
    G = SymmetricGroup(pi.size())
    f = G(pi).stanley_symmetric_function()
    return sum(s(f).coefficients())
Created
Aug 09, 2016 at 19:54 by Martin Rubey
Updated
Aug 10, 2016 at 09:47 by Martin Rubey