edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,1]=>0 [1,2]=>1 [2,1]=>0 [1,1,1]=>0 [1,1,2]=>1 [1,2,1]=>0 [2,1,1]=>0 [1,1,3]=>1 [1,3,1]=>1 [3,1,1]=>0 [1,2,2]=>2 [2,1,2]=>1 [2,2,1]=>0 [1,2,3]=>3 [1,3,2]=>2 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>2 [3,2,1]=>0 [1,1,1,1]=>0 [1,1,1,2]=>1 [1,1,2,1]=>0 [1,2,1,1]=>0 [2,1,1,1]=>0 [1,1,1,3]=>1 [1,1,3,1]=>1 [1,3,1,1]=>0 [3,1,1,1]=>0 [1,1,1,4]=>1 [1,1,4,1]=>1 [1,4,1,1]=>1 [4,1,1,1]=>0 [1,1,2,2]=>2 [1,2,1,2]=>1 [1,2,2,1]=>0 [2,1,1,2]=>1 [2,1,2,1]=>0 [2,2,1,1]=>0 [1,1,2,3]=>2 [1,1,3,2]=>2 [1,2,1,3]=>1 [1,2,3,1]=>1 [1,3,1,2]=>2 [1,3,2,1]=>0 [2,1,1,3]=>1 [2,1,3,1]=>1 [2,3,1,1]=>0 [3,1,1,2]=>1 [3,1,2,1]=>0 [3,2,1,1]=>0 [1,1,2,4]=>3 [1,1,4,2]=>2 [1,2,1,4]=>1 [1,2,4,1]=>1 [1,4,1,2]=>2 [1,4,2,1]=>1 [2,1,1,4]=>1 [2,1,4,1]=>1 [2,4,1,1]=>1 [4,1,1,2]=>2 [4,1,2,1]=>0 [4,2,1,1]=>0 [1,1,3,3]=>2 [1,3,1,3]=>2 [1,3,3,1]=>2 [3,1,1,3]=>1 [3,1,3,1]=>1 [3,3,1,1]=>0 [1,1,3,4]=>3 [1,1,4,3]=>2 [1,3,1,4]=>3 [1,3,4,1]=>3 [1,4,1,3]=>2 [1,4,3,1]=>2 [3,1,1,4]=>1 [3,1,4,1]=>1 [3,4,1,1]=>1 [4,1,1,3]=>2 [4,1,3,1]=>2 [4,3,1,1]=>0 [1,2,2,2]=>3 [2,1,2,2]=>2 [2,2,1,2]=>1 [2,2,2,1]=>0 [1,2,2,3]=>4 [1,2,3,2]=>3 [1,3,2,2]=>3 [2,1,2,3]=>2 [2,1,3,2]=>2 [2,2,1,3]=>1 [2,2,3,1]=>1 [2,3,1,2]=>2 [2,3,2,1]=>0 [3,1,2,2]=>3 [3,2,1,2]=>1 [3,2,2,1]=>0 [1,2,2,4]=>4 [1,2,4,2]=>4 [1,4,2,2]=>3 [2,1,2,4]=>3 [2,1,4,2]=>2 [2,2,1,4]=>1 [2,2,4,1]=>1 [2,4,1,2]=>2 [2,4,2,1]=>1 [4,1,2,2]=>3 [4,2,1,2]=>2 [4,2,2,1]=>0 [1,2,3,3]=>5 [1,3,2,3]=>4 [1,3,3,2]=>3 [2,1,3,3]=>2 [2,3,1,3]=>2 [2,3,3,1]=>2 [3,1,2,3]=>4 [3,1,3,2]=>3 [3,2,1,3]=>1 [3,2,3,1]=>1 [3,3,1,2]=>3 [3,3,2,1]=>0 [1,2,3,4]=>6 [1,2,4,3]=>5 [1,3,2,4]=>4 [1,3,4,2]=>4 [1,4,2,3]=>5 [1,4,3,2]=>3 [2,1,3,4]=>3 [2,1,4,3]=>2 [2,3,1,4]=>3 [2,3,4,1]=>3 [2,4,1,3]=>2 [2,4,3,1]=>2 [3,1,2,4]=>4 [3,1,4,2]=>4 [3,2,1,4]=>1 [3,2,4,1]=>1 [3,4,1,2]=>4 [3,4,2,1]=>1 [4,1,2,3]=>5 [4,1,3,2]=>3 [4,2,1,3]=>2 [4,2,3,1]=>2 [4,3,1,2]=>3 [4,3,2,1]=>0 [1,1,1,1,1]=>0 [1,1,1,1,2]=>1 [1,1,1,2,1]=>0 [1,1,2,1,1]=>0 [1,2,1,1,1]=>0 [2,1,1,1,1]=>0 [1,1,1,1,3]=>1 [1,1,1,3,1]=>1 [1,1,3,1,1]=>0 [1,3,1,1,1]=>0 [3,1,1,1,1]=>0 [1,1,1,1,4]=>1 [1,1,1,4,1]=>1 [1,1,4,1,1]=>1 [1,4,1,1,1]=>0 [4,1,1,1,1]=>0 [1,1,1,1,5]=>1 [1,1,1,5,1]=>1 [1,1,5,1,1]=>1 [1,5,1,1,1]=>1 [5,1,1,1,1]=>0 [1,1,1,2,2]=>2 [1,1,2,1,2]=>1 [1,1,2,2,1]=>0 [1,2,1,1,2]=>1 [1,2,1,2,1]=>0 [1,2,2,1,1]=>0 [2,1,1,1,2]=>1 [2,1,1,2,1]=>0 [2,1,2,1,1]=>0 [2,2,1,1,1]=>0 [1,1,1,2,3]=>2 [1,1,1,3,2]=>2 [1,1,2,1,3]=>1 [1,1,2,3,1]=>1 [1,1,3,1,2]=>2 [1,1,3,2,1]=>0 [1,2,1,1,3]=>1 [1,2,1,3,1]=>1 [1,2,3,1,1]=>0 [1,3,1,1,2]=>1 [1,3,1,2,1]=>0 [1,3,2,1,1]=>0 [2,1,1,1,3]=>1 [2,1,1,3,1]=>1 [2,1,3,1,1]=>0 [2,3,1,1,1]=>0 [3,1,1,1,2]=>1 [3,1,1,2,1]=>0 [3,1,2,1,1]=>0 [3,2,1,1,1]=>0 [1,1,1,2,4]=>2 [1,1,1,4,2]=>2 [1,1,2,1,4]=>1 [1,1,2,4,1]=>1 [1,1,4,1,2]=>2 [1,1,4,2,1]=>1 [1,2,1,1,4]=>1 [1,2,1,4,1]=>1 [1,2,4,1,1]=>1 [1,4,1,1,2]=>2 [1,4,1,2,1]=>0 [1,4,2,1,1]=>0 [2,1,1,1,4]=>1 [2,1,1,4,1]=>1 [2,1,4,1,1]=>1 [2,4,1,1,1]=>0 [4,1,1,1,2]=>1 [4,1,1,2,1]=>0 [4,1,2,1,1]=>0 [4,2,1,1,1]=>0 [1,1,1,2,5]=>3 [1,1,1,5,2]=>2 [1,1,2,1,5]=>1 [1,1,2,5,1]=>1 [1,1,5,1,2]=>2 [1,1,5,2,1]=>1 [1,2,1,1,5]=>1 [1,2,1,5,1]=>1 [1,2,5,1,1]=>1 [1,5,1,1,2]=>2 [1,5,1,2,1]=>1 [1,5,2,1,1]=>1 [2,1,1,1,5]=>1 [2,1,1,5,1]=>1 [2,1,5,1,1]=>1 [2,5,1,1,1]=>1 [5,1,1,1,2]=>2 [5,1,1,2,1]=>0 [5,1,2,1,1]=>0 [5,2,1,1,1]=>0 [1,1,1,3,3]=>2 [1,1,3,1,3]=>2 [1,1,3,3,1]=>2 [1,3,1,1,3]=>1 [1,3,1,3,1]=>1 [1,3,3,1,1]=>0 [3,1,1,1,3]=>1 [3,1,1,3,1]=>1 [3,1,3,1,1]=>0 [3,3,1,1,1]=>0 [1,1,1,3,4]=>2 [1,1,1,4,3]=>2 [1,1,3,1,4]=>2 [1,1,3,4,1]=>2 [1,1,4,1,3]=>2 [1,1,4,3,1]=>2 [1,3,1,1,4]=>1 [1,3,1,4,1]=>1 [1,3,4,1,1]=>1 [1,4,1,1,3]=>2 [1,4,1,3,1]=>2 [1,4,3,1,1]=>0 [3,1,1,1,4]=>1 [3,1,1,4,1]=>1 [3,1,4,1,1]=>1 [3,4,1,1,1]=>0 [4,1,1,1,3]=>1 [4,1,1,3,1]=>1 [4,1,3,1,1]=>0 [4,3,1,1,1]=>0 [1,1,1,3,5]=>3 [1,1,1,5,3]=>2 [1,1,3,1,5]=>3 [1,1,3,5,1]=>3 [1,1,5,1,3]=>2 [1,1,5,3,1]=>2 [1,3,1,1,5]=>1 [1,3,1,5,1]=>1 [1,3,5,1,1]=>1 [1,5,1,1,3]=>2 [1,5,1,3,1]=>2 [1,5,3,1,1]=>1 [3,1,1,1,5]=>1 [3,1,1,5,1]=>1 [3,1,5,1,1]=>1 [3,5,1,1,1]=>1 [5,1,1,1,3]=>2 [5,1,1,3,1]=>2 [5,1,3,1,1]=>0 [5,3,1,1,1]=>0 [1,1,1,4,4]=>2 [1,1,4,1,4]=>2 [1,1,4,4,1]=>2 [1,4,1,1,4]=>2 [1,4,1,4,1]=>2 [1,4,4,1,1]=>2 [4,1,1,1,4]=>1 [4,1,1,4,1]=>1 [4,1,4,1,1]=>1 [4,4,1,1,1]=>0 [1,1,1,4,5]=>3 [1,1,1,5,4]=>2 [1,1,4,1,5]=>3 [1,1,4,5,1]=>3 [1,1,5,1,4]=>2 [1,1,5,4,1]=>2 [1,4,1,1,5]=>3 [1,4,1,5,1]=>3 [1,4,5,1,1]=>3 [1,5,1,1,4]=>2 [1,5,1,4,1]=>2 [1,5,4,1,1]=>2 [4,1,1,1,5]=>1 [4,1,1,5,1]=>1 [4,1,5,1,1]=>1 [4,5,1,1,1]=>1 [5,1,1,1,4]=>2 [5,1,1,4,1]=>2 [5,1,4,1,1]=>2 [5,4,1,1,1]=>0 [1,1,2,2,2]=>3 [1,2,1,2,2]=>2 [1,2,2,1,2]=>1 [1,2,2,2,1]=>0 [2,1,1,2,2]=>2 [2,1,2,1,2]=>1 [2,1,2,2,1]=>0 [2,2,1,1,2]=>1 [2,2,1,2,1]=>0 [2,2,2,1,1]=>0 [1,1,2,2,3]=>3 [1,1,2,3,2]=>3 [1,1,3,2,2]=>3 [1,2,1,2,3]=>2 [1,2,1,3,2]=>2 [1,2,2,1,3]=>1 [1,2,2,3,1]=>1 [1,2,3,1,2]=>2 [1,2,3,2,1]=>0 [1,3,1,2,2]=>3 [1,3,2,1,2]=>1 [1,3,2,2,1]=>0 [2,1,1,2,3]=>2 [2,1,1,3,2]=>2 [2,1,2,1,3]=>1 [2,1,2,3,1]=>1 [2,1,3,1,2]=>2 [2,1,3,2,1]=>0 [2,2,1,1,3]=>1 [2,2,1,3,1]=>1 [2,2,3,1,1]=>0 [2,3,1,1,2]=>1 [2,3,1,2,1]=>0 [2,3,2,1,1]=>0 [3,1,1,2,2]=>2 [3,1,2,1,2]=>1 [3,1,2,2,1]=>0 [3,2,1,1,2]=>1 [3,2,1,2,1]=>0 [3,2,2,1,1]=>0 [1,1,2,2,4]=>4 [1,1,2,4,2]=>3 [1,1,4,2,2]=>3 [1,2,1,2,4]=>2 [1,2,1,4,2]=>2 [1,2,2,1,4]=>1 [1,2,2,4,1]=>1 [1,2,4,1,2]=>2 [1,2,4,2,1]=>1 [1,4,1,2,2]=>3 [1,4,2,1,2]=>2 [1,4,2,2,1]=>0 [2,1,1,2,4]=>2 [2,1,1,4,2]=>2 [2,1,2,1,4]=>1 [2,1,2,4,1]=>1 [2,1,4,1,2]=>2 [2,1,4,2,1]=>1 [2,2,1,1,4]=>1 [2,2,1,4,1]=>1 [2,2,4,1,1]=>1 [2,4,1,1,2]=>2 [2,4,1,2,1]=>0 [2,4,2,1,1]=>0 [4,1,1,2,2]=>3 [4,1,2,1,2]=>1 [4,1,2,2,1]=>0 [4,2,1,1,2]=>1 [4,2,1,2,1]=>0 [4,2,2,1,1]=>0 [1,1,2,2,5]=>4 [1,1,2,5,2]=>4 [1,1,5,2,2]=>3 [1,2,1,2,5]=>3 [1,2,1,5,2]=>2 [1,2,2,1,5]=>1 [1,2,2,5,1]=>1 [1,2,5,1,2]=>2 [1,2,5,2,1]=>1 [1,5,1,2,2]=>3 [1,5,2,1,2]=>2 [1,5,2,2,1]=>1 [2,1,1,2,5]=>3 [2,1,1,5,2]=>2 [2,1,2,1,5]=>1 [2,1,2,5,1]=>1 [2,1,5,1,2]=>2 [2,1,5,2,1]=>1 [2,2,1,1,5]=>1 [2,2,1,5,1]=>1 [2,2,5,1,1]=>1 [2,5,1,1,2]=>2 [2,5,1,2,1]=>1 [2,5,2,1,1]=>1 [5,1,1,2,2]=>3 [5,1,2,1,2]=>2 [5,1,2,2,1]=>0 [5,2,1,1,2]=>2 [5,2,1,2,1]=>0 [5,2,2,1,1]=>0 [1,1,2,3,3]=>3 [1,1,3,2,3]=>3 [1,1,3,3,2]=>3 [1,2,1,3,3]=>2 [1,2,3,1,3]=>2 [1,2,3,3,1]=>2 [1,3,1,2,3]=>3 [1,3,1,3,2]=>3 [1,3,2,1,3]=>1 [1,3,2,3,1]=>1 [1,3,3,1,2]=>3 [1,3,3,2,1]=>0 [2,1,1,3,3]=>2 [2,1,3,1,3]=>2 [2,1,3,3,1]=>2 [2,3,1,1,3]=>1 [2,3,1,3,1]=>1 [2,3,3,1,1]=>0 [3,1,1,2,3]=>2 [3,1,1,3,2]=>2 [3,1,2,1,3]=>1 [3,1,2,3,1]=>1 [3,1,3,1,2]=>2 [3,1,3,2,1]=>0 [3,2,1,1,3]=>1 [3,2,1,3,1]=>1 [3,2,3,1,1]=>0 [3,3,1,1,2]=>1 [3,3,1,2,1]=>0 [3,3,2,1,1]=>0 [1,1,2,3,4]=>4 [1,1,2,4,3]=>3 [1,1,3,2,4]=>4 [1,1,3,4,2]=>3 [1,1,4,2,3]=>3 [1,1,4,3,2]=>3 [1,2,1,3,4]=>2 [1,2,1,4,3]=>2 [1,2,3,1,4]=>2 [1,2,3,4,1]=>2 [1,2,4,1,3]=>2 [1,2,4,3,1]=>2 [1,3,1,2,4]=>4 [1,3,1,4,2]=>3 [1,3,2,1,4]=>1 [1,3,2,4,1]=>1 [1,3,4,1,2]=>3 [1,3,4,2,1]=>1 [1,4,1,2,3]=>3 [1,4,1,3,2]=>3 [1,4,2,1,3]=>2 [1,4,2,3,1]=>2 [1,4,3,1,2]=>3 [1,4,3,2,1]=>0 [2,1,1,3,4]=>2 [2,1,1,4,3]=>2 [2,1,3,1,4]=>2 [2,1,3,4,1]=>2 [2,1,4,1,3]=>2 [2,1,4,3,1]=>2 [2,3,1,1,4]=>1 [2,3,1,4,1]=>1 [2,3,4,1,1]=>1 [2,4,1,1,3]=>2 [2,4,1,3,1]=>2 [2,4,3,1,1]=>0 [3,1,1,2,4]=>2 [3,1,1,4,2]=>2 [3,1,2,1,4]=>1 [3,1,2,4,1]=>1 [3,1,4,1,2]=>2 [3,1,4,2,1]=>1 [3,2,1,1,4]=>1 [3,2,1,4,1]=>1 [3,2,4,1,1]=>1 [3,4,1,1,2]=>2 [3,4,1,2,1]=>0 [3,4,2,1,1]=>0 [4,1,1,2,3]=>3 [4,1,1,3,2]=>3 [4,1,2,1,3]=>1 [4,1,2,3,1]=>1 [4,1,3,1,2]=>3 [4,1,3,2,1]=>0 [4,2,1,1,3]=>1 [4,2,1,3,1]=>1 [4,2,3,1,1]=>0 [4,3,1,1,2]=>1 [4,3,1,2,1]=>0 [4,3,2,1,1]=>0 [1,1,2,3,5]=>4 [1,1,2,5,3]=>4 [1,1,3,2,5]=>4 [1,1,3,5,2]=>4 [1,1,5,2,3]=>3 [1,1,5,3,2]=>3 [1,2,1,3,5]=>3 [1,2,1,5,3]=>2 [1,2,3,1,5]=>3 [1,2,3,5,1]=>3 [1,2,5,1,3]=>2 [1,2,5,3,1]=>2 [1,3,1,2,5]=>4 [1,3,1,5,2]=>4 [1,3,2,1,5]=>1 [1,3,2,5,1]=>1 [1,3,5,1,2]=>4 [1,3,5,2,1]=>1 [1,5,1,2,3]=>3 [1,5,1,3,2]=>3 [1,5,2,1,3]=>2 [1,5,2,3,1]=>2 [1,5,3,1,2]=>3 [1,5,3,2,1]=>1 [2,1,1,3,5]=>3 [2,1,1,5,3]=>2 [2,1,3,1,5]=>3 [2,1,3,5,1]=>3 [2,1,5,1,3]=>2 [2,1,5,3,1]=>2 [2,3,1,1,5]=>1 [2,3,1,5,1]=>1 [2,3,5,1,1]=>1 [2,5,1,1,3]=>2 [2,5,1,3,1]=>2 [2,5,3,1,1]=>1 [3,1,1,2,5]=>3 [3,1,1,5,2]=>2 [3,1,2,1,5]=>1 [3,1,2,5,1]=>1 [3,1,5,1,2]=>2 [3,1,5,2,1]=>1 [3,2,1,1,5]=>1 [3,2,1,5,1]=>1 [3,2,5,1,1]=>1 [3,5,1,1,2]=>2 [3,5,1,2,1]=>1 [3,5,2,1,1]=>1 [5,1,1,2,3]=>3 [5,1,1,3,2]=>3 [5,1,2,1,3]=>2 [5,1,2,3,1]=>2 [5,1,3,1,2]=>3 [5,1,3,2,1]=>0 [5,2,1,1,3]=>2 [5,2,1,3,1]=>2 [5,2,3,1,1]=>0 [5,3,1,1,2]=>2 [5,3,1,2,1]=>0 [5,3,2,1,1]=>0 [1,1,2,4,4]=>5 [1,1,4,2,4]=>4 [1,1,4,4,2]=>3 [1,2,1,4,4]=>2 [1,2,4,1,4]=>2 [1,2,4,4,1]=>2 [1,4,1,2,4]=>4 [1,4,1,4,2]=>3 [1,4,2,1,4]=>2 [1,4,2,4,1]=>2 [1,4,4,1,2]=>3 [1,4,4,2,1]=>2 [2,1,1,4,4]=>2 [2,1,4,1,4]=>2 [2,1,4,4,1]=>2 [2,4,1,1,4]=>2 [2,4,1,4,1]=>2 [2,4,4,1,1]=>2 [4,1,1,2,4]=>4 [4,1,1,4,2]=>3 [4,1,2,1,4]=>1 [4,1,2,4,1]=>1 [4,1,4,1,2]=>3 [4,1,4,2,1]=>1 [4,2,1,1,4]=>1 [4,2,1,4,1]=>1 [4,2,4,1,1]=>1 [4,4,1,1,2]=>3 [4,4,1,2,1]=>0 [4,4,2,1,1]=>0 [1,1,2,4,5]=>6 [1,1,2,5,4]=>5 [1,1,4,2,5]=>4 [1,1,4,5,2]=>4 [1,1,5,2,4]=>5 [1,1,5,4,2]=>3 [1,2,1,4,5]=>3 [1,2,1,5,4]=>2 [1,2,4,1,5]=>3 [1,2,4,5,1]=>3 [1,2,5,1,4]=>2 [1,2,5,4,1]=>2 [1,4,1,2,5]=>4 [1,4,1,5,2]=>4 [1,4,2,1,5]=>3 [1,4,2,5,1]=>3 [1,4,5,1,2]=>4 [1,4,5,2,1]=>3 [1,5,1,2,4]=>5 [1,5,1,4,2]=>3 [1,5,2,1,4]=>2 [1,5,2,4,1]=>2 [1,5,4,1,2]=>3 [1,5,4,2,1]=>2 [2,1,1,4,5]=>3 [2,1,1,5,4]=>2 [2,1,4,1,5]=>3 [2,1,4,5,1]=>3 [2,1,5,1,4]=>2 [2,1,5,4,1]=>2 [2,4,1,1,5]=>3 [2,4,1,5,1]=>3 [2,4,5,1,1]=>3 [2,5,1,1,4]=>2 [2,5,1,4,1]=>2 [2,5,4,1,1]=>2 [4,1,1,2,5]=>4 [4,1,1,5,2]=>4 [4,1,2,1,5]=>1 [4,1,2,5,1]=>1 [4,1,5,1,2]=>4 [4,1,5,2,1]=>1 [4,2,1,1,5]=>1 [4,2,1,5,1]=>1 [4,2,5,1,1]=>1 [4,5,1,1,2]=>4 [4,5,1,2,1]=>1 [4,5,2,1,1]=>1 [5,1,1,2,4]=>5 [5,1,1,4,2]=>3 [5,1,2,1,4]=>2 [5,1,2,4,1]=>2 [5,1,4,1,2]=>3 [5,1,4,2,1]=>2 [5,2,1,1,4]=>2 [5,2,1,4,1]=>2 [5,2,4,1,1]=>2 [5,4,1,1,2]=>3 [5,4,1,2,1]=>0 [5,4,2,1,1]=>0 [1,1,3,3,3]=>3 [1,3,1,3,3]=>3 [1,3,3,1,3]=>3 [1,3,3,3,1]=>3 [3,1,1,3,3]=>2 [3,1,3,1,3]=>2 [3,1,3,3,1]=>2 [3,3,1,1,3]=>1 [3,3,1,3,1]=>1 [3,3,3,1,1]=>0 [1,1,3,3,4]=>4 [1,1,3,4,3]=>3 [1,1,4,3,3]=>3 [1,3,1,3,4]=>4 [1,3,1,4,3]=>3 [1,3,3,1,4]=>4 [1,3,3,4,1]=>4 [1,3,4,1,3]=>3 [1,3,4,3,1]=>3 [1,4,1,3,3]=>3 [1,4,3,1,3]=>3 [1,4,3,3,1]=>3 [3,1,1,3,4]=>2 [3,1,1,4,3]=>2 [3,1,3,1,4]=>2 [3,1,3,4,1]=>2 [3,1,4,1,3]=>2 [3,1,4,3,1]=>2 [3,3,1,1,4]=>1 [3,3,1,4,1]=>1 [3,3,4,1,1]=>1 [3,4,1,1,3]=>2 [3,4,1,3,1]=>2 [3,4,3,1,1]=>0 [4,1,1,3,3]=>3 [4,1,3,1,3]=>3 [4,1,3,3,1]=>3 [4,3,1,1,3]=>1 [4,3,1,3,1]=>1 [4,3,3,1,1]=>0 [1,1,3,3,5]=>4 [1,1,3,5,3]=>4 [1,1,5,3,3]=>3 [1,3,1,3,5]=>4 [1,3,1,5,3]=>4 [1,3,3,1,5]=>4 [1,3,3,5,1]=>4 [1,3,5,1,3]=>4 [1,3,5,3,1]=>4 [1,5,1,3,3]=>3 [1,5,3,1,3]=>3 [1,5,3,3,1]=>3 [3,1,1,3,5]=>3 [3,1,1,5,3]=>2 [3,1,3,1,5]=>3 [3,1,3,5,1]=>3 [3,1,5,1,3]=>2 [3,1,5,3,1]=>2 [3,3,1,1,5]=>1 [3,3,1,5,1]=>1 [3,3,5,1,1]=>1 [3,5,1,1,3]=>2 [3,5,1,3,1]=>2 [3,5,3,1,1]=>1 [5,1,1,3,3]=>3 [5,1,3,1,3]=>3 [5,1,3,3,1]=>3 [5,3,1,1,3]=>2 [5,3,1,3,1]=>2 [5,3,3,1,1]=>0 [1,1,3,4,4]=>5 [1,1,4,3,4]=>4 [1,1,4,4,3]=>3 [1,3,1,4,4]=>5 [1,3,4,1,4]=>5 [1,3,4,4,1]=>5 [1,4,1,3,4]=>4 [1,4,1,4,3]=>3 [1,4,3,1,4]=>4 [1,4,3,4,1]=>4 [1,4,4,1,3]=>3 [1,4,4,3,1]=>3 [3,1,1,4,4]=>2 [3,1,4,1,4]=>2 [3,1,4,4,1]=>2 [3,4,1,1,4]=>2 [3,4,1,4,1]=>2 [3,4,4,1,1]=>2 [4,1,1,3,4]=>4 [4,1,1,4,3]=>3 [4,1,3,1,4]=>4 [4,1,3,4,1]=>4 [4,1,4,1,3]=>3 [4,1,4,3,1]=>3 [4,3,1,1,4]=>1 [4,3,1,4,1]=>1 [4,3,4,1,1]=>1 [4,4,1,1,3]=>3 [4,4,1,3,1]=>3 [4,4,3,1,1]=>0 [1,1,3,4,5]=>6 [1,1,3,5,4]=>5 [1,1,4,3,5]=>4 [1,1,4,5,3]=>4 [1,1,5,3,4]=>5 [1,1,5,4,3]=>3 [1,3,1,4,5]=>6 [1,3,1,5,4]=>5 [1,3,4,1,5]=>6 [1,3,4,5,1]=>6 [1,3,5,1,4]=>5 [1,3,5,4,1]=>5 [1,4,1,3,5]=>4 [1,4,1,5,3]=>4 [1,4,3,1,5]=>4 [1,4,3,5,1]=>4 [1,4,5,1,3]=>4 [1,4,5,3,1]=>4 [1,5,1,3,4]=>5 [1,5,1,4,3]=>3 [1,5,3,1,4]=>5 [1,5,3,4,1]=>5 [1,5,4,1,3]=>3 [1,5,4,3,1]=>3 [3,1,1,4,5]=>3 [3,1,1,5,4]=>2 [3,1,4,1,5]=>3 [3,1,4,5,1]=>3 [3,1,5,1,4]=>2 [3,1,5,4,1]=>2 [3,4,1,1,5]=>3 [3,4,1,5,1]=>3 [3,4,5,1,1]=>3 [3,5,1,1,4]=>2 [3,5,1,4,1]=>2 [3,5,4,1,1]=>2 [4,1,1,3,5]=>4 [4,1,1,5,3]=>4 [4,1,3,1,5]=>4 [4,1,3,5,1]=>4 [4,1,5,1,3]=>4 [4,1,5,3,1]=>4 [4,3,1,1,5]=>1 [4,3,1,5,1]=>1 [4,3,5,1,1]=>1 [4,5,1,1,3]=>4 [4,5,1,3,1]=>4 [4,5,3,1,1]=>1 [5,1,1,3,4]=>5 [5,1,1,4,3]=>3 [5,1,3,1,4]=>5 [5,1,3,4,1]=>5 [5,1,4,1,3]=>3 [5,1,4,3,1]=>3 [5,3,1,1,4]=>2 [5,3,1,4,1]=>2 [5,3,4,1,1]=>2 [5,4,1,1,3]=>3 [5,4,1,3,1]=>3 [5,4,3,1,1]=>0 [1,2,2,2,2]=>4 [2,1,2,2,2]=>3 [2,2,1,2,2]=>2 [2,2,2,1,2]=>1 [2,2,2,2,1]=>0 [1,2,2,2,3]=>5 [1,2,2,3,2]=>4 [1,2,3,2,2]=>4 [1,3,2,2,2]=>4 [2,1,2,2,3]=>3 [2,1,2,3,2]=>3 [2,1,3,2,2]=>3 [2,2,1,2,3]=>2 [2,2,1,3,2]=>2 [2,2,2,1,3]=>1 [2,2,2,3,1]=>1 [2,2,3,1,2]=>2 [2,2,3,2,1]=>0 [2,3,1,2,2]=>3 [2,3,2,1,2]=>1 [2,3,2,2,1]=>0 [3,1,2,2,2]=>4 [3,2,1,2,2]=>2 [3,2,2,1,2]=>1 [3,2,2,2,1]=>0 [1,2,2,2,4]=>5 [1,2,2,4,2]=>5 [1,2,4,2,2]=>4 [1,4,2,2,2]=>4 [2,1,2,2,4]=>4 [2,1,2,4,2]=>3 [2,1,4,2,2]=>3 [2,2,1,2,4]=>2 [2,2,1,4,2]=>2 [2,2,2,1,4]=>1 [2,2,2,4,1]=>1 [2,2,4,1,2]=>2 [2,2,4,2,1]=>1 [2,4,1,2,2]=>3 [2,4,2,1,2]=>2 [2,4,2,2,1]=>0 [4,1,2,2,2]=>4 [4,2,1,2,2]=>3 [4,2,2,1,2]=>1 [4,2,2,2,1]=>0 [1,2,2,2,5]=>5 [1,2,2,5,2]=>5 [1,2,5,2,2]=>5 [1,5,2,2,2]=>4 [2,1,2,2,5]=>4 [2,1,2,5,2]=>4 [2,1,5,2,2]=>3 [2,2,1,2,5]=>3 [2,2,1,5,2]=>2 [2,2,2,1,5]=>1 [2,2,2,5,1]=>1 [2,2,5,1,2]=>2 [2,2,5,2,1]=>1 [2,5,1,2,2]=>3 [2,5,2,1,2]=>2 [2,5,2,2,1]=>1 [5,1,2,2,2]=>4 [5,2,1,2,2]=>3 [5,2,2,1,2]=>2 [5,2,2,2,1]=>0 [1,2,2,3,3]=>6 [1,2,3,2,3]=>5 [1,2,3,3,2]=>4 [1,3,2,2,3]=>5 [1,3,2,3,2]=>4 [1,3,3,2,2]=>4 [2,1,2,3,3]=>3 [2,1,3,2,3]=>3 [2,1,3,3,2]=>3 [2,2,1,3,3]=>2 [2,2,3,1,3]=>2 [2,2,3,3,1]=>2 [2,3,1,2,3]=>3 [2,3,1,3,2]=>3 [2,3,2,1,3]=>1 [2,3,2,3,1]=>1 [2,3,3,1,2]=>3 [2,3,3,2,1]=>0 [3,1,2,2,3]=>5 [3,1,2,3,2]=>4 [3,1,3,2,2]=>4 [3,2,1,2,3]=>2 [3,2,1,3,2]=>2 [3,2,2,1,3]=>1 [3,2,2,3,1]=>1 [3,2,3,1,2]=>2 [3,2,3,2,1]=>0 [3,3,1,2,2]=>4 [3,3,2,1,2]=>1 [3,3,2,2,1]=>0 [1,2,2,3,4]=>6 [1,2,2,4,3]=>6 [1,2,3,2,4]=>5 [1,2,3,4,2]=>5 [1,2,4,2,3]=>6 [1,2,4,3,2]=>4 [1,3,2,2,4]=>5 [1,3,2,4,2]=>5 [1,3,4,2,2]=>4 [1,4,2,2,3]=>5 [1,4,2,3,2]=>4 [1,4,3,2,2]=>4 [2,1,2,3,4]=>4 [2,1,2,4,3]=>3 [2,1,3,2,4]=>4 [2,1,3,4,2]=>3 [2,1,4,2,3]=>3 [2,1,4,3,2]=>3 [2,2,1,3,4]=>2 [2,2,1,4,3]=>2 [2,2,3,1,4]=>2 [2,2,3,4,1]=>2 [2,2,4,1,3]=>2 [2,2,4,3,1]=>2 [2,3,1,2,4]=>4 [2,3,1,4,2]=>3 [2,3,2,1,4]=>1 [2,3,2,4,1]=>1 [2,3,4,1,2]=>3 [2,3,4,2,1]=>1 [2,4,1,2,3]=>3 [2,4,1,3,2]=>3 [2,4,2,1,3]=>2 [2,4,2,3,1]=>2 [2,4,3,1,2]=>3 [2,4,3,2,1]=>0 [3,1,2,2,4]=>5 [3,1,2,4,2]=>5 [3,1,4,2,2]=>4 [3,2,1,2,4]=>2 [3,2,1,4,2]=>2 [3,2,2,1,4]=>1 [3,2,2,4,1]=>1 [3,2,4,1,2]=>2 [3,2,4,2,1]=>1 [3,4,1,2,2]=>4 [3,4,2,1,2]=>2 [3,4,2,2,1]=>0 [4,1,2,2,3]=>5 [4,1,2,3,2]=>4 [4,1,3,2,2]=>4 [4,2,1,2,3]=>3 [4,2,1,3,2]=>3 [4,2,2,1,3]=>1 [4,2,2,3,1]=>1 [4,2,3,1,2]=>3 [4,2,3,2,1]=>0 [4,3,1,2,2]=>4 [4,3,2,1,2]=>1 [4,3,2,2,1]=>0 [1,2,2,3,5]=>7 [1,2,2,5,3]=>6 [1,2,3,2,5]=>5 [1,2,3,5,2]=>5 [1,2,5,2,3]=>6 [1,2,5,3,2]=>5 [1,3,2,2,5]=>5 [1,3,2,5,2]=>5 [1,3,5,2,2]=>5 [1,5,2,2,3]=>6 [1,5,2,3,2]=>4 [1,5,3,2,2]=>4 [2,1,2,3,5]=>4 [2,1,2,5,3]=>4 [2,1,3,2,5]=>4 [2,1,3,5,2]=>4 [2,1,5,2,3]=>3 [2,1,5,3,2]=>3 [2,2,1,3,5]=>3 [2,2,1,5,3]=>2 [2,2,3,1,5]=>3 [2,2,3,5,1]=>3 [2,2,5,1,3]=>2 [2,2,5,3,1]=>2 [2,3,1,2,5]=>4 [2,3,1,5,2]=>4 [2,3,2,1,5]=>1 [2,3,2,5,1]=>1 [2,3,5,1,2]=>4 [2,3,5,2,1]=>1 [2,5,1,2,3]=>3 [2,5,1,3,2]=>3 [2,5,2,1,3]=>2 [2,5,2,3,1]=>2 [2,5,3,1,2]=>3 [2,5,3,2,1]=>1 [3,1,2,2,5]=>5 [3,1,2,5,2]=>5 [3,1,5,2,2]=>5 [3,2,1,2,5]=>3 [3,2,1,5,2]=>2 [3,2,2,1,5]=>1 [3,2,2,5,1]=>1 [3,2,5,1,2]=>2 [3,2,5,2,1]=>1 [3,5,1,2,2]=>5 [3,5,2,1,2]=>2 [3,5,2,2,1]=>1 [5,1,2,2,3]=>6 [5,1,2,3,2]=>4 [5,1,3,2,2]=>4 [5,2,1,2,3]=>3 [5,2,1,3,2]=>3 [5,2,2,1,3]=>2 [5,2,2,3,1]=>2 [5,2,3,1,2]=>3 [5,2,3,2,1]=>0 [5,3,1,2,2]=>4 [5,3,2,1,2]=>2 [5,3,2,2,1]=>0 [1,2,2,4,4]=>6 [1,2,4,2,4]=>6 [1,2,4,4,2]=>6 [1,4,2,2,4]=>5 [1,4,2,4,2]=>5 [1,4,4,2,2]=>4 [2,1,2,4,4]=>5 [2,1,4,2,4]=>4 [2,1,4,4,2]=>3 [2,2,1,4,4]=>2 [2,2,4,1,4]=>2 [2,2,4,4,1]=>2 [2,4,1,2,4]=>4 [2,4,1,4,2]=>3 [2,4,2,1,4]=>2 [2,4,2,4,1]=>2 [2,4,4,1,2]=>3 [2,4,4,2,1]=>2 [4,1,2,2,4]=>5 [4,1,2,4,2]=>5 [4,1,4,2,2]=>4 [4,2,1,2,4]=>4 [4,2,1,4,2]=>3 [4,2,2,1,4]=>1 [4,2,2,4,1]=>1 [4,2,4,1,2]=>3 [4,2,4,2,1]=>1 [4,4,1,2,2]=>4 [4,4,2,1,2]=>3 [4,4,2,2,1]=>0 [1,2,2,4,5]=>7 [1,2,2,5,4]=>6 [1,2,4,2,5]=>7 [1,2,4,5,2]=>7 [1,2,5,2,4]=>6 [1,2,5,4,2]=>6 [1,4,2,2,5]=>5 [1,4,2,5,2]=>5 [1,4,5,2,2]=>5 [1,5,2,2,4]=>6 [1,5,2,4,2]=>6 [1,5,4,2,2]=>4 [2,1,2,4,5]=>6 [2,1,2,5,4]=>5 [2,1,4,2,5]=>4 [2,1,4,5,2]=>4 [2,1,5,2,4]=>5 [2,1,5,4,2]=>3 [2,2,1,4,5]=>3 [2,2,1,5,4]=>2 [2,2,4,1,5]=>3 [2,2,4,5,1]=>3 [2,2,5,1,4]=>2 [2,2,5,4,1]=>2 [2,4,1,2,5]=>4 [2,4,1,5,2]=>4 [2,4,2,1,5]=>3 [2,4,2,5,1]=>3 [2,4,5,1,2]=>4 [2,4,5,2,1]=>3 [2,5,1,2,4]=>5 [2,5,1,4,2]=>3 [2,5,2,1,4]=>2 [2,5,2,4,1]=>2 [2,5,4,1,2]=>3 [2,5,4,2,1]=>2 [4,1,2,2,5]=>5 [4,1,2,5,2]=>5 [4,1,5,2,2]=>5 [4,2,1,2,5]=>4 [4,2,1,5,2]=>4 [4,2,2,1,5]=>1 [4,2,2,5,1]=>1 [4,2,5,1,2]=>4 [4,2,5,2,1]=>1 [4,5,1,2,2]=>5 [4,5,2,1,2]=>4 [4,5,2,2,1]=>1 [5,1,2,2,4]=>6 [5,1,2,4,2]=>6 [5,1,4,2,2]=>4 [5,2,1,2,4]=>5 [5,2,1,4,2]=>3 [5,2,2,1,4]=>2 [5,2,2,4,1]=>2 [5,2,4,1,2]=>3 [5,2,4,2,1]=>2 [5,4,1,2,2]=>4 [5,4,2,1,2]=>3 [5,4,2,2,1]=>0 [1,2,3,3,3]=>7 [1,3,2,3,3]=>6 [1,3,3,2,3]=>5 [1,3,3,3,2]=>4 [2,1,3,3,3]=>3 [2,3,1,3,3]=>3 [2,3,3,1,3]=>3 [2,3,3,3,1]=>3 [3,1,2,3,3]=>6 [3,1,3,2,3]=>5 [3,1,3,3,2]=>4 [3,2,1,3,3]=>2 [3,2,3,1,3]=>2 [3,2,3,3,1]=>2 [3,3,1,2,3]=>5 [3,3,1,3,2]=>4 [3,3,2,1,3]=>1 [3,3,2,3,1]=>1 [3,3,3,1,2]=>4 [3,3,3,2,1]=>0 [1,2,3,3,4]=>8 [1,2,3,4,3]=>7 [1,2,4,3,3]=>7 [1,3,2,3,4]=>6 [1,3,2,4,3]=>6 [1,3,3,2,4]=>5 [1,3,3,4,2]=>5 [1,3,4,2,3]=>6 [1,3,4,3,2]=>4 [1,4,2,3,3]=>7 [1,4,3,2,3]=>5 [1,4,3,3,2]=>4 [2,1,3,3,4]=>4 [2,1,3,4,3]=>3 [2,1,4,3,3]=>3 [2,3,1,3,4]=>4 [2,3,1,4,3]=>3 [2,3,3,1,4]=>4 [2,3,3,4,1]=>4 [2,3,4,1,3]=>3 [2,3,4,3,1]=>3 [2,4,1,3,3]=>3 [2,4,3,1,3]=>3 [2,4,3,3,1]=>3 [3,1,2,3,4]=>6 [3,1,2,4,3]=>6 [3,1,3,2,4]=>5 [3,1,3,4,2]=>5 [3,1,4,2,3]=>6 [3,1,4,3,2]=>4 [3,2,1,3,4]=>2 [3,2,1,4,3]=>2 [3,2,3,1,4]=>2 [3,2,3,4,1]=>2 [3,2,4,1,3]=>2 [3,2,4,3,1]=>2 [3,3,1,2,4]=>5 [3,3,1,4,2]=>5 [3,3,2,1,4]=>1 [3,3,2,4,1]=>1 [3,3,4,1,2]=>5 [3,3,4,2,1]=>1 [3,4,1,2,3]=>6 [3,4,1,3,2]=>4 [3,4,2,1,3]=>2 [3,4,2,3,1]=>2 [3,4,3,1,2]=>4 [3,4,3,2,1]=>0 [4,1,2,3,3]=>7 [4,1,3,2,3]=>5 [4,1,3,3,2]=>4 [4,2,1,3,3]=>3 [4,2,3,1,3]=>3 [4,2,3,3,1]=>3 [4,3,1,2,3]=>5 [4,3,1,3,2]=>4 [4,3,2,1,3]=>1 [4,3,2,3,1]=>1 [4,3,3,1,2]=>4
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Description
The pmaj statistic of a parking function.
This is the parking function analogue of the bounce statistic, see [1, Section 1.3].
The definition given there is equivalent to the following: One again and again scans the parking function from right to left, keeping track of how often one has started over again. At step $i$, one marks the next position whose value is at most $i$ with the number of restarts from the end of the parking function. The pmaj statistic is then the sum of the markings.
For example, consider the parking function $[6,2,4,1,4,1,7,3]$.
In the first round, we mark positions $6,4,2$ with $0$'s.
In the second round, we mark positions $8,5,3,1$ with $1$'s.
In the third round, we mark position $7$ with a $2$.
In total, we obtain that
$$\operatorname{pmaj}([6,2,4,1,4,1,7,3]) = 6.$$
This statistic is equidistributed with the area statistic St000188The area of the Dyck path corresponding to a parking function and the total displacement of a parking function. and the dinv statistic St000136The dinv of a parking function..
References
[1] Loehr, N. A. Combinatorics of $q$, $t$-parking functions MathSciNet:2110560
Code
def statistic(PF):
    PF = list(PF)
    PF.reverse()
    n = len(PF)
    count = 1
    run   = 0
    pm    = 0
    while any( not x is Infinity for x in PF ):
        for i in range(n):
            if PF[i] <= count:
                count += 1
                PF[i] = Infinity
                pm += run
        run += 1
    return pm
Created
Jun 14, 2018 at 11:31 by Christian Stump
Updated
Jun 14, 2018 at 11:31 by Christian Stump