edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,2]=>1 [2,1]=>2 [1,2,3]=>1 [1,3,2]=>2 [2,1,3]=>2 [2,3,1]=>2 [3,1,2]=>2 [3,2,1]=>3 [1,2,3,4]=>1 [1,2,4,3]=>2 [1,3,2,4]=>2 [1,3,4,2]=>2 [1,4,2,3]=>2 [1,4,3,2]=>3 [2,1,3,4]=>2 [2,1,4,3]=>3 [2,3,1,4]=>2 [2,3,4,1]=>2 [2,4,1,3]=>2 [2,4,3,1]=>3 [3,1,2,4]=>2 [3,1,4,2]=>3 [3,2,1,4]=>3 [3,2,4,1]=>3 [3,4,1,2]=>2 [3,4,2,1]=>3 [4,1,2,3]=>2 [4,1,3,2]=>3 [4,2,1,3]=>3 [4,2,3,1]=>3 [4,3,1,2]=>3 [4,3,2,1]=>4 [1,2,3,4,5]=>1 [1,2,3,5,4]=>2 [1,2,4,3,5]=>2 [1,2,4,5,3]=>2 [1,2,5,3,4]=>2 [1,2,5,4,3]=>3 [1,3,2,4,5]=>2 [1,3,2,5,4]=>3 [1,3,4,2,5]=>2 [1,3,4,5,2]=>2 [1,3,5,2,4]=>2 [1,3,5,4,2]=>3 [1,4,2,3,5]=>2 [1,4,2,5,3]=>3 [1,4,3,2,5]=>3 [1,4,3,5,2]=>3 [1,4,5,2,3]=>2 [1,4,5,3,2]=>3 [1,5,2,3,4]=>2 [1,5,2,4,3]=>3 [1,5,3,2,4]=>3 [1,5,3,4,2]=>3 [1,5,4,2,3]=>3 [1,5,4,3,2]=>4 [2,1,3,4,5]=>2 [2,1,3,5,4]=>3 [2,1,4,3,5]=>3 [2,1,4,5,3]=>3 [2,1,5,3,4]=>3 [2,1,5,4,3]=>4 [2,3,1,4,5]=>2 [2,3,1,5,4]=>3 [2,3,4,1,5]=>2 [2,3,4,5,1]=>2 [2,3,5,1,4]=>2 [2,3,5,4,1]=>3 [2,4,1,3,5]=>2 [2,4,1,5,3]=>3 [2,4,3,1,5]=>3 [2,4,3,5,1]=>3 [2,4,5,1,3]=>2 [2,4,5,3,1]=>3 [2,5,1,3,4]=>2 [2,5,1,4,3]=>3 [2,5,3,1,4]=>3 [2,5,3,4,1]=>3 [2,5,4,1,3]=>3 [2,5,4,3,1]=>4 [3,1,2,4,5]=>2 [3,1,2,5,4]=>3 [3,1,4,2,5]=>3 [3,1,4,5,2]=>3 [3,1,5,2,4]=>3 [3,1,5,4,2]=>4 [3,2,1,4,5]=>3 [3,2,1,5,4]=>4 [3,2,4,1,5]=>3 [3,2,4,5,1]=>3 [3,2,5,1,4]=>3 [3,2,5,4,1]=>4 [3,4,1,2,5]=>2 [3,4,1,5,2]=>3 [3,4,2,1,5]=>3 [3,4,2,5,1]=>3 [3,4,5,1,2]=>2 [3,4,5,2,1]=>3 [3,5,1,2,4]=>2 [3,5,1,4,2]=>3 [3,5,2,1,4]=>3 [3,5,2,4,1]=>3 [3,5,4,1,2]=>3 [3,5,4,2,1]=>4 [4,1,2,3,5]=>2 [4,1,2,5,3]=>3 [4,1,3,2,5]=>3 [4,1,3,5,2]=>3 [4,1,5,2,3]=>3 [4,1,5,3,2]=>4 [4,2,1,3,5]=>3 [4,2,1,5,3]=>4 [4,2,3,1,5]=>3 [4,2,3,5,1]=>3 [4,2,5,1,3]=>3 [4,2,5,3,1]=>4 [4,3,1,2,5]=>3 [4,3,1,5,2]=>4 [4,3,2,1,5]=>4 [4,3,2,5,1]=>4 [4,3,5,1,2]=>3 [4,3,5,2,1]=>4 [4,5,1,2,3]=>2 [4,5,1,3,2]=>3 [4,5,2,1,3]=>3 [4,5,2,3,1]=>3 [4,5,3,1,2]=>3 [4,5,3,2,1]=>4 [5,1,2,3,4]=>2 [5,1,2,4,3]=>3 [5,1,3,2,4]=>3 [5,1,3,4,2]=>3 [5,1,4,2,3]=>3 [5,1,4,3,2]=>4 [5,2,1,3,4]=>3 [5,2,1,4,3]=>4 [5,2,3,1,4]=>3 [5,2,3,4,1]=>3 [5,2,4,1,3]=>3 [5,2,4,3,1]=>4 [5,3,1,2,4]=>3 [5,3,1,4,2]=>4 [5,3,2,1,4]=>4 [5,3,2,4,1]=>4 [5,3,4,1,2]=>3 [5,3,4,2,1]=>4 [5,4,1,2,3]=>3 [5,4,1,3,2]=>4 [5,4,2,1,3]=>4 [5,4,2,3,1]=>4 [5,4,3,1,2]=>4 [5,4,3,2,1]=>5 [1,2,3,4,5,6]=>1 [1,2,3,4,6,5]=>2 [1,2,3,5,4,6]=>2 [1,2,3,5,6,4]=>2 [1,2,3,6,4,5]=>2 [1,2,3,6,5,4]=>3 [1,2,4,3,5,6]=>2 [1,2,4,3,6,5]=>3 [1,2,4,5,3,6]=>2 [1,2,4,5,6,3]=>2 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>3 [1,2,5,3,4,6]=>2 [1,2,5,3,6,4]=>3 [1,2,5,4,3,6]=>3 [1,2,5,4,6,3]=>3 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>3 [1,2,6,3,4,5]=>2 [1,2,6,3,5,4]=>3 [1,2,6,4,3,5]=>3 [1,2,6,4,5,3]=>3 [1,2,6,5,3,4]=>3 [1,2,6,5,4,3]=>4 [1,3,2,4,5,6]=>2 [1,3,2,4,6,5]=>3 [1,3,2,5,4,6]=>3 [1,3,2,5,6,4]=>3 [1,3,2,6,4,5]=>3 [1,3,2,6,5,4]=>4 [1,3,4,2,5,6]=>2 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>2 [1,3,4,5,6,2]=>2 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>3 [1,3,5,2,4,6]=>2 [1,3,5,2,6,4]=>3 [1,3,5,4,2,6]=>3 [1,3,5,4,6,2]=>3 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>3 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>3 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>3 [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]=>3 [1,4,2,5,6,3]=>3 [1,4,2,6,3,5]=>3 [1,4,2,6,5,3]=>4 [1,4,3,2,5,6]=>3 [1,4,3,2,6,5]=>4 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>3 [1,4,3,6,2,5]=>3 [1,4,3,6,5,2]=>4 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>3 [1,4,5,3,2,6]=>3 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>2 [1,4,5,6,3,2]=>3 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>3 [1,4,6,3,5,2]=>3 [1,4,6,5,2,3]=>3 [1,4,6,5,3,2]=>4 [1,5,2,3,4,6]=>2 [1,5,2,3,6,4]=>3 [1,5,2,4,3,6]=>3 [1,5,2,4,6,3]=>3 [1,5,2,6,3,4]=>3 [1,5,2,6,4,3]=>4 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>4 [1,5,3,4,2,6]=>3 [1,5,3,4,6,2]=>3 [1,5,3,6,2,4]=>3 [1,5,3,6,4,2]=>4 [1,5,4,2,3,6]=>3 [1,5,4,2,6,3]=>4 [1,5,4,3,2,6]=>4 [1,5,4,3,6,2]=>4 [1,5,4,6,2,3]=>3 [1,5,4,6,3,2]=>4 [1,5,6,2,3,4]=>2 [1,5,6,2,4,3]=>3 [1,5,6,3,2,4]=>3 [1,5,6,3,4,2]=>3 [1,5,6,4,2,3]=>3 [1,5,6,4,3,2]=>4 [1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>3 [1,6,2,4,3,5]=>3 [1,6,2,4,5,3]=>3 [1,6,2,5,3,4]=>3 [1,6,2,5,4,3]=>4 [1,6,3,2,4,5]=>3 [1,6,3,2,5,4]=>4 [1,6,3,4,2,5]=>3 [1,6,3,4,5,2]=>3 [1,6,3,5,2,4]=>3 [1,6,3,5,4,2]=>4 [1,6,4,2,3,5]=>3 [1,6,4,2,5,3]=>4 [1,6,4,3,2,5]=>4 [1,6,4,3,5,2]=>4 [1,6,4,5,2,3]=>3 [1,6,4,5,3,2]=>4 [1,6,5,2,3,4]=>3 [1,6,5,2,4,3]=>4 [1,6,5,3,2,4]=>4 [1,6,5,3,4,2]=>4 [1,6,5,4,2,3]=>4 [1,6,5,4,3,2]=>5 [2,1,3,4,5,6]=>2 [2,1,3,4,6,5]=>3 [2,1,3,5,4,6]=>3 [2,1,3,5,6,4]=>3 [2,1,3,6,4,5]=>3 [2,1,3,6,5,4]=>4 [2,1,4,3,5,6]=>3 [2,1,4,3,6,5]=>4 [2,1,4,5,3,6]=>3 [2,1,4,5,6,3]=>3 [2,1,4,6,3,5]=>3 [2,1,4,6,5,3]=>4 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>4 [2,1,5,4,3,6]=>4 [2,1,5,4,6,3]=>4 [2,1,5,6,3,4]=>3 [2,1,5,6,4,3]=>4 [2,1,6,3,4,5]=>3 [2,1,6,3,5,4]=>4 [2,1,6,4,3,5]=>4 [2,1,6,4,5,3]=>4 [2,1,6,5,3,4]=>4 [2,1,6,5,4,3]=>5 [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]=>3 [2,3,1,6,4,5]=>3 [2,3,1,6,5,4]=>4 [2,3,4,1,5,6]=>2 [2,3,4,1,6,5]=>3 [2,3,4,5,1,6]=>2 [2,3,4,5,6,1]=>2 [2,3,4,6,1,5]=>2 [2,3,4,6,5,1]=>3 [2,3,5,1,4,6]=>2 [2,3,5,1,6,4]=>3 [2,3,5,4,1,6]=>3 [2,3,5,4,6,1]=>3 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>3 [2,3,6,1,4,5]=>2 [2,3,6,1,5,4]=>3 [2,3,6,4,1,5]=>3 [2,3,6,4,5,1]=>3 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>4 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>3 [2,4,1,5,3,6]=>3 [2,4,1,5,6,3]=>3 [2,4,1,6,3,5]=>3 [2,4,1,6,5,3]=>4 [2,4,3,1,5,6]=>3 [2,4,3,1,6,5]=>4 [2,4,3,5,1,6]=>3 [2,4,3,5,6,1]=>3 [2,4,3,6,1,5]=>3 [2,4,3,6,5,1]=>4 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>3 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>2 [2,4,5,6,3,1]=>3 [2,4,6,1,3,5]=>2 [2,4,6,1,5,3]=>3 [2,4,6,3,1,5]=>3 [2,4,6,3,5,1]=>3 [2,4,6,5,1,3]=>3 [2,4,6,5,3,1]=>4 [2,5,1,3,4,6]=>2 [2,5,1,3,6,4]=>3 [2,5,1,4,3,6]=>3 [2,5,1,4,6,3]=>3 [2,5,1,6,3,4]=>3 [2,5,1,6,4,3]=>4 [2,5,3,1,4,6]=>3 [2,5,3,1,6,4]=>4 [2,5,3,4,1,6]=>3 [2,5,3,4,6,1]=>3 [2,5,3,6,1,4]=>3 [2,5,3,6,4,1]=>4 [2,5,4,1,3,6]=>3 [2,5,4,1,6,3]=>4 [2,5,4,3,1,6]=>4 [2,5,4,3,6,1]=>4 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>4 [2,5,6,1,3,4]=>2 [2,5,6,1,4,3]=>3 [2,5,6,3,1,4]=>3 [2,5,6,3,4,1]=>3 [2,5,6,4,1,3]=>3 [2,5,6,4,3,1]=>4 [2,6,1,3,4,5]=>2 [2,6,1,3,5,4]=>3 [2,6,1,4,3,5]=>3 [2,6,1,4,5,3]=>3 [2,6,1,5,3,4]=>3 [2,6,1,5,4,3]=>4 [2,6,3,1,4,5]=>3 [2,6,3,1,5,4]=>4 [2,6,3,4,1,5]=>3 [2,6,3,4,5,1]=>3 [2,6,3,5,1,4]=>3 [2,6,3,5,4,1]=>4 [2,6,4,1,3,5]=>3 [2,6,4,1,5,3]=>4 [2,6,4,3,1,5]=>4 [2,6,4,3,5,1]=>4 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>4 [2,6,5,1,3,4]=>3 [2,6,5,1,4,3]=>4 [2,6,5,3,1,4]=>4 [2,6,5,3,4,1]=>4 [2,6,5,4,1,3]=>4 [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]=>3 [3,1,2,6,4,5]=>3 [3,1,2,6,5,4]=>4 [3,1,4,2,5,6]=>3 [3,1,4,2,6,5]=>4 [3,1,4,5,2,6]=>3 [3,1,4,5,6,2]=>3 [3,1,4,6,2,5]=>3 [3,1,4,6,5,2]=>4 [3,1,5,2,4,6]=>3 [3,1,5,2,6,4]=>4 [3,1,5,4,2,6]=>4 [3,1,5,4,6,2]=>4 [3,1,5,6,2,4]=>3 [3,1,5,6,4,2]=>4 [3,1,6,2,4,5]=>3 [3,1,6,2,5,4]=>4 [3,1,6,4,2,5]=>4 [3,1,6,4,5,2]=>4 [3,1,6,5,2,4]=>4 [3,1,6,5,4,2]=>5 [3,2,1,4,5,6]=>3 [3,2,1,4,6,5]=>4 [3,2,1,5,4,6]=>4 [3,2,1,5,6,4]=>4 [3,2,1,6,4,5]=>4 [3,2,1,6,5,4]=>5 [3,2,4,1,5,6]=>3 [3,2,4,1,6,5]=>4 [3,2,4,5,1,6]=>3 [3,2,4,5,6,1]=>3 [3,2,4,6,1,5]=>3 [3,2,4,6,5,1]=>4 [3,2,5,1,4,6]=>3 [3,2,5,1,6,4]=>4 [3,2,5,4,1,6]=>4 [3,2,5,4,6,1]=>4 [3,2,5,6,1,4]=>3 [3,2,5,6,4,1]=>4 [3,2,6,1,4,5]=>3 [3,2,6,1,5,4]=>4 [3,2,6,4,1,5]=>4 [3,2,6,4,5,1]=>4 [3,2,6,5,1,4]=>4 [3,2,6,5,4,1]=>5 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>3 [3,4,1,5,2,6]=>3 [3,4,1,5,6,2]=>3 [3,4,1,6,2,5]=>3 [3,4,1,6,5,2]=>4 [3,4,2,1,5,6]=>3 [3,4,2,1,6,5]=>4 [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]=>4 [3,4,5,1,2,6]=>2 [3,4,5,1,6,2]=>3 [3,4,5,2,1,6]=>3 [3,4,5,2,6,1]=>3 [3,4,5,6,1,2]=>2 [3,4,5,6,2,1]=>3 [3,4,6,1,2,5]=>2 [3,4,6,1,5,2]=>3 [3,4,6,2,1,5]=>3 [3,4,6,2,5,1]=>3 [3,4,6,5,1,2]=>3 [3,4,6,5,2,1]=>4 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>3 [3,5,1,4,2,6]=>3 [3,5,1,4,6,2]=>3 [3,5,1,6,2,4]=>3 [3,5,1,6,4,2]=>4 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>4 [3,5,2,4,1,6]=>3 [3,5,2,4,6,1]=>3 [3,5,2,6,1,4]=>3 [3,5,2,6,4,1]=>4 [3,5,4,1,2,6]=>3 [3,5,4,1,6,2]=>4 [3,5,4,2,1,6]=>4 [3,5,4,2,6,1]=>4 [3,5,4,6,1,2]=>3 [3,5,4,6,2,1]=>4 [3,5,6,1,2,4]=>2 [3,5,6,1,4,2]=>3 [3,5,6,2,1,4]=>3 [3,5,6,2,4,1]=>3 [3,5,6,4,1,2]=>3 [3,5,6,4,2,1]=>4 [3,6,1,2,4,5]=>2 [3,6,1,2,5,4]=>3 [3,6,1,4,2,5]=>3 [3,6,1,4,5,2]=>3 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>4 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>4 [3,6,2,4,1,5]=>3 [3,6,2,4,5,1]=>3 [3,6,2,5,1,4]=>3 [3,6,2,5,4,1]=>4 [3,6,4,1,2,5]=>3 [3,6,4,1,5,2]=>4 [3,6,4,2,1,5]=>4 [3,6,4,2,5,1]=>4 [3,6,4,5,1,2]=>3 [3,6,4,5,2,1]=>4 [3,6,5,1,2,4]=>3 [3,6,5,1,4,2]=>4 [3,6,5,2,1,4]=>4 [3,6,5,2,4,1]=>4 [3,6,5,4,1,2]=>4 [3,6,5,4,2,1]=>5 [4,1,2,3,5,6]=>2 [4,1,2,3,6,5]=>3 [4,1,2,5,3,6]=>3 [4,1,2,5,6,3]=>3 [4,1,2,6,3,5]=>3 [4,1,2,6,5,3]=>4 [4,1,3,2,5,6]=>3 [4,1,3,2,6,5]=>4 [4,1,3,5,2,6]=>3 [4,1,3,5,6,2]=>3 [4,1,3,6,2,5]=>3 [4,1,3,6,5,2]=>4 [4,1,5,2,3,6]=>3 [4,1,5,2,6,3]=>4 [4,1,5,3,2,6]=>4 [4,1,5,3,6,2]=>4 [4,1,5,6,2,3]=>3 [4,1,5,6,3,2]=>4 [4,1,6,2,3,5]=>3 [4,1,6,2,5,3]=>4 [4,1,6,3,2,5]=>4 [4,1,6,3,5,2]=>4 [4,1,6,5,2,3]=>4 [4,1,6,5,3,2]=>5 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>4 [4,2,1,5,3,6]=>4 [4,2,1,5,6,3]=>4 [4,2,1,6,3,5]=>4 [4,2,1,6,5,3]=>5 [4,2,3,1,5,6]=>3 [4,2,3,1,6,5]=>4 [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]=>4 [4,2,5,1,3,6]=>3 [4,2,5,1,6,3]=>4 [4,2,5,3,1,6]=>4 [4,2,5,3,6,1]=>4 [4,2,5,6,1,3]=>3 [4,2,5,6,3,1]=>4 [4,2,6,1,3,5]=>3 [4,2,6,1,5,3]=>4 [4,2,6,3,1,5]=>4 [4,2,6,3,5,1]=>4 [4,2,6,5,1,3]=>4 [4,2,6,5,3,1]=>5 [4,3,1,2,5,6]=>3 [4,3,1,2,6,5]=>4 [4,3,1,5,2,6]=>4 [4,3,1,5,6,2]=>4 [4,3,1,6,2,5]=>4 [4,3,1,6,5,2]=>5 [4,3,2,1,5,6]=>4 [4,3,2,1,6,5]=>5 [4,3,2,5,1,6]=>4 [4,3,2,5,6,1]=>4 [4,3,2,6,1,5]=>4 [4,3,2,6,5,1]=>5 [4,3,5,1,2,6]=>3 [4,3,5,1,6,2]=>4 [4,3,5,2,1,6]=>4 [4,3,5,2,6,1]=>4 [4,3,5,6,1,2]=>3 [4,3,5,6,2,1]=>4 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>4 [4,3,6,2,1,5]=>4 [4,3,6,2,5,1]=>4 [4,3,6,5,1,2]=>4 [4,3,6,5,2,1]=>5 [4,5,1,2,3,6]=>2 [4,5,1,2,6,3]=>3 [4,5,1,3,2,6]=>3 [4,5,1,3,6,2]=>3 [4,5,1,6,2,3]=>3 [4,5,1,6,3,2]=>4 [4,5,2,1,3,6]=>3 [4,5,2,1,6,3]=>4 [4,5,2,3,1,6]=>3 [4,5,2,3,6,1]=>3 [4,5,2,6,1,3]=>3 [4,5,2,6,3,1]=>4 [4,5,3,1,2,6]=>3 [4,5,3,1,6,2]=>4 [4,5,3,2,1,6]=>4 [4,5,3,2,6,1]=>4 [4,5,3,6,1,2]=>3 [4,5,3,6,2,1]=>4 [4,5,6,1,2,3]=>2 [4,5,6,1,3,2]=>3 [4,5,6,2,1,3]=>3 [4,5,6,2,3,1]=>3 [4,5,6,3,1,2]=>3 [4,5,6,3,2,1]=>4 [4,6,1,2,3,5]=>2 [4,6,1,2,5,3]=>3 [4,6,1,3,2,5]=>3 [4,6,1,3,5,2]=>3 [4,6,1,5,2,3]=>3 [4,6,1,5,3,2]=>4 [4,6,2,1,3,5]=>3 [4,6,2,1,5,3]=>4 [4,6,2,3,1,5]=>3 [4,6,2,3,5,1]=>3 [4,6,2,5,1,3]=>3 [4,6,2,5,3,1]=>4 [4,6,3,1,2,5]=>3 [4,6,3,1,5,2]=>4 [4,6,3,2,1,5]=>4 [4,6,3,2,5,1]=>4 [4,6,3,5,1,2]=>3 [4,6,3,5,2,1]=>4 [4,6,5,1,2,3]=>3 [4,6,5,1,3,2]=>4 [4,6,5,2,1,3]=>4 [4,6,5,2,3,1]=>4 [4,6,5,3,1,2]=>4 [4,6,5,3,2,1]=>5 [5,1,2,3,4,6]=>2 [5,1,2,3,6,4]=>3 [5,1,2,4,3,6]=>3 [5,1,2,4,6,3]=>3 [5,1,2,6,3,4]=>3 [5,1,2,6,4,3]=>4 [5,1,3,2,4,6]=>3 [5,1,3,2,6,4]=>4 [5,1,3,4,2,6]=>3 [5,1,3,4,6,2]=>3 [5,1,3,6,2,4]=>3 [5,1,3,6,4,2]=>4 [5,1,4,2,3,6]=>3 [5,1,4,2,6,3]=>4 [5,1,4,3,2,6]=>4 [5,1,4,3,6,2]=>4 [5,1,4,6,2,3]=>3 [5,1,4,6,3,2]=>4 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>4 [5,1,6,3,2,4]=>4 [5,1,6,3,4,2]=>4 [5,1,6,4,2,3]=>4 [5,1,6,4,3,2]=>5 [5,2,1,3,4,6]=>3 [5,2,1,3,6,4]=>4 [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]=>5 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>4 [5,2,3,4,1,6]=>3 [5,2,3,4,6,1]=>3 [5,2,3,6,1,4]=>3 [5,2,3,6,4,1]=>4 [5,2,4,1,3,6]=>3 [5,2,4,1,6,3]=>4 [5,2,4,3,1,6]=>4 [5,2,4,3,6,1]=>4 [5,2,4,6,1,3]=>3 [5,2,4,6,3,1]=>4 [5,2,6,1,3,4]=>3 [5,2,6,1,4,3]=>4 [5,2,6,3,1,4]=>4 [5,2,6,3,4,1]=>4 [5,2,6,4,1,3]=>4 [5,2,6,4,3,1]=>5 [5,3,1,2,4,6]=>3 [5,3,1,2,6,4]=>4 [5,3,1,4,2,6]=>4 [5,3,1,4,6,2]=>4 [5,3,1,6,2,4]=>4 [5,3,1,6,4,2]=>5 [5,3,2,1,4,6]=>4 [5,3,2,1,6,4]=>5 [5,3,2,4,1,6]=>4 [5,3,2,4,6,1]=>4 [5,3,2,6,1,4]=>4 [5,3,2,6,4,1]=>5 [5,3,4,1,2,6]=>3 [5,3,4,1,6,2]=>4 [5,3,4,2,1,6]=>4 [5,3,4,2,6,1]=>4 [5,3,4,6,1,2]=>3 [5,3,4,6,2,1]=>4 [5,3,6,1,2,4]=>3 [5,3,6,1,4,2]=>4 [5,3,6,2,1,4]=>4 [5,3,6,2,4,1]=>4 [5,3,6,4,1,2]=>4 [5,3,6,4,2,1]=>5 [5,4,1,2,3,6]=>3 [5,4,1,2,6,3]=>4 [5,4,1,3,2,6]=>4 [5,4,1,3,6,2]=>4 [5,4,1,6,2,3]=>4 [5,4,1,6,3,2]=>5 [5,4,2,1,3,6]=>4 [5,4,2,1,6,3]=>5 [5,4,2,3,1,6]=>4 [5,4,2,3,6,1]=>4 [5,4,2,6,1,3]=>4 [5,4,2,6,3,1]=>5 [5,4,3,1,2,6]=>4 [5,4,3,1,6,2]=>5 [5,4,3,2,1,6]=>5 [5,4,3,2,6,1]=>5 [5,4,3,6,1,2]=>4 [5,4,3,6,2,1]=>5 [5,4,6,1,2,3]=>3 [5,4,6,1,3,2]=>4 [5,4,6,2,1,3]=>4 [5,4,6,2,3,1]=>4 [5,4,6,3,1,2]=>4 [5,4,6,3,2,1]=>5 [5,6,1,2,3,4]=>2 [5,6,1,2,4,3]=>3 [5,6,1,3,2,4]=>3 [5,6,1,3,4,2]=>3 [5,6,1,4,2,3]=>3 [5,6,1,4,3,2]=>4 [5,6,2,1,3,4]=>3 [5,6,2,1,4,3]=>4 [5,6,2,3,1,4]=>3 [5,6,2,3,4,1]=>3 [5,6,2,4,1,3]=>3 [5,6,2,4,3,1]=>4 [5,6,3,1,2,4]=>3 [5,6,3,1,4,2]=>4 [5,6,3,2,1,4]=>4 [5,6,3,2,4,1]=>4 [5,6,3,4,1,2]=>3 [5,6,3,4,2,1]=>4 [5,6,4,1,2,3]=>3 [5,6,4,1,3,2]=>4 [5,6,4,2,1,3]=>4 [5,6,4,2,3,1]=>4 [5,6,4,3,1,2]=>4 [5,6,4,3,2,1]=>5 [6,1,2,3,4,5]=>2 [6,1,2,3,5,4]=>3 [6,1,2,4,3,5]=>3 [6,1,2,4,5,3]=>3 [6,1,2,5,3,4]=>3 [6,1,2,5,4,3]=>4 [6,1,3,2,4,5]=>3 [6,1,3,2,5,4]=>4 [6,1,3,4,2,5]=>3 [6,1,3,4,5,2]=>3 [6,1,3,5,2,4]=>3 [6,1,3,5,4,2]=>4 [6,1,4,2,3,5]=>3 [6,1,4,2,5,3]=>4 [6,1,4,3,2,5]=>4 [6,1,4,3,5,2]=>4 [6,1,4,5,2,3]=>3 [6,1,4,5,3,2]=>4 [6,1,5,2,3,4]=>3 [6,1,5,2,4,3]=>4 [6,1,5,3,2,4]=>4 [6,1,5,3,4,2]=>4 [6,1,5,4,2,3]=>4 [6,1,5,4,3,2]=>5 [6,2,1,3,4,5]=>3 [6,2,1,3,5,4]=>4 [6,2,1,4,3,5]=>4 [6,2,1,4,5,3]=>4 [6,2,1,5,3,4]=>4 [6,2,1,5,4,3]=>5 [6,2,3,1,4,5]=>3 [6,2,3,1,5,4]=>4 [6,2,3,4,1,5]=>3 [6,2,3,4,5,1]=>3 [6,2,3,5,1,4]=>3 [6,2,3,5,4,1]=>4 [6,2,4,1,3,5]=>3 [6,2,4,1,5,3]=>4 [6,2,4,3,1,5]=>4 [6,2,4,3,5,1]=>4 [6,2,4,5,1,3]=>3 [6,2,4,5,3,1]=>4 [6,2,5,1,3,4]=>3 [6,2,5,1,4,3]=>4 [6,2,5,3,1,4]=>4 [6,2,5,3,4,1]=>4 [6,2,5,4,1,3]=>4 [6,2,5,4,3,1]=>5 [6,3,1,2,4,5]=>3 [6,3,1,2,5,4]=>4 [6,3,1,4,2,5]=>4 [6,3,1,4,5,2]=>4 [6,3,1,5,2,4]=>4 [6,3,1,5,4,2]=>5 [6,3,2,1,4,5]=>4 [6,3,2,1,5,4]=>5 [6,3,2,4,1,5]=>4 [6,3,2,4,5,1]=>4 [6,3,2,5,1,4]=>4 [6,3,2,5,4,1]=>5 [6,3,4,1,2,5]=>3 [6,3,4,1,5,2]=>4 [6,3,4,2,1,5]=>4 [6,3,4,2,5,1]=>4 [6,3,4,5,1,2]=>3 [6,3,4,5,2,1]=>4 [6,3,5,1,2,4]=>3 [6,3,5,1,4,2]=>4 [6,3,5,2,1,4]=>4 [6,3,5,2,4,1]=>4 [6,3,5,4,1,2]=>4 [6,3,5,4,2,1]=>5 [6,4,1,2,3,5]=>3 [6,4,1,2,5,3]=>4 [6,4,1,3,2,5]=>4 [6,4,1,3,5,2]=>4 [6,4,1,5,2,3]=>4 [6,4,1,5,3,2]=>5 [6,4,2,1,3,5]=>4 [6,4,2,1,5,3]=>5 [6,4,2,3,1,5]=>4 [6,4,2,3,5,1]=>4 [6,4,2,5,1,3]=>4 [6,4,2,5,3,1]=>5 [6,4,3,1,2,5]=>4 [6,4,3,1,5,2]=>5 [6,4,3,2,1,5]=>5 [6,4,3,2,5,1]=>5 [6,4,3,5,1,2]=>4 [6,4,3,5,2,1]=>5 [6,4,5,1,2,3]=>3 [6,4,5,1,3,2]=>4 [6,4,5,2,1,3]=>4 [6,4,5,2,3,1]=>4 [6,4,5,3,1,2]=>4 [6,4,5,3,2,1]=>5 [6,5,1,2,3,4]=>3 [6,5,1,2,4,3]=>4 [6,5,1,3,2,4]=>4 [6,5,1,3,4,2]=>4 [6,5,1,4,2,3]=>4 [6,5,1,4,3,2]=>5 [6,5,2,1,3,4]=>4 [6,5,2,1,4,3]=>5 [6,5,2,3,1,4]=>4 [6,5,2,3,4,1]=>4 [6,5,2,4,1,3]=>4 [6,5,2,4,3,1]=>5 [6,5,3,1,2,4]=>4 [6,5,3,1,4,2]=>5 [6,5,3,2,1,4]=>5 [6,5,3,2,4,1]=>5 [6,5,3,4,1,2]=>4 [6,5,3,4,2,1]=>5 [6,5,4,1,2,3]=>4 [6,5,4,1,3,2]=>5 [6,5,4,2,1,3]=>5 [6,5,4,2,3,1]=>5 [6,5,4,3,1,2]=>5 [6,5,4,3,2,1]=>6
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Description
The width of the tree associated to a permutation.
A permutation can be mapped to a rooted tree with vertices $\{0,1,2,\ldots,n\}$ and root $0$ in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1].
The width of the tree is given by the number of leaves of this tree.
Note that, due to the construction of this tree, the width of the tree is always one more than the number of descents St000021The number of descents of a permutation.. This also matches the number of runs in a permutation St000470The number of runs in a permutation..
See also St000308The height of the tree associated to a permutation. for the height of this tree.
References
[1] Triangle of Eulerian numbers T(n,k), 0<=k<=n, read by rows. OEIS:A123125
[2] http://oeis.org/wiki/User:Peter_Luschny/PermutationTrees
Code
def statistic(pi):
    if pi == []: return 0
    w, i, branch, next = 1, 0, [0], pi[0]
    while true:
        while next < branch[len(branch)-1]:
            branch.pop()
        current = 0
        while next > current:
            i += 1
            if i == len(pi): return w
            branch.append(next)
            current, next = next, pi[i]
        w += 1
Created
Dec 11, 2015 at 11:05 by Peter Luschny
Updated
Feb 25, 2022 at 14:38 by Nadia Lafreniere