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]=>2 [2,1,3]=>1 [2,3,1]=>2 [3,1,2]=>1 [3,2,1]=>1 [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]=>2 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>2 [2,3,4,1]=>2 [2,4,1,3]=>2 [2,4,3,1]=>2 [3,1,2,4]=>1 [3,1,4,2]=>2 [3,2,1,4]=>1 [3,2,4,1]=>2 [3,4,1,2]=>2 [3,4,2,1]=>2 [4,1,2,3]=>1 [4,1,3,2]=>2 [4,2,1,3]=>1 [4,2,3,1]=>2 [4,3,1,2]=>1 [4,3,2,1]=>1 [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]=>2 [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]=>2 [1,4,2,3,5]=>2 [1,4,2,5,3]=>3 [1,4,3,2,5]=>2 [1,4,3,5,2]=>3 [1,4,5,2,3]=>2 [1,4,5,3,2]=>2 [1,5,2,3,4]=>2 [1,5,2,4,3]=>3 [1,5,3,2,4]=>2 [1,5,3,4,2]=>3 [1,5,4,2,3]=>2 [1,5,4,3,2]=>2 [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]=>2 [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]=>2 [2,4,1,3,5]=>2 [2,4,1,5,3]=>3 [2,4,3,1,5]=>2 [2,4,3,5,1]=>3 [2,4,5,1,3]=>2 [2,4,5,3,1]=>2 [2,5,1,3,4]=>2 [2,5,1,4,3]=>3 [2,5,3,1,4]=>2 [2,5,3,4,1]=>3 [2,5,4,1,3]=>2 [2,5,4,3,1]=>2 [3,1,2,4,5]=>1 [3,1,2,5,4]=>2 [3,1,4,2,5]=>2 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,4,2]=>2 [3,2,1,4,5]=>1 [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]=>2 [3,4,1,2,5]=>2 [3,4,1,5,2]=>3 [3,4,2,1,5]=>2 [3,4,2,5,1]=>3 [3,4,5,1,2]=>2 [3,4,5,2,1]=>2 [3,5,1,2,4]=>2 [3,5,1,4,2]=>3 [3,5,2,1,4]=>2 [3,5,2,4,1]=>3 [3,5,4,1,2]=>2 [3,5,4,2,1]=>2 [4,1,2,3,5]=>1 [4,1,2,5,3]=>2 [4,1,3,2,5]=>2 [4,1,3,5,2]=>2 [4,1,5,2,3]=>2 [4,1,5,3,2]=>2 [4,2,1,3,5]=>1 [4,2,1,5,3]=>2 [4,2,3,1,5]=>2 [4,2,3,5,1]=>2 [4,2,5,1,3]=>2 [4,2,5,3,1]=>2 [4,3,1,2,5]=>1 [4,3,1,5,2]=>2 [4,3,2,1,5]=>1 [4,3,2,5,1]=>2 [4,3,5,1,2]=>2 [4,3,5,2,1]=>2 [4,5,1,2,3]=>2 [4,5,1,3,2]=>3 [4,5,2,1,3]=>2 [4,5,2,3,1]=>3 [4,5,3,1,2]=>2 [4,5,3,2,1]=>2 [5,1,2,3,4]=>1 [5,1,2,4,3]=>2 [5,1,3,2,4]=>2 [5,1,3,4,2]=>2 [5,1,4,2,3]=>2 [5,1,4,3,2]=>2 [5,2,1,3,4]=>1 [5,2,1,4,3]=>2 [5,2,3,1,4]=>2 [5,2,3,4,1]=>2 [5,2,4,1,3]=>2 [5,2,4,3,1]=>2 [5,3,1,2,4]=>1 [5,3,1,4,2]=>2 [5,3,2,1,4]=>1 [5,3,2,4,1]=>2 [5,3,4,1,2]=>2 [5,3,4,2,1]=>2 [5,4,1,2,3]=>1 [5,4,1,3,2]=>2 [5,4,2,1,3]=>1 [5,4,2,3,1]=>2 [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]=>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]=>2 [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]=>2 [1,2,5,3,4,6]=>2 [1,2,5,3,6,4]=>3 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>3 [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]=>3 [1,2,6,4,3,5]=>2 [1,2,6,4,5,3]=>3 [1,2,6,5,3,4]=>2 [1,2,6,5,4,3]=>2 [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]=>3 [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]=>2 [1,3,5,2,4,6]=>2 [1,3,5,2,6,4]=>3 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>3 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>2 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>2 [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]=>3 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>3 [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]=>3 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>3 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>2 [1,4,5,6,3,2]=>2 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>2 [1,4,6,3,5,2]=>3 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>2 [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]=>3 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>3 [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]=>3 [1,5,4,2,3,6]=>2 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>2 [1,5,4,3,6,2]=>3 [1,5,4,6,2,3]=>3 [1,5,4,6,3,2]=>3 [1,5,6,2,3,4]=>2 [1,5,6,2,4,3]=>3 [1,5,6,3,2,4]=>2 [1,5,6,3,4,2]=>3 [1,5,6,4,2,3]=>2 [1,5,6,4,3,2]=>2 [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]=>3 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>3 [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]=>3 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>3 [1,6,4,3,2,5]=>2 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>3 [1,6,4,5,3,2]=>3 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>3 [1,6,5,3,2,4]=>2 [1,6,5,3,4,2]=>3 [1,6,5,4,2,3]=>2 [1,6,5,4,3,2]=>2 [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]=>2 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>2 [2,1,4,5,6,3]=>2 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>2 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>3 [2,1,5,4,3,6]=>2 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>2 [2,1,6,3,4,5]=>2 [2,1,6,3,5,4]=>3 [2,1,6,4,3,5]=>2 [2,1,6,4,5,3]=>3 [2,1,6,5,3,4]=>2 [2,1,6,5,4,3]=>2 [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]=>3 [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]=>2 [2,3,5,1,4,6]=>2 [2,3,5,1,6,4]=>3 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>3 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>2 [2,3,6,1,4,5]=>2 [2,3,6,1,5,4]=>3 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>3 [2,3,6,5,1,4]=>2 [2,3,6,5,4,1]=>2 [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]=>3 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>3 [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]=>3 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>3 [2,4,5,3,1,6]=>2 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>2 [2,4,5,6,3,1]=>2 [2,4,6,1,3,5]=>2 [2,4,6,1,5,3]=>3 [2,4,6,3,1,5]=>2 [2,4,6,3,5,1]=>3 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>2 [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]=>3 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>3 [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]=>3 [2,5,4,1,3,6]=>2 [2,5,4,1,6,3]=>3 [2,5,4,3,1,6]=>2 [2,5,4,3,6,1]=>3 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>3 [2,5,6,1,3,4]=>2 [2,5,6,1,4,3]=>3 [2,5,6,3,1,4]=>2 [2,5,6,3,4,1]=>3 [2,5,6,4,1,3]=>2 [2,5,6,4,3,1]=>2 [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]=>3 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>3 [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]=>3 [2,6,4,1,3,5]=>2 [2,6,4,1,5,3]=>3 [2,6,4,3,1,5]=>2 [2,6,4,3,5,1]=>3 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>3 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>3 [2,6,5,3,1,4]=>2 [2,6,5,3,4,1]=>3 [2,6,5,4,1,3]=>2 [2,6,5,4,3,1]=>2 [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]=>2 [3,1,2,6,5,4]=>2 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>3 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>2 [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]=>3 [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]=>3 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>3 [3,1,6,5,2,4]=>2 [3,1,6,5,4,2]=>2 [3,2,1,4,5,6]=>1 [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]=>2 [3,2,4,1,5,6]=>2 [3,2,4,1,6,5]=>3 [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]=>2 [3,2,5,1,4,6]=>2 [3,2,5,1,6,4]=>3 [3,2,5,4,1,6]=>2 [3,2,5,4,6,1]=>3 [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]=>3 [3,2,6,4,1,5]=>2 [3,2,6,4,5,1]=>3 [3,2,6,5,1,4]=>2 [3,2,6,5,4,1]=>2 [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]=>3 [3,4,2,1,5,6]=>2 [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]=>3 [3,4,5,1,2,6]=>2 [3,4,5,1,6,2]=>3 [3,4,5,2,1,6]=>2 [3,4,5,2,6,1]=>3 [3,4,5,6,1,2]=>2 [3,4,5,6,2,1]=>2 [3,4,6,1,2,5]=>2 [3,4,6,1,5,2]=>3 [3,4,6,2,1,5]=>2 [3,4,6,2,5,1]=>3 [3,4,6,5,1,2]=>2 [3,4,6,5,2,1]=>2 [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]=>3 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>3 [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]=>3 [3,5,4,1,2,6]=>2 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>3 [3,5,4,6,1,2]=>3 [3,5,4,6,2,1]=>3 [3,5,6,1,2,4]=>2 [3,5,6,1,4,2]=>3 [3,5,6,2,1,4]=>2 [3,5,6,2,4,1]=>3 [3,5,6,4,1,2]=>2 [3,5,6,4,2,1]=>2 [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]=>3 [3,6,2,1,4,5]=>2 [3,6,2,1,5,4]=>3 [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]=>3 [3,6,4,1,2,5]=>2 [3,6,4,1,5,2]=>3 [3,6,4,2,1,5]=>2 [3,6,4,2,5,1]=>3 [3,6,4,5,1,2]=>3 [3,6,4,5,2,1]=>3 [3,6,5,1,2,4]=>2 [3,6,5,1,4,2]=>3 [3,6,5,2,1,4]=>2 [3,6,5,2,4,1]=>3 [3,6,5,4,1,2]=>2 [3,6,5,4,2,1]=>2 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>2 [4,1,2,5,3,6]=>2 [4,1,2,5,6,3]=>2 [4,1,2,6,3,5]=>2 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>3 [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]=>2 [4,1,5,2,3,6]=>2 [4,1,5,2,6,3]=>3 [4,1,5,3,2,6]=>2 [4,1,5,3,6,2]=>3 [4,1,5,6,2,3]=>2 [4,1,5,6,3,2]=>2 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>3 [4,1,6,3,2,5]=>2 [4,1,6,3,5,2]=>3 [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]=>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]=>2 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>3 [4,2,3,5,1,6]=>2 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>2 [4,2,3,6,5,1]=>2 [4,2,5,1,3,6]=>2 [4,2,5,1,6,3]=>3 [4,2,5,3,1,6]=>2 [4,2,5,3,6,1]=>3 [4,2,5,6,1,3]=>2 [4,2,5,6,3,1]=>2 [4,2,6,1,3,5]=>2 [4,2,6,1,5,3]=>3 [4,2,6,3,1,5]=>2 [4,2,6,3,5,1]=>3 [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]=>2 [4,3,1,5,2,6]=>2 [4,3,1,5,6,2]=>2 [4,3,1,6,2,5]=>2 [4,3,1,6,5,2]=>2 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>2 [4,3,2,5,1,6]=>2 [4,3,2,5,6,1]=>2 [4,3,2,6,1,5]=>2 [4,3,2,6,5,1]=>2 [4,3,5,1,2,6]=>2 [4,3,5,1,6,2]=>3 [4,3,5,2,1,6]=>2 [4,3,5,2,6,1]=>3 [4,3,5,6,1,2]=>2 [4,3,5,6,2,1]=>2 [4,3,6,1,2,5]=>2 [4,3,6,1,5,2]=>3 [4,3,6,2,1,5]=>2 [4,3,6,2,5,1]=>3 [4,3,6,5,1,2]=>2 [4,3,6,5,2,1]=>2 [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]=>3 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>3 [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]=>3 [4,5,3,1,2,6]=>2 [4,5,3,1,6,2]=>3 [4,5,3,2,1,6]=>2 [4,5,3,2,6,1]=>3 [4,5,3,6,1,2]=>3 [4,5,3,6,2,1]=>3 [4,5,6,1,2,3]=>2 [4,5,6,1,3,2]=>3 [4,5,6,2,1,3]=>2 [4,5,6,2,3,1]=>3 [4,5,6,3,1,2]=>2 [4,5,6,3,2,1]=>2 [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]=>3 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>3 [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]=>3 [4,6,3,1,2,5]=>2 [4,6,3,1,5,2]=>3 [4,6,3,2,1,5]=>2 [4,6,3,2,5,1]=>3 [4,6,3,5,1,2]=>3 [4,6,3,5,2,1]=>3 [4,6,5,1,2,3]=>2 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>2 [4,6,5,2,3,1]=>3 [4,6,5,3,1,2]=>2 [4,6,5,3,2,1]=>2 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>2 [5,1,2,4,3,6]=>2 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>2 [5,1,2,6,4,3]=>2 [5,1,3,2,4,6]=>2 [5,1,3,2,6,4]=>3 [5,1,3,4,2,6]=>2 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>2 [5,1,3,6,4,2]=>2 [5,1,4,2,3,6]=>2 [5,1,4,2,6,3]=>3 [5,1,4,3,2,6]=>2 [5,1,4,3,6,2]=>3 [5,1,4,6,2,3]=>2 [5,1,4,6,3,2]=>2 [5,1,6,2,3,4]=>2 [5,1,6,2,4,3]=>3 [5,1,6,3,2,4]=>2 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>2 [5,1,6,4,3,2]=>2 [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]=>2 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>3 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>2 [5,2,4,1,3,6]=>2 [5,2,4,1,6,3]=>3 [5,2,4,3,1,6]=>2 [5,2,4,3,6,1]=>3 [5,2,4,6,1,3]=>2 [5,2,4,6,3,1]=>2 [5,2,6,1,3,4]=>2 [5,2,6,1,4,3]=>3 [5,2,6,3,1,4]=>2 [5,2,6,3,4,1]=>3 [5,2,6,4,1,3]=>2 [5,2,6,4,3,1]=>2 [5,3,1,2,4,6]=>1 [5,3,1,2,6,4]=>2 [5,3,1,4,2,6]=>2 [5,3,1,4,6,2]=>2 [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]=>2 [5,3,2,4,1,6]=>2 [5,3,2,4,6,1]=>2 [5,3,2,6,1,4]=>2 [5,3,2,6,4,1]=>2 [5,3,4,1,2,6]=>2 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>2 [5,3,4,2,6,1]=>3 [5,3,4,6,1,2]=>2 [5,3,4,6,2,1]=>2 [5,3,6,1,2,4]=>2 [5,3,6,1,4,2]=>3 [5,3,6,2,1,4]=>2 [5,3,6,2,4,1]=>3 [5,3,6,4,1,2]=>2 [5,3,6,4,2,1]=>2 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>2 [5,4,1,3,2,6]=>2 [5,4,1,3,6,2]=>2 [5,4,1,6,2,3]=>2 [5,4,1,6,3,2]=>2 [5,4,2,1,3,6]=>1 [5,4,2,1,6,3]=>2 [5,4,2,3,1,6]=>2 [5,4,2,3,6,1]=>2 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>2 [5,4,3,1,2,6]=>1 [5,4,3,1,6,2]=>2 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>2 [5,4,3,6,1,2]=>2 [5,4,3,6,2,1]=>2 [5,4,6,1,2,3]=>2 [5,4,6,1,3,2]=>3 [5,4,6,2,1,3]=>2 [5,4,6,2,3,1]=>3 [5,4,6,3,1,2]=>2 [5,4,6,3,2,1]=>2 [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]=>3 [5,6,2,1,3,4]=>2 [5,6,2,1,4,3]=>3 [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]=>3 [5,6,3,1,2,4]=>2 [5,6,3,1,4,2]=>3 [5,6,3,2,1,4]=>2 [5,6,3,2,4,1]=>3 [5,6,3,4,1,2]=>3 [5,6,3,4,2,1]=>3 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>3 [5,6,4,2,1,3]=>2 [5,6,4,2,3,1]=>3 [5,6,4,3,1,2]=>2 [5,6,4,3,2,1]=>2 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>2 [6,1,2,4,3,5]=>2 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>2 [6,1,2,5,4,3]=>2 [6,1,3,2,4,5]=>2 [6,1,3,2,5,4]=>3 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>2 [6,1,3,5,2,4]=>2 [6,1,3,5,4,2]=>2 [6,1,4,2,3,5]=>2 [6,1,4,2,5,3]=>3 [6,1,4,3,2,5]=>2 [6,1,4,3,5,2]=>3 [6,1,4,5,2,3]=>2 [6,1,4,5,3,2]=>2 [6,1,5,2,3,4]=>2 [6,1,5,2,4,3]=>3 [6,1,5,3,2,4]=>2 [6,1,5,3,4,2]=>3 [6,1,5,4,2,3]=>2 [6,1,5,4,3,2]=>2 [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]=>2 [6,2,3,1,4,5]=>2 [6,2,3,1,5,4]=>3 [6,2,3,4,1,5]=>2 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>2 [6,2,3,5,4,1]=>2 [6,2,4,1,3,5]=>2 [6,2,4,1,5,3]=>3 [6,2,4,3,1,5]=>2 [6,2,4,3,5,1]=>3 [6,2,4,5,1,3]=>2 [6,2,4,5,3,1]=>2 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>3 [6,2,5,3,1,4]=>2 [6,2,5,3,4,1]=>3 [6,2,5,4,1,3]=>2 [6,2,5,4,3,1]=>2 [6,3,1,2,4,5]=>1 [6,3,1,2,5,4]=>2 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>2 [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]=>2 [6,3,2,4,1,5]=>2 [6,3,2,4,5,1]=>2 [6,3,2,5,1,4]=>2 [6,3,2,5,4,1]=>2 [6,3,4,1,2,5]=>2 [6,3,4,1,5,2]=>3 [6,3,4,2,1,5]=>2 [6,3,4,2,5,1]=>3 [6,3,4,5,1,2]=>2 [6,3,4,5,2,1]=>2 [6,3,5,1,2,4]=>2 [6,3,5,1,4,2]=>3 [6,3,5,2,1,4]=>2 [6,3,5,2,4,1]=>3 [6,3,5,4,1,2]=>2 [6,3,5,4,2,1]=>2 [6,4,1,2,3,5]=>1 [6,4,1,2,5,3]=>2 [6,4,1,3,2,5]=>2 [6,4,1,3,5,2]=>2 [6,4,1,5,2,3]=>2 [6,4,1,5,3,2]=>2 [6,4,2,1,3,5]=>1 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>2 [6,4,2,3,5,1]=>2 [6,4,2,5,1,3]=>2 [6,4,2,5,3,1]=>2 [6,4,3,1,2,5]=>1 [6,4,3,1,5,2]=>2 [6,4,3,2,1,5]=>1 [6,4,3,2,5,1]=>2 [6,4,3,5,1,2]=>2 [6,4,3,5,2,1]=>2 [6,4,5,1,2,3]=>2 [6,4,5,1,3,2]=>3 [6,4,5,2,1,3]=>2 [6,4,5,2,3,1]=>3 [6,4,5,3,1,2]=>2 [6,4,5,3,2,1]=>2 [6,5,1,2,3,4]=>1 [6,5,1,2,4,3]=>2 [6,5,1,3,2,4]=>2 [6,5,1,3,4,2]=>2 [6,5,1,4,2,3]=>2 [6,5,1,4,3,2]=>2 [6,5,2,1,3,4]=>1 [6,5,2,1,4,3]=>2 [6,5,2,3,1,4]=>2 [6,5,2,3,4,1]=>2 [6,5,2,4,1,3]=>2 [6,5,2,4,3,1]=>2 [6,5,3,1,2,4]=>1 [6,5,3,1,4,2]=>2 [6,5,3,2,1,4]=>1 [6,5,3,2,4,1]=>2 [6,5,3,4,1,2]=>2 [6,5,3,4,2,1]=>2 [6,5,4,1,2,3]=>1 [6,5,4,1,3,2]=>2 [6,5,4,2,1,3]=>1 [6,5,4,2,3,1]=>2 [6,5,4,3,1,2]=>1 [6,5,4,3,2,1]=>1
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Description
The number of valleys of a permutation, including the boundary.
The number of valleys excluding the boundary is St000353The number of inner valleys of a permutation..
References
[1] Claesson, A., Kitaev, S. Classification of bijections between 321- and 132-avoiding permutations MathSciNet:2465405
Code
def statistic(pi):
    pi1 = [len(pi)+1] + list(pi) + [len(pi)+1]
    return len([i for i in range(1,len(pi1)-1) if pi1[i-1] > pi1[i] < pi1[i+1]])
Created
Jun 13, 2013 at 16:16 by Chris Berg
Updated
Jan 08, 2016 at 14:15 by Martin Rubey