edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>1 [2,1]=>0 [1,2,3]=>2 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>0 [3,1,2]=>0 [3,2,1]=>0 [1,2,3,4]=>3 [1,2,4,3]=>2 [1,3,2,4]=>2 [1,3,4,2]=>1 [1,4,2,3]=>1 [1,4,3,2]=>1 [2,1,3,4]=>2 [2,1,4,3]=>1 [2,3,1,4]=>1 [2,3,4,1]=>0 [2,4,1,3]=>0 [2,4,3,1]=>0 [3,1,2,4]=>1 [3,1,4,2]=>0 [3,2,1,4]=>1 [3,2,4,1]=>0 [3,4,1,2]=>0 [3,4,2,1]=>0 [4,1,2,3]=>0 [4,1,3,2]=>0 [4,2,1,3]=>0 [4,2,3,1]=>0 [4,3,1,2]=>0 [4,3,2,1]=>0 [1,2,3,4,5]=>4 [1,2,3,5,4]=>3 [1,2,4,3,5]=>3 [1,2,4,5,3]=>2 [1,2,5,3,4]=>2 [1,2,5,4,3]=>2 [1,3,2,4,5]=>3 [1,3,2,5,4]=>2 [1,3,4,2,5]=>2 [1,3,4,5,2]=>1 [1,3,5,2,4]=>1 [1,3,5,4,2]=>1 [1,4,2,3,5]=>2 [1,4,2,5,3]=>1 [1,4,3,2,5]=>2 [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]=>3 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>1 [2,1,5,3,4]=>1 [2,1,5,4,3]=>1 [2,3,1,4,5]=>2 [2,3,1,5,4]=>1 [2,3,4,1,5]=>1 [2,3,4,5,1]=>0 [2,3,5,1,4]=>0 [2,3,5,4,1]=>0 [2,4,1,3,5]=>1 [2,4,1,5,3]=>0 [2,4,3,1,5]=>1 [2,4,3,5,1]=>0 [2,4,5,1,3]=>0 [2,4,5,3,1]=>0 [2,5,1,3,4]=>0 [2,5,1,4,3]=>0 [2,5,3,1,4]=>0 [2,5,3,4,1]=>0 [2,5,4,1,3]=>0 [2,5,4,3,1]=>0 [3,1,2,4,5]=>2 [3,1,2,5,4]=>1 [3,1,4,2,5]=>1 [3,1,4,5,2]=>0 [3,1,5,2,4]=>0 [3,1,5,4,2]=>0 [3,2,1,4,5]=>2 [3,2,1,5,4]=>1 [3,2,4,1,5]=>1 [3,2,4,5,1]=>0 [3,2,5,1,4]=>0 [3,2,5,4,1]=>0 [3,4,1,2,5]=>1 [3,4,1,5,2]=>0 [3,4,2,1,5]=>1 [3,4,2,5,1]=>0 [3,4,5,1,2]=>0 [3,4,5,2,1]=>0 [3,5,1,2,4]=>0 [3,5,1,4,2]=>0 [3,5,2,1,4]=>0 [3,5,2,4,1]=>0 [3,5,4,1,2]=>0 [3,5,4,2,1]=>0 [4,1,2,3,5]=>1 [4,1,2,5,3]=>0 [4,1,3,2,5]=>1 [4,1,3,5,2]=>0 [4,1,5,2,3]=>0 [4,1,5,3,2]=>0 [4,2,1,3,5]=>1 [4,2,1,5,3]=>0 [4,2,3,1,5]=>1 [4,2,3,5,1]=>0 [4,2,5,1,3]=>0 [4,2,5,3,1]=>0 [4,3,1,2,5]=>1 [4,3,1,5,2]=>0 [4,3,2,1,5]=>1 [4,3,2,5,1]=>0 [4,3,5,1,2]=>0 [4,3,5,2,1]=>0 [4,5,1,2,3]=>0 [4,5,1,3,2]=>0 [4,5,2,1,3]=>0 [4,5,2,3,1]=>0 [4,5,3,1,2]=>0 [4,5,3,2,1]=>0 [5,1,2,3,4]=>0 [5,1,2,4,3]=>0 [5,1,3,2,4]=>0 [5,1,3,4,2]=>0 [5,1,4,2,3]=>0 [5,1,4,3,2]=>0 [5,2,1,3,4]=>0 [5,2,1,4,3]=>0 [5,2,3,1,4]=>0 [5,2,3,4,1]=>0 [5,2,4,1,3]=>0 [5,2,4,3,1]=>0 [5,3,1,2,4]=>0 [5,3,1,4,2]=>0 [5,3,2,1,4]=>0 [5,3,2,4,1]=>0 [5,3,4,1,2]=>0 [5,3,4,2,1]=>0 [5,4,1,2,3]=>0 [5,4,1,3,2]=>0 [5,4,2,1,3]=>0 [5,4,2,3,1]=>0 [5,4,3,1,2]=>0 [5,4,3,2,1]=>0 [1,2,3,4,5,6]=>5 [1,2,3,4,6,5]=>4 [1,2,3,5,4,6]=>4 [1,2,3,5,6,4]=>3 [1,2,3,6,4,5]=>3 [1,2,3,6,5,4]=>3 [1,2,4,3,5,6]=>4 [1,2,4,3,6,5]=>3 [1,2,4,5,3,6]=>3 [1,2,4,5,6,3]=>2 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>2 [1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>2 [1,2,5,4,3,6]=>3 [1,2,5,4,6,3]=>2 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>2 [1,2,6,3,4,5]=>2 [1,2,6,3,5,4]=>2 [1,2,6,4,3,5]=>2 [1,2,6,4,5,3]=>2 [1,2,6,5,3,4]=>2 [1,2,6,5,4,3]=>2 [1,3,2,4,5,6]=>4 [1,3,2,4,6,5]=>3 [1,3,2,5,4,6]=>3 [1,3,2,5,6,4]=>2 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>2 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>2 [1,3,4,5,2,6]=>2 [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]=>2 [1,3,5,2,6,4]=>1 [1,3,5,4,2,6]=>2 [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]=>1 [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]=>3 [1,4,2,3,6,5]=>2 [1,4,2,5,3,6]=>2 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>1 [1,4,2,6,5,3]=>1 [1,4,3,2,5,6]=>3 [1,4,3,2,6,5]=>2 [1,4,3,5,2,6]=>2 [1,4,3,5,6,2]=>1 [1,4,3,6,2,5]=>1 [1,4,3,6,5,2]=>1 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>2 [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]=>2 [1,5,2,3,6,4]=>1 [1,5,2,4,3,6]=>2 [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]=>2 [1,5,3,2,6,4]=>1 [1,5,3,4,2,6]=>2 [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]=>2 [1,5,4,2,6,3]=>1 [1,5,4,3,2,6]=>2 [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]=>1 [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]=>4 [2,1,3,4,6,5]=>3 [2,1,3,5,4,6]=>3 [2,1,3,5,6,4]=>2 [2,1,3,6,4,5]=>2 [2,1,3,6,5,4]=>2 [2,1,4,3,5,6]=>3 [2,1,4,3,6,5]=>2 [2,1,4,5,3,6]=>2 [2,1,4,5,6,3]=>1 [2,1,4,6,3,5]=>1 [2,1,4,6,5,3]=>1 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>1 [2,1,5,4,3,6]=>2 [2,1,5,4,6,3]=>1 [2,1,5,6,3,4]=>1 [2,1,5,6,4,3]=>1 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>1 [2,1,6,4,3,5]=>1 [2,1,6,4,5,3]=>1 [2,1,6,5,3,4]=>1 [2,1,6,5,4,3]=>1 [2,3,1,4,5,6]=>3 [2,3,1,4,6,5]=>2 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>1 [2,3,1,6,4,5]=>1 [2,3,1,6,5,4]=>1 [2,3,4,1,5,6]=>2 [2,3,4,1,6,5]=>1 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>0 [2,3,4,6,1,5]=>0 [2,3,4,6,5,1]=>0 [2,3,5,1,4,6]=>1 [2,3,5,1,6,4]=>0 [2,3,5,4,1,6]=>1 [2,3,5,4,6,1]=>0 [2,3,5,6,1,4]=>0 [2,3,5,6,4,1]=>0 [2,3,6,1,4,5]=>0 [2,3,6,1,5,4]=>0 [2,3,6,4,1,5]=>0 [2,3,6,4,5,1]=>0 [2,3,6,5,1,4]=>0 [2,3,6,5,4,1]=>0 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>1 [2,4,1,5,3,6]=>1 [2,4,1,5,6,3]=>0 [2,4,1,6,3,5]=>0 [2,4,1,6,5,3]=>0 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>1 [2,4,3,5,1,6]=>1 [2,4,3,5,6,1]=>0 [2,4,3,6,1,5]=>0 [2,4,3,6,5,1]=>0 [2,4,5,1,3,6]=>1 [2,4,5,1,6,3]=>0 [2,4,5,3,1,6]=>1 [2,4,5,3,6,1]=>0 [2,4,5,6,1,3]=>0 [2,4,5,6,3,1]=>0 [2,4,6,1,3,5]=>0 [2,4,6,1,5,3]=>0 [2,4,6,3,1,5]=>0 [2,4,6,3,5,1]=>0 [2,4,6,5,1,3]=>0 [2,4,6,5,3,1]=>0 [2,5,1,3,4,6]=>1 [2,5,1,3,6,4]=>0 [2,5,1,4,3,6]=>1 [2,5,1,4,6,3]=>0 [2,5,1,6,3,4]=>0 [2,5,1,6,4,3]=>0 [2,5,3,1,4,6]=>1 [2,5,3,1,6,4]=>0 [2,5,3,4,1,6]=>1 [2,5,3,4,6,1]=>0 [2,5,3,6,1,4]=>0 [2,5,3,6,4,1]=>0 [2,5,4,1,3,6]=>1 [2,5,4,1,6,3]=>0 [2,5,4,3,1,6]=>1 [2,5,4,3,6,1]=>0 [2,5,4,6,1,3]=>0 [2,5,4,6,3,1]=>0 [2,5,6,1,3,4]=>0 [2,5,6,1,4,3]=>0 [2,5,6,3,1,4]=>0 [2,5,6,3,4,1]=>0 [2,5,6,4,1,3]=>0 [2,5,6,4,3,1]=>0 [2,6,1,3,4,5]=>0 [2,6,1,3,5,4]=>0 [2,6,1,4,3,5]=>0 [2,6,1,4,5,3]=>0 [2,6,1,5,3,4]=>0 [2,6,1,5,4,3]=>0 [2,6,3,1,4,5]=>0 [2,6,3,1,5,4]=>0 [2,6,3,4,1,5]=>0 [2,6,3,4,5,1]=>0 [2,6,3,5,1,4]=>0 [2,6,3,5,4,1]=>0 [2,6,4,1,3,5]=>0 [2,6,4,1,5,3]=>0 [2,6,4,3,1,5]=>0 [2,6,4,3,5,1]=>0 [2,6,4,5,1,3]=>0 [2,6,4,5,3,1]=>0 [2,6,5,1,3,4]=>0 [2,6,5,1,4,3]=>0 [2,6,5,3,1,4]=>0 [2,6,5,3,4,1]=>0 [2,6,5,4,1,3]=>0 [2,6,5,4,3,1]=>0 [3,1,2,4,5,6]=>3 [3,1,2,4,6,5]=>2 [3,1,2,5,4,6]=>2 [3,1,2,5,6,4]=>1 [3,1,2,6,4,5]=>1 [3,1,2,6,5,4]=>1 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>1 [3,1,4,5,2,6]=>1 [3,1,4,5,6,2]=>0 [3,1,4,6,2,5]=>0 [3,1,4,6,5,2]=>0 [3,1,5,2,4,6]=>1 [3,1,5,2,6,4]=>0 [3,1,5,4,2,6]=>1 [3,1,5,4,6,2]=>0 [3,1,5,6,2,4]=>0 [3,1,5,6,4,2]=>0 [3,1,6,2,4,5]=>0 [3,1,6,2,5,4]=>0 [3,1,6,4,2,5]=>0 [3,1,6,4,5,2]=>0 [3,1,6,5,2,4]=>0 [3,1,6,5,4,2]=>0 [3,2,1,4,5,6]=>3 [3,2,1,4,6,5]=>2 [3,2,1,5,4,6]=>2 [3,2,1,5,6,4]=>1 [3,2,1,6,4,5]=>1 [3,2,1,6,5,4]=>1 [3,2,4,1,5,6]=>2 [3,2,4,1,6,5]=>1 [3,2,4,5,1,6]=>1 [3,2,4,5,6,1]=>0 [3,2,4,6,1,5]=>0 [3,2,4,6,5,1]=>0 [3,2,5,1,4,6]=>1 [3,2,5,1,6,4]=>0 [3,2,5,4,1,6]=>1 [3,2,5,4,6,1]=>0 [3,2,5,6,1,4]=>0 [3,2,5,6,4,1]=>0 [3,2,6,1,4,5]=>0 [3,2,6,1,5,4]=>0 [3,2,6,4,1,5]=>0 [3,2,6,4,5,1]=>0 [3,2,6,5,1,4]=>0 [3,2,6,5,4,1]=>0 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>1 [3,4,1,5,2,6]=>1 [3,4,1,5,6,2]=>0 [3,4,1,6,2,5]=>0 [3,4,1,6,5,2]=>0 [3,4,2,1,5,6]=>2 [3,4,2,1,6,5]=>1 [3,4,2,5,1,6]=>1 [3,4,2,5,6,1]=>0 [3,4,2,6,1,5]=>0 [3,4,2,6,5,1]=>0 [3,4,5,1,2,6]=>1 [3,4,5,1,6,2]=>0 [3,4,5,2,1,6]=>1 [3,4,5,2,6,1]=>0 [3,4,5,6,1,2]=>0 [3,4,5,6,2,1]=>0 [3,4,6,1,2,5]=>0 [3,4,6,1,5,2]=>0 [3,4,6,2,1,5]=>0 [3,4,6,2,5,1]=>0 [3,4,6,5,1,2]=>0 [3,4,6,5,2,1]=>0 [3,5,1,2,4,6]=>1 [3,5,1,2,6,4]=>0 [3,5,1,4,2,6]=>1 [3,5,1,4,6,2]=>0 [3,5,1,6,2,4]=>0 [3,5,1,6,4,2]=>0 [3,5,2,1,4,6]=>1 [3,5,2,1,6,4]=>0 [3,5,2,4,1,6]=>1 [3,5,2,4,6,1]=>0 [3,5,2,6,1,4]=>0 [3,5,2,6,4,1]=>0 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>0 [3,5,4,2,1,6]=>1 [3,5,4,2,6,1]=>0 [3,5,4,6,1,2]=>0 [3,5,4,6,2,1]=>0 [3,5,6,1,2,4]=>0 [3,5,6,1,4,2]=>0 [3,5,6,2,1,4]=>0 [3,5,6,2,4,1]=>0 [3,5,6,4,1,2]=>0 [3,5,6,4,2,1]=>0 [3,6,1,2,4,5]=>0 [3,6,1,2,5,4]=>0 [3,6,1,4,2,5]=>0 [3,6,1,4,5,2]=>0 [3,6,1,5,2,4]=>0 [3,6,1,5,4,2]=>0 [3,6,2,1,4,5]=>0 [3,6,2,1,5,4]=>0 [3,6,2,4,1,5]=>0 [3,6,2,4,5,1]=>0 [3,6,2,5,1,4]=>0 [3,6,2,5,4,1]=>0 [3,6,4,1,2,5]=>0 [3,6,4,1,5,2]=>0 [3,6,4,2,1,5]=>0 [3,6,4,2,5,1]=>0 [3,6,4,5,1,2]=>0 [3,6,4,5,2,1]=>0 [3,6,5,1,2,4]=>0 [3,6,5,1,4,2]=>0 [3,6,5,2,1,4]=>0 [3,6,5,2,4,1]=>0 [3,6,5,4,1,2]=>0 [3,6,5,4,2,1]=>0 [4,1,2,3,5,6]=>2 [4,1,2,3,6,5]=>1 [4,1,2,5,3,6]=>1 [4,1,2,5,6,3]=>0 [4,1,2,6,3,5]=>0 [4,1,2,6,5,3]=>0 [4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>1 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>0 [4,1,3,6,2,5]=>0 [4,1,3,6,5,2]=>0 [4,1,5,2,3,6]=>1 [4,1,5,2,6,3]=>0 [4,1,5,3,2,6]=>1 [4,1,5,3,6,2]=>0 [4,1,5,6,2,3]=>0 [4,1,5,6,3,2]=>0 [4,1,6,2,3,5]=>0 [4,1,6,2,5,3]=>0 [4,1,6,3,2,5]=>0 [4,1,6,3,5,2]=>0 [4,1,6,5,2,3]=>0 [4,1,6,5,3,2]=>0 [4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>1 [4,2,1,5,3,6]=>1 [4,2,1,5,6,3]=>0 [4,2,1,6,3,5]=>0 [4,2,1,6,5,3]=>0 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>1 [4,2,3,5,1,6]=>1 [4,2,3,5,6,1]=>0 [4,2,3,6,1,5]=>0 [4,2,3,6,5,1]=>0 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>0 [4,2,5,3,1,6]=>1 [4,2,5,3,6,1]=>0 [4,2,5,6,1,3]=>0 [4,2,5,6,3,1]=>0 [4,2,6,1,3,5]=>0 [4,2,6,1,5,3]=>0 [4,2,6,3,1,5]=>0 [4,2,6,3,5,1]=>0 [4,2,6,5,1,3]=>0 [4,2,6,5,3,1]=>0 [4,3,1,2,5,6]=>2 [4,3,1,2,6,5]=>1 [4,3,1,5,2,6]=>1 [4,3,1,5,6,2]=>0 [4,3,1,6,2,5]=>0 [4,3,1,6,5,2]=>0 [4,3,2,1,5,6]=>2 [4,3,2,1,6,5]=>1 [4,3,2,5,1,6]=>1 [4,3,2,5,6,1]=>0 [4,3,2,6,1,5]=>0 [4,3,2,6,5,1]=>0 [4,3,5,1,2,6]=>1 [4,3,5,1,6,2]=>0 [4,3,5,2,1,6]=>1 [4,3,5,2,6,1]=>0 [4,3,5,6,1,2]=>0 [4,3,5,6,2,1]=>0 [4,3,6,1,2,5]=>0 [4,3,6,1,5,2]=>0 [4,3,6,2,1,5]=>0 [4,3,6,2,5,1]=>0 [4,3,6,5,1,2]=>0 [4,3,6,5,2,1]=>0 [4,5,1,2,3,6]=>1 [4,5,1,2,6,3]=>0 [4,5,1,3,2,6]=>1 [4,5,1,3,6,2]=>0 [4,5,1,6,2,3]=>0 [4,5,1,6,3,2]=>0 [4,5,2,1,3,6]=>1 [4,5,2,1,6,3]=>0 [4,5,2,3,1,6]=>1 [4,5,2,3,6,1]=>0 [4,5,2,6,1,3]=>0 [4,5,2,6,3,1]=>0 [4,5,3,1,2,6]=>1 [4,5,3,1,6,2]=>0 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>0 [4,5,3,6,1,2]=>0 [4,5,3,6,2,1]=>0 [4,5,6,1,2,3]=>0 [4,5,6,1,3,2]=>0 [4,5,6,2,1,3]=>0 [4,5,6,2,3,1]=>0 [4,5,6,3,1,2]=>0 [4,5,6,3,2,1]=>0 [4,6,1,2,3,5]=>0 [4,6,1,2,5,3]=>0 [4,6,1,3,2,5]=>0 [4,6,1,3,5,2]=>0 [4,6,1,5,2,3]=>0 [4,6,1,5,3,2]=>0 [4,6,2,1,3,5]=>0 [4,6,2,1,5,3]=>0 [4,6,2,3,1,5]=>0 [4,6,2,3,5,1]=>0 [4,6,2,5,1,3]=>0 [4,6,2,5,3,1]=>0 [4,6,3,1,2,5]=>0 [4,6,3,1,5,2]=>0 [4,6,3,2,1,5]=>0 [4,6,3,2,5,1]=>0 [4,6,3,5,1,2]=>0 [4,6,3,5,2,1]=>0 [4,6,5,1,2,3]=>0 [4,6,5,1,3,2]=>0 [4,6,5,2,1,3]=>0 [4,6,5,2,3,1]=>0 [4,6,5,3,1,2]=>0 [4,6,5,3,2,1]=>0 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>0 [5,1,2,4,3,6]=>1 [5,1,2,4,6,3]=>0 [5,1,2,6,3,4]=>0 [5,1,2,6,4,3]=>0 [5,1,3,2,4,6]=>1 [5,1,3,2,6,4]=>0 [5,1,3,4,2,6]=>1 [5,1,3,4,6,2]=>0 [5,1,3,6,2,4]=>0 [5,1,3,6,4,2]=>0 [5,1,4,2,3,6]=>1 [5,1,4,2,6,3]=>0 [5,1,4,3,2,6]=>1 [5,1,4,3,6,2]=>0 [5,1,4,6,2,3]=>0 [5,1,4,6,3,2]=>0 [5,1,6,2,3,4]=>0 [5,1,6,2,4,3]=>0 [5,1,6,3,2,4]=>0 [5,1,6,3,4,2]=>0 [5,1,6,4,2,3]=>0 [5,1,6,4,3,2]=>0 [5,2,1,3,4,6]=>1 [5,2,1,3,6,4]=>0 [5,2,1,4,3,6]=>1 [5,2,1,4,6,3]=>0 [5,2,1,6,3,4]=>0 [5,2,1,6,4,3]=>0 [5,2,3,1,4,6]=>1 [5,2,3,1,6,4]=>0 [5,2,3,4,1,6]=>1 [5,2,3,4,6,1]=>0 [5,2,3,6,1,4]=>0 [5,2,3,6,4,1]=>0 [5,2,4,1,3,6]=>1 [5,2,4,1,6,3]=>0 [5,2,4,3,1,6]=>1 [5,2,4,3,6,1]=>0 [5,2,4,6,1,3]=>0 [5,2,4,6,3,1]=>0 [5,2,6,1,3,4]=>0 [5,2,6,1,4,3]=>0 [5,2,6,3,1,4]=>0 [5,2,6,3,4,1]=>0 [5,2,6,4,1,3]=>0 [5,2,6,4,3,1]=>0 [5,3,1,2,4,6]=>1 [5,3,1,2,6,4]=>0 [5,3,1,4,2,6]=>1 [5,3,1,4,6,2]=>0 [5,3,1,6,2,4]=>0 [5,3,1,6,4,2]=>0 [5,3,2,1,4,6]=>1 [5,3,2,1,6,4]=>0 [5,3,2,4,1,6]=>1 [5,3,2,4,6,1]=>0 [5,3,2,6,1,4]=>0 [5,3,2,6,4,1]=>0 [5,3,4,1,2,6]=>1 [5,3,4,1,6,2]=>0 [5,3,4,2,1,6]=>1 [5,3,4,2,6,1]=>0 [5,3,4,6,1,2]=>0 [5,3,4,6,2,1]=>0 [5,3,6,1,2,4]=>0 [5,3,6,1,4,2]=>0 [5,3,6,2,1,4]=>0 [5,3,6,2,4,1]=>0 [5,3,6,4,1,2]=>0 [5,3,6,4,2,1]=>0 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>0 [5,4,1,3,2,6]=>1 [5,4,1,3,6,2]=>0 [5,4,1,6,2,3]=>0 [5,4,1,6,3,2]=>0 [5,4,2,1,3,6]=>1 [5,4,2,1,6,3]=>0 [5,4,2,3,1,6]=>1 [5,4,2,3,6,1]=>0 [5,4,2,6,1,3]=>0 [5,4,2,6,3,1]=>0 [5,4,3,1,2,6]=>1 [5,4,3,1,6,2]=>0 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>0 [5,4,3,6,1,2]=>0 [5,4,3,6,2,1]=>0 [5,4,6,1,2,3]=>0 [5,4,6,1,3,2]=>0 [5,4,6,2,1,3]=>0 [5,4,6,2,3,1]=>0 [5,4,6,3,1,2]=>0 [5,4,6,3,2,1]=>0 [5,6,1,2,3,4]=>0 [5,6,1,2,4,3]=>0 [5,6,1,3,2,4]=>0 [5,6,1,3,4,2]=>0 [5,6,1,4,2,3]=>0 [5,6,1,4,3,2]=>0 [5,6,2,1,3,4]=>0 [5,6,2,1,4,3]=>0 [5,6,2,3,1,4]=>0 [5,6,2,3,4,1]=>0 [5,6,2,4,1,3]=>0 [5,6,2,4,3,1]=>0 [5,6,3,1,2,4]=>0 [5,6,3,1,4,2]=>0 [5,6,3,2,1,4]=>0 [5,6,3,2,4,1]=>0 [5,6,3,4,1,2]=>0 [5,6,3,4,2,1]=>0 [5,6,4,1,2,3]=>0 [5,6,4,1,3,2]=>0 [5,6,4,2,1,3]=>0 [5,6,4,2,3,1]=>0 [5,6,4,3,1,2]=>0 [5,6,4,3,2,1]=>0 [6,1,2,3,4,5]=>0 [6,1,2,3,5,4]=>0 [6,1,2,4,3,5]=>0 [6,1,2,4,5,3]=>0 [6,1,2,5,3,4]=>0 [6,1,2,5,4,3]=>0 [6,1,3,2,4,5]=>0 [6,1,3,2,5,4]=>0 [6,1,3,4,2,5]=>0 [6,1,3,4,5,2]=>0 [6,1,3,5,2,4]=>0 [6,1,3,5,4,2]=>0 [6,1,4,2,3,5]=>0 [6,1,4,2,5,3]=>0 [6,1,4,3,2,5]=>0 [6,1,4,3,5,2]=>0 [6,1,4,5,2,3]=>0 [6,1,4,5,3,2]=>0 [6,1,5,2,3,4]=>0 [6,1,5,2,4,3]=>0 [6,1,5,3,2,4]=>0 [6,1,5,3,4,2]=>0 [6,1,5,4,2,3]=>0 [6,1,5,4,3,2]=>0 [6,2,1,3,4,5]=>0 [6,2,1,3,5,4]=>0 [6,2,1,4,3,5]=>0 [6,2,1,4,5,3]=>0 [6,2,1,5,3,4]=>0 [6,2,1,5,4,3]=>0 [6,2,3,1,4,5]=>0 [6,2,3,1,5,4]=>0 [6,2,3,4,1,5]=>0 [6,2,3,4,5,1]=>0 [6,2,3,5,1,4]=>0 [6,2,3,5,4,1]=>0 [6,2,4,1,3,5]=>0 [6,2,4,1,5,3]=>0 [6,2,4,3,1,5]=>0 [6,2,4,3,5,1]=>0 [6,2,4,5,1,3]=>0 [6,2,4,5,3,1]=>0 [6,2,5,1,3,4]=>0 [6,2,5,1,4,3]=>0 [6,2,5,3,1,4]=>0 [6,2,5,3,4,1]=>0 [6,2,5,4,1,3]=>0 [6,2,5,4,3,1]=>0 [6,3,1,2,4,5]=>0 [6,3,1,2,5,4]=>0 [6,3,1,4,2,5]=>0 [6,3,1,4,5,2]=>0 [6,3,1,5,2,4]=>0 [6,3,1,5,4,2]=>0 [6,3,2,1,4,5]=>0 [6,3,2,1,5,4]=>0 [6,3,2,4,1,5]=>0 [6,3,2,4,5,1]=>0 [6,3,2,5,1,4]=>0 [6,3,2,5,4,1]=>0 [6,3,4,1,2,5]=>0 [6,3,4,1,5,2]=>0 [6,3,4,2,1,5]=>0 [6,3,4,2,5,1]=>0 [6,3,4,5,1,2]=>0 [6,3,4,5,2,1]=>0 [6,3,5,1,2,4]=>0 [6,3,5,1,4,2]=>0 [6,3,5,2,1,4]=>0 [6,3,5,2,4,1]=>0 [6,3,5,4,1,2]=>0 [6,3,5,4,2,1]=>0 [6,4,1,2,3,5]=>0 [6,4,1,2,5,3]=>0 [6,4,1,3,2,5]=>0 [6,4,1,3,5,2]=>0 [6,4,1,5,2,3]=>0 [6,4,1,5,3,2]=>0 [6,4,2,1,3,5]=>0 [6,4,2,1,5,3]=>0 [6,4,2,3,1,5]=>0 [6,4,2,3,5,1]=>0 [6,4,2,5,1,3]=>0 [6,4,2,5,3,1]=>0 [6,4,3,1,2,5]=>0 [6,4,3,1,5,2]=>0 [6,4,3,2,1,5]=>0 [6,4,3,2,5,1]=>0 [6,4,3,5,1,2]=>0 [6,4,3,5,2,1]=>0 [6,4,5,1,2,3]=>0 [6,4,5,1,3,2]=>0 [6,4,5,2,1,3]=>0 [6,4,5,2,3,1]=>0 [6,4,5,3,1,2]=>0 [6,4,5,3,2,1]=>0 [6,5,1,2,3,4]=>0 [6,5,1,2,4,3]=>0 [6,5,1,3,2,4]=>0 [6,5,1,3,4,2]=>0 [6,5,1,4,2,3]=>0 [6,5,1,4,3,2]=>0 [6,5,2,1,3,4]=>0 [6,5,2,1,4,3]=>0 [6,5,2,3,1,4]=>0 [6,5,2,3,4,1]=>0 [6,5,2,4,1,3]=>0 [6,5,2,4,3,1]=>0 [6,5,3,1,2,4]=>0 [6,5,3,1,4,2]=>0 [6,5,3,2,1,4]=>0 [6,5,3,2,4,1]=>0 [6,5,3,4,1,2]=>0 [6,5,3,4,2,1]=>0 [6,5,4,1,2,3]=>0 [6,5,4,1,3,2]=>0 [6,5,4,2,1,3]=>0 [6,5,4,2,3,1]=>0 [6,5,4,3,1,2]=>0 [6,5,4,3,2,1]=>0
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Description
The number of global ascents of a permutation.
The global ascents are the integers $i$ such that
$$C(\pi)=\{i\in [n-1] : \forall 1 \leq j \leq i < k \leq n \quad \pi(j)<\pi(k)\}.$$
For $n>1$ it can also be described as an occurrence of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
According to [2], this is also the cardinality of the connectivity set of a permutation. The permutation is connected, when the connectivity set is empty. This gives oeis:A003319.
References
[1] Stanley, R. P. The descent set and connectivity set of a permutation MathSciNet:2167418 arXiv:math/0507224
[2] Bergeron, N., Hohlweg, C., Zabrocki, M. Posets related to the connectivity set of Coxeter groups MathSciNet:2255139 arXiv:math/0509271
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
Code
def statistic(pi):
    return len([i for i in range(1, pi.size()) if all(pi(j) < pi(k) for j in range(1, i+1) for k in range(i+1, pi.size()+1))])

            
Created
Feb 17, 2015 at 20:44 by Martin Rubey
Updated
Jul 15, 2016 at 12:14 by Christian Stump