edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [-1]=>0 [1,2]=>0 [1,-2]=>0 [-1,2]=>0 [-1,-2]=>0 [2,1]=>0 [2,-1]=>1 [-2,1]=>0 [-2,-1]=>1 [1,2,3]=>0 [1,2,-3]=>0 [1,-2,3]=>0 [1,-2,-3]=>0 [-1,2,3]=>0 [-1,2,-3]=>0 [-1,-2,3]=>0 [-1,-2,-3]=>0 [1,3,2]=>0 [1,3,-2]=>1 [1,-3,2]=>0 [1,-3,-2]=>1 [-1,3,2]=>0 [-1,3,-2]=>1 [-1,-3,2]=>0 [-1,-3,-2]=>1 [2,1,3]=>0 [2,1,-3]=>0 [2,-1,3]=>1 [2,-1,-3]=>1 [-2,1,3]=>0 [-2,1,-3]=>0 [-2,-1,3]=>1 [-2,-1,-3]=>1 [2,3,1]=>1 [2,3,-1]=>2 [2,-3,1]=>1 [2,-3,-1]=>2 [-2,3,1]=>1 [-2,3,-1]=>2 [-2,-3,1]=>1 [-2,-3,-1]=>2 [3,1,2]=>0 [3,1,-2]=>1 [3,-1,2]=>1 [3,-1,-2]=>2 [-3,1,2]=>0 [-3,1,-2]=>1 [-3,-1,2]=>1 [-3,-1,-2]=>2 [3,2,1]=>0 [3,2,-1]=>1 [3,-2,1]=>2 [3,-2,-1]=>3 [-3,2,1]=>0 [-3,2,-1]=>1 [-3,-2,1]=>2 [-3,-2,-1]=>3 [1,2,3,4]=>0 [1,2,3,-4]=>0 [1,2,-3,4]=>0 [1,2,-3,-4]=>0 [1,-2,3,4]=>0 [1,-2,3,-4]=>0 [1,-2,-3,4]=>0 [1,-2,-3,-4]=>0 [-1,2,3,4]=>0 [-1,2,3,-4]=>0 [-1,2,-3,4]=>0 [-1,2,-3,-4]=>0 [-1,-2,3,4]=>0 [-1,-2,3,-4]=>0 [-1,-2,-3,4]=>0 [-1,-2,-3,-4]=>0 [1,2,4,3]=>0 [1,2,4,-3]=>1 [1,2,-4,3]=>0 [1,2,-4,-3]=>1 [1,-2,4,3]=>0 [1,-2,4,-3]=>1 [1,-2,-4,3]=>0 [1,-2,-4,-3]=>1 [-1,2,4,3]=>0 [-1,2,4,-3]=>1 [-1,2,-4,3]=>0 [-1,2,-4,-3]=>1 [-1,-2,4,3]=>0 [-1,-2,4,-3]=>1 [-1,-2,-4,3]=>0 [-1,-2,-4,-3]=>1 [1,3,2,4]=>0 [1,3,2,-4]=>0 [1,3,-2,4]=>1 [1,3,-2,-4]=>1 [1,-3,2,4]=>0 [1,-3,2,-4]=>0 [1,-3,-2,4]=>1 [1,-3,-2,-4]=>1 [-1,3,2,4]=>0 [-1,3,2,-4]=>0 [-1,3,-2,4]=>1 [-1,3,-2,-4]=>1 [-1,-3,2,4]=>0 [-1,-3,2,-4]=>0 [-1,-3,-2,4]=>1 [-1,-3,-2,-4]=>1 [1,3,4,2]=>1 [1,3,4,-2]=>2 [1,3,-4,2]=>1 [1,3,-4,-2]=>2 [1,-3,4,2]=>1 [1,-3,4,-2]=>2 [1,-3,-4,2]=>1 [1,-3,-4,-2]=>2 [-1,3,4,2]=>1 [-1,3,4,-2]=>2 [-1,3,-4,2]=>1 [-1,3,-4,-2]=>2 [-1,-3,4,2]=>1 [-1,-3,4,-2]=>2 [-1,-3,-4,2]=>1 [-1,-3,-4,-2]=>2 [1,4,2,3]=>0 [1,4,2,-3]=>1 [1,4,-2,3]=>1 [1,4,-2,-3]=>2 [1,-4,2,3]=>0 [1,-4,2,-3]=>1 [1,-4,-2,3]=>1 [1,-4,-2,-3]=>2 [-1,4,2,3]=>0 [-1,4,2,-3]=>1 [-1,4,-2,3]=>1 [-1,4,-2,-3]=>2 [-1,-4,2,3]=>0 [-1,-4,2,-3]=>1 [-1,-4,-2,3]=>1 [-1,-4,-2,-3]=>2 [1,4,3,2]=>0 [1,4,3,-2]=>1 [1,4,-3,2]=>2 [1,4,-3,-2]=>3 [1,-4,3,2]=>0 [1,-4,3,-2]=>1 [1,-4,-3,2]=>2 [1,-4,-3,-2]=>3 [-1,4,3,2]=>0 [-1,4,3,-2]=>1 [-1,4,-3,2]=>2 [-1,4,-3,-2]=>3 [-1,-4,3,2]=>0 [-1,-4,3,-2]=>1 [-1,-4,-3,2]=>2 [-1,-4,-3,-2]=>3 [2,1,3,4]=>0 [2,1,3,-4]=>0 [2,1,-3,4]=>0 [2,1,-3,-4]=>0 [2,-1,3,4]=>1 [2,-1,3,-4]=>1 [2,-1,-3,4]=>1 [2,-1,-3,-4]=>1 [-2,1,3,4]=>0 [-2,1,3,-4]=>0 [-2,1,-3,4]=>0 [-2,1,-3,-4]=>0 [-2,-1,3,4]=>1 [-2,-1,3,-4]=>1 [-2,-1,-3,4]=>1 [-2,-1,-3,-4]=>1 [2,1,4,3]=>0 [2,1,4,-3]=>1 [2,1,-4,3]=>0 [2,1,-4,-3]=>1 [2,-1,4,3]=>1 [2,-1,4,-3]=>2 [2,-1,-4,3]=>1 [2,-1,-4,-3]=>2 [-2,1,4,3]=>0 [-2,1,4,-3]=>1 [-2,1,-4,3]=>0 [-2,1,-4,-3]=>1 [-2,-1,4,3]=>1 [-2,-1,4,-3]=>2 [-2,-1,-4,3]=>1 [-2,-1,-4,-3]=>2 [2,3,1,4]=>1 [2,3,1,-4]=>1 [2,3,-1,4]=>2 [2,3,-1,-4]=>2 [2,-3,1,4]=>1 [2,-3,1,-4]=>1 [2,-3,-1,4]=>2 [2,-3,-1,-4]=>2 [-2,3,1,4]=>1 [-2,3,1,-4]=>1 [-2,3,-1,4]=>2 [-2,3,-1,-4]=>2 [-2,-3,1,4]=>1 [-2,-3,1,-4]=>1 [-2,-3,-1,4]=>2 [-2,-3,-1,-4]=>2 [2,3,4,1]=>2 [2,3,4,-1]=>3 [2,3,-4,1]=>2 [2,3,-4,-1]=>3 [2,-3,4,1]=>2 [2,-3,4,-1]=>3 [2,-3,-4,1]=>2 [2,-3,-4,-1]=>3 [-2,3,4,1]=>2 [-2,3,4,-1]=>3 [-2,3,-4,1]=>2 [-2,3,-4,-1]=>3 [-2,-3,4,1]=>2 [-2,-3,4,-1]=>3 [-2,-3,-4,1]=>2 [-2,-3,-4,-1]=>3 [2,4,1,3]=>1 [2,4,1,-3]=>2 [2,4,-1,3]=>2 [2,4,-1,-3]=>3 [2,-4,1,3]=>1 [2,-4,1,-3]=>2 [2,-4,-1,3]=>2 [2,-4,-1,-3]=>3 [-2,4,1,3]=>1 [-2,4,1,-3]=>2 [-2,4,-1,3]=>2 [-2,4,-1,-3]=>3 [-2,-4,1,3]=>1 [-2,-4,1,-3]=>2 [-2,-4,-1,3]=>2 [-2,-4,-1,-3]=>3 [2,4,3,1]=>1 [2,4,3,-1]=>2 [2,4,-3,1]=>3 [2,4,-3,-1]=>4 [2,-4,3,1]=>1 [2,-4,3,-1]=>2 [2,-4,-3,1]=>3 [2,-4,-3,-1]=>4 [-2,4,3,1]=>1 [-2,4,3,-1]=>2 [-2,4,-3,1]=>3 [-2,4,-3,-1]=>4 [-2,-4,3,1]=>1 [-2,-4,3,-1]=>2 [-2,-4,-3,1]=>3 [-2,-4,-3,-1]=>4 [3,1,2,4]=>0 [3,1,2,-4]=>0 [3,1,-2,4]=>1 [3,1,-2,-4]=>1 [3,-1,2,4]=>1 [3,-1,2,-4]=>1 [3,-1,-2,4]=>2 [3,-1,-2,-4]=>2 [-3,1,2,4]=>0 [-3,1,2,-4]=>0 [-3,1,-2,4]=>1 [-3,1,-2,-4]=>1 [-3,-1,2,4]=>1 [-3,-1,2,-4]=>1 [-3,-1,-2,4]=>2 [-3,-1,-2,-4]=>2 [3,1,4,2]=>1 [3,1,4,-2]=>2 [3,1,-4,2]=>1 [3,1,-4,-2]=>2 [3,-1,4,2]=>2 [3,-1,4,-2]=>3 [3,-1,-4,2]=>2 [3,-1,-4,-2]=>3 [-3,1,4,2]=>1 [-3,1,4,-2]=>2 [-3,1,-4,2]=>1 [-3,1,-4,-2]=>2 [-3,-1,4,2]=>2 [-3,-1,4,-2]=>3 [-3,-1,-4,2]=>2 [-3,-1,-4,-2]=>3 [3,2,1,4]=>0 [3,2,1,-4]=>0 [3,2,-1,4]=>1 [3,2,-1,-4]=>1 [3,-2,1,4]=>2 [3,-2,1,-4]=>2 [3,-2,-1,4]=>3 [3,-2,-1,-4]=>3 [-3,2,1,4]=>0 [-3,2,1,-4]=>0 [-3,2,-1,4]=>1 [-3,2,-1,-4]=>1 [-3,-2,1,4]=>2 [-3,-2,1,-4]=>2 [-3,-2,-1,4]=>3 [-3,-2,-1,-4]=>3 [3,2,4,1]=>1 [3,2,4,-1]=>2 [3,2,-4,1]=>1 [3,2,-4,-1]=>2 [3,-2,4,1]=>3 [3,-2,4,-1]=>4 [3,-2,-4,1]=>3 [3,-2,-4,-1]=>4 [-3,2,4,1]=>1 [-3,2,4,-1]=>2 [-3,2,-4,1]=>1 [-3,2,-4,-1]=>2 [-3,-2,4,1]=>3 [-3,-2,4,-1]=>4 [-3,-2,-4,1]=>3 [-3,-2,-4,-1]=>4 [3,4,1,2]=>2 [3,4,1,-2]=>3 [3,4,-1,2]=>3 [3,4,-1,-2]=>4 [3,-4,1,2]=>2 [3,-4,1,-2]=>3 [3,-4,-1,2]=>3 [3,-4,-1,-2]=>4 [-3,4,1,2]=>2 [-3,4,1,-2]=>3 [-3,4,-1,2]=>3 [-3,4,-1,-2]=>4 [-3,-4,1,2]=>2 [-3,-4,1,-2]=>3 [-3,-4,-1,2]=>3 [-3,-4,-1,-2]=>4 [3,4,2,1]=>1 [3,4,2,-1]=>2 [3,4,-2,1]=>4 [3,4,-2,-1]=>5 [3,-4,2,1]=>1 [3,-4,2,-1]=>2 [3,-4,-2,1]=>4 [3,-4,-2,-1]=>5 [-3,4,2,1]=>1 [-3,4,2,-1]=>2 [-3,4,-2,1]=>4 [-3,4,-2,-1]=>5 [-3,-4,2,1]=>1 [-3,-4,2,-1]=>2 [-3,-4,-2,1]=>4 [-3,-4,-2,-1]=>5 [4,1,2,3]=>0 [4,1,2,-3]=>1 [4,1,-2,3]=>1 [4,1,-2,-3]=>2 [4,-1,2,3]=>1 [4,-1,2,-3]=>2 [4,-1,-2,3]=>2 [4,-1,-2,-3]=>3 [-4,1,2,3]=>0 [-4,1,2,-3]=>1 [-4,1,-2,3]=>1 [-4,1,-2,-3]=>2 [-4,-1,2,3]=>1 [-4,-1,2,-3]=>2 [-4,-1,-2,3]=>2 [-4,-1,-2,-3]=>3 [4,1,3,2]=>0 [4,1,3,-2]=>1 [4,1,-3,2]=>2 [4,1,-3,-2]=>3 [4,-1,3,2]=>1 [4,-1,3,-2]=>2 [4,-1,-3,2]=>3 [4,-1,-3,-2]=>4 [-4,1,3,2]=>0 [-4,1,3,-2]=>1 [-4,1,-3,2]=>2 [-4,1,-3,-2]=>3 [-4,-1,3,2]=>1 [-4,-1,3,-2]=>2 [-4,-1,-3,2]=>3 [-4,-1,-3,-2]=>4 [4,2,1,3]=>0 [4,2,1,-3]=>1 [4,2,-1,3]=>1 [4,2,-1,-3]=>2 [4,-2,1,3]=>2 [4,-2,1,-3]=>3 [4,-2,-1,3]=>3 [4,-2,-1,-3]=>4 [-4,2,1,3]=>0 [-4,2,1,-3]=>1 [-4,2,-1,3]=>1 [-4,2,-1,-3]=>2 [-4,-2,1,3]=>2 [-4,-2,1,-3]=>3 [-4,-2,-1,3]=>3 [-4,-2,-1,-3]=>4 [4,2,3,1]=>0 [4,2,3,-1]=>1 [4,2,-3,1]=>2 [4,2,-3,-1]=>3 [4,-2,3,1]=>2 [4,-2,3,-1]=>3 [4,-2,-3,1]=>4 [4,-2,-3,-1]=>5 [-4,2,3,1]=>0 [-4,2,3,-1]=>1 [-4,2,-3,1]=>2 [-4,2,-3,-1]=>3 [-4,-2,3,1]=>2 [-4,-2,3,-1]=>3 [-4,-2,-3,1]=>4 [-4,-2,-3,-1]=>5 [4,3,1,2]=>1 [4,3,1,-2]=>2 [4,3,-1,2]=>2 [4,3,-1,-2]=>3 [4,-3,1,2]=>3 [4,-3,1,-2]=>4 [4,-3,-1,2]=>4 [4,-3,-1,-2]=>5 [-4,3,1,2]=>1 [-4,3,1,-2]=>2 [-4,3,-1,2]=>2 [-4,3,-1,-2]=>3 [-4,-3,1,2]=>3 [-4,-3,1,-2]=>4 [-4,-3,-1,2]=>4 [-4,-3,-1,-2]=>5 [4,3,2,1]=>0 [4,3,2,-1]=>1 [4,3,-2,1]=>3 [4,3,-2,-1]=>4 [4,-3,2,1]=>2 [4,-3,2,-1]=>3 [4,-3,-2,1]=>5 [4,-3,-2,-1]=>6 [-4,3,2,1]=>0 [-4,3,2,-1]=>1 [-4,3,-2,1]=>3 [-4,3,-2,-1]=>4 [-4,-3,2,1]=>2 [-4,-3,2,-1]=>3 [-4,-3,-2,1]=>5 [-4,-3,-2,-1]=>6 [1,2,3,4,5]=>0 [1,2,3,4,-5]=>0 [1,2,3,-4,5]=>0 [1,2,3,-4,-5]=>0 [1,2,-3,4,5]=>0 [1,2,-3,4,-5]=>0 [1,2,-3,-4,5]=>0 [1,2,-3,-4,-5]=>0 [1,-2,3,4,5]=>0 [1,-2,3,4,-5]=>0 [1,-2,3,-4,5]=>0 [1,-2,3,-4,-5]=>0 [1,-2,-3,4,5]=>0 [1,-2,-3,4,-5]=>0 [1,-2,-3,-4,5]=>0 [1,-2,-3,-4,-5]=>0 [-1,2,3,4,5]=>0 [-1,2,3,4,-5]=>0 [-1,2,3,-4,5]=>0 [-1,2,3,-4,-5]=>0 [-1,2,-3,4,5]=>0 [-1,2,-3,4,-5]=>0 [-1,2,-3,-4,5]=>0 [-1,2,-3,-4,-5]=>0 [-1,-2,3,4,5]=>0 [-1,-2,3,4,-5]=>0 [-1,-2,3,-4,5]=>0 [-1,-2,3,-4,-5]=>0 [-1,-2,-3,4,5]=>0 [-1,-2,-3,4,-5]=>0 [-1,-2,-3,-4,5]=>0 [-1,-2,-3,-4,-5]=>0 [1,2,3,5,4]=>0 [1,2,3,5,-4]=>1 [1,2,3,-5,4]=>0 [1,2,3,-5,-4]=>1 [1,2,-3,5,4]=>0 [1,2,-3,5,-4]=>1 [1,2,-3,-5,4]=>0 [1,2,-3,-5,-4]=>1 [1,-2,3,5,4]=>0 [1,-2,3,5,-4]=>1 [1,-2,3,-5,4]=>0 [1,-2,3,-5,-4]=>1 [1,-2,-3,5,4]=>0 [1,-2,-3,5,-4]=>1 [1,-2,-3,-5,4]=>0 [1,-2,-3,-5,-4]=>1 [-1,2,3,5,4]=>0 [-1,2,3,5,-4]=>1 [-1,2,3,-5,4]=>0 [-1,2,3,-5,-4]=>1 [-1,2,-3,5,4]=>0 [-1,2,-3,5,-4]=>1 [-1,2,-3,-5,4]=>0 [-1,2,-3,-5,-4]=>1 [-1,-2,3,5,4]=>0 [-1,-2,3,5,-4]=>1 [-1,-2,3,-5,4]=>0 [-1,-2,3,-5,-4]=>1 [-1,-2,-3,5,4]=>0 [-1,-2,-3,5,-4]=>1 [-1,-2,-3,-5,4]=>0 [-1,-2,-3,-5,-4]=>1 [1,2,4,3,5]=>0 [1,2,4,3,-5]=>0 [1,2,4,-3,5]=>1 [1,2,4,-3,-5]=>1 [1,2,-4,3,5]=>0 [1,2,-4,3,-5]=>0 [1,2,-4,-3,5]=>1 [1,2,-4,-3,-5]=>1 [1,-2,4,3,5]=>0 [1,-2,4,3,-5]=>0 [1,-2,4,-3,5]=>1 [1,-2,4,-3,-5]=>1 [1,-2,-4,3,5]=>0 [1,-2,-4,3,-5]=>0 [1,-2,-4,-3,5]=>1 [1,-2,-4,-3,-5]=>1 [-1,2,4,3,5]=>0 [-1,2,4,3,-5]=>0 [-1,2,4,-3,5]=>1 [-1,2,4,-3,-5]=>1 [-1,2,-4,3,5]=>0 [-1,2,-4,3,-5]=>0 [-1,2,-4,-3,5]=>1 [-1,2,-4,-3,-5]=>1 [-1,-2,4,3,5]=>0 [-1,-2,4,3,-5]=>0 [-1,-2,4,-3,5]=>1 [-1,-2,4,-3,-5]=>1 [-1,-2,-4,3,5]=>0 [-1,-2,-4,3,-5]=>0 [-1,-2,-4,-3,5]=>1 [-1,-2,-4,-3,-5]=>1 [1,2,4,5,3]=>1 [1,2,4,5,-3]=>2 [1,2,4,-5,3]=>1 [1,2,4,-5,-3]=>2 [1,2,-4,5,3]=>1 [1,2,-4,5,-3]=>2 [1,2,-4,-5,3]=>1 [1,2,-4,-5,-3]=>2 [1,-2,4,5,3]=>1 [1,-2,4,5,-3]=>2 [1,-2,4,-5,3]=>1 [1,-2,4,-5,-3]=>2 [1,-2,-4,5,3]=>1 [1,-2,-4,5,-3]=>2 [1,-2,-4,-5,3]=>1 [1,-2,-4,-5,-3]=>2 [-1,2,4,5,3]=>1 [-1,2,4,5,-3]=>2 [-1,2,4,-5,3]=>1 [-1,2,4,-5,-3]=>2 [-1,2,-4,5,3]=>1 [-1,2,-4,5,-3]=>2 [-1,2,-4,-5,3]=>1 [-1,2,-4,-5,-3]=>2 [-1,-2,4,5,3]=>1 [-1,-2,4,5,-3]=>2 [-1,-2,4,-5,3]=>1 [-1,-2,4,-5,-3]=>2 [-1,-2,-4,5,3]=>1 [-1,-2,-4,5,-3]=>2 [-1,-2,-4,-5,3]=>1 [-1,-2,-4,-5,-3]=>2 [1,2,5,3,4]=>0 [1,2,5,3,-4]=>1 [1,2,5,-3,4]=>1 [1,2,5,-3,-4]=>2 [1,2,-5,3,4]=>0 [1,2,-5,3,-4]=>1 [1,2,-5,-3,4]=>1 [1,2,-5,-3,-4]=>2 [1,-2,5,3,4]=>0 [1,-2,5,3,-4]=>1 [1,-2,5,-3,4]=>1 [1,-2,5,-3,-4]=>2 [1,-2,-5,3,4]=>0 [1,-2,-5,3,-4]=>1 [1,-2,-5,-3,4]=>1 [1,-2,-5,-3,-4]=>2 [-1,2,5,3,4]=>0 [-1,2,5,3,-4]=>1 [-1,2,5,-3,4]=>1 [-1,2,5,-3,-4]=>2 [-1,2,-5,3,4]=>0 [-1,2,-5,3,-4]=>1 [-1,2,-5,-3,4]=>1 [-1,2,-5,-3,-4]=>2 [-1,-2,5,3,4]=>0 [-1,-2,5,3,-4]=>1 [-1,-2,5,-3,4]=>1 [-1,-2,5,-3,-4]=>2 [-1,-2,-5,3,4]=>0 [-1,-2,-5,3,-4]=>1 [-1,-2,-5,-3,4]=>1 [-1,-2,-5,-3,-4]=>2 [1,2,5,4,3]=>0 [1,2,5,4,-3]=>1 [1,2,5,-4,3]=>2 [1,2,5,-4,-3]=>3 [1,2,-5,4,3]=>0 [1,2,-5,4,-3]=>1 [1,2,-5,-4,3]=>2 [1,2,-5,-4,-3]=>3 [1,-2,5,4,3]=>0 [1,-2,5,4,-3]=>1 [1,-2,5,-4,3]=>2 [1,-2,5,-4,-3]=>3 [1,-2,-5,4,3]=>0 [1,-2,-5,4,-3]=>1 [1,-2,-5,-4,3]=>2 [1,-2,-5,-4,-3]=>3 [-1,2,5,4,3]=>0 [-1,2,5,4,-3]=>1 [-1,2,5,-4,3]=>2 [-1,2,5,-4,-3]=>3 [-1,2,-5,4,3]=>0 [-1,2,-5,4,-3]=>1 [-1,2,-5,-4,3]=>2 [-1,2,-5,-4,-3]=>3 [-1,-2,5,4,3]=>0 [-1,-2,5,4,-3]=>1 [-1,-2,5,-4,3]=>2 [-1,-2,5,-4,-3]=>3 [-1,-2,-5,4,3]=>0 [-1,-2,-5,4,-3]=>1 [-1,-2,-5,-4,3]=>2 [-1,-2,-5,-4,-3]=>3 [1,3,2,4,5]=>0 [1,3,2,4,-5]=>0 [1,3,2,-4,5]=>0 [1,3,2,-4,-5]=>0 [1,3,-2,4,5]=>1 [1,3,-2,4,-5]=>1 [1,3,-2,-4,5]=>1 [1,3,-2,-4,-5]=>1 [1,-3,2,4,5]=>0 [1,-3,2,4,-5]=>0 [1,-3,2,-4,5]=>0 [1,-3,2,-4,-5]=>0 [1,-3,-2,4,5]=>1 [1,-3,-2,4,-5]=>1 [1,-3,-2,-4,5]=>1 [1,-3,-2,-4,-5]=>1 [-1,3,2,4,5]=>0 [-1,3,2,4,-5]=>0 [-1,3,2,-4,5]=>0 [-1,3,2,-4,-5]=>0 [-1,3,-2,4,5]=>1 [-1,3,-2,4,-5]=>1 [-1,3,-2,-4,5]=>1 [-1,3,-2,-4,-5]=>1 [-1,-3,2,4,5]=>0 [-1,-3,2,4,-5]=>0 [-1,-3,2,-4,5]=>0 [-1,-3,2,-4,-5]=>0 [-1,-3,-2,4,5]=>1 [-1,-3,-2,4,-5]=>1 [-1,-3,-2,-4,5]=>1 [-1,-3,-2,-4,-5]=>1 [1,3,2,5,4]=>0 [1,3,2,5,-4]=>1 [1,3,2,-5,4]=>0 [1,3,2,-5,-4]=>1 [1,3,-2,5,4]=>1 [1,3,-2,5,-4]=>2 [1,3,-2,-5,4]=>1 [1,3,-2,-5,-4]=>2 [1,-3,2,5,4]=>0 [1,-3,2,5,-4]=>1 [1,-3,2,-5,4]=>0 [1,-3,2,-5,-4]=>1 [1,-3,-2,5,4]=>1 [1,-3,-2,5,-4]=>2 [1,-3,-2,-5,4]=>1 [1,-3,-2,-5,-4]=>2 [-1,3,2,5,4]=>0 [-1,3,2,5,-4]=>1 [-1,3,2,-5,4]=>0 [-1,3,2,-5,-4]=>1 [-1,3,-2,5,4]=>1 [-1,3,-2,5,-4]=>2 [-1,3,-2,-5,4]=>1 [-1,3,-2,-5,-4]=>2 [-1,-3,2,5,4]=>0 [-1,-3,2,5,-4]=>1 [-1,-3,2,-5,4]=>0 [-1,-3,2,-5,-4]=>1 [-1,-3,-2,5,4]=>1 [-1,-3,-2,5,-4]=>2 [-1,-3,-2,-5,4]=>1 [-1,-3,-2,-5,-4]=>2 [1,3,4,2,5]=>1 [1,3,4,2,-5]=>1 [1,3,4,-2,5]=>2 [1,3,4,-2,-5]=>2 [1,3,-4,2,5]=>1 [1,3,-4,2,-5]=>1 [1,3,-4,-2,5]=>2 [1,3,-4,-2,-5]=>2 [1,-3,4,2,5]=>1 [1,-3,4,2,-5]=>1 [1,-3,4,-2,5]=>2 [1,-3,4,-2,-5]=>2 [1,-3,-4,2,5]=>1 [1,-3,-4,2,-5]=>1 [1,-3,-4,-2,5]=>2 [1,-3,-4,-2,-5]=>2 [-1,3,4,2,5]=>1 [-1,3,4,2,-5]=>1 [-1,3,4,-2,5]=>2 [-1,3,4,-2,-5]=>2 [-1,3,-4,2,5]=>1 [-1,3,-4,2,-5]=>1 [-1,3,-4,-2,5]=>2 [-1,3,-4,-2,-5]=>2 [-1,-3,4,2,5]=>1 [-1,-3,4,2,-5]=>1 [-1,-3,4,-2,5]=>2 [-1,-3,4,-2,-5]=>2 [-1,-3,-4,2,5]=>1 [-1,-3,-4,2,-5]=>1 [-1,-3,-4,-2,5]=>2 [-1,-3,-4,-2,-5]=>2 [1,3,4,5,2]=>2 [1,3,4,5,-2]=>3 [1,3,4,-5,2]=>2 [1,3,4,-5,-2]=>3 [1,3,-4,5,2]=>2 [1,3,-4,5,-2]=>3 [1,3,-4,-5,2]=>2 [1,3,-4,-5,-2]=>3 [1,-3,4,5,2]=>2 [1,-3,4,5,-2]=>3 [1,-3,4,-5,2]=>2 [1,-3,4,-5,-2]=>3 [1,-3,-4,5,2]=>2 [1,-3,-4,5,-2]=>3 [1,-3,-4,-5,2]=>2 [1,-3,-4,-5,-2]=>3 [-1,3,4,5,2]=>2 [-1,3,4,5,-2]=>3 [-1,3,4,-5,2]=>2 [-1,3,4,-5,-2]=>3 [-1,3,-4,5,2]=>2 [-1,3,-4,5,-2]=>3 [-1,3,-4,-5,2]=>2 [-1,3,-4,-5,-2]=>3 [-1,-3,4,5,2]=>2 [-1,-3,4,5,-2]=>3 [-1,-3,4,-5,2]=>2 [-1,-3,4,-5,-2]=>3 [-1,-3,-4,5,2]=>2 [-1,-3,-4,5,-2]=>3 [-1,-3,-4,-5,2]=>2 [-1,-3,-4,-5,-2]=>3 [1,3,5,2,4]=>1 [1,3,5,2,-4]=>2 [1,3,5,-2,4]=>2 [1,3,5,-2,-4]=>3 [1,3,-5,2,4]=>1 [1,3,-5,2,-4]=>2 [1,3,-5,-2,4]=>2 [1,3,-5,-2,-4]=>3 [1,-3,5,2,4]=>1 [1,-3,5,2,-4]=>2 [1,-3,5,-2,4]=>2 [1,-3,5,-2,-4]=>3 [1,-3,-5,2,4]=>1 [1,-3,-5,2,-4]=>2 [1,-3,-5,-2,4]=>2 [1,-3,-5,-2,-4]=>3 [-1,3,5,2,4]=>1 [-1,3,5,2,-4]=>2 [-1,3,5,-2,4]=>2 [-1,3,5,-2,-4]=>3 [-1,3,-5,2,4]=>1 [-1,3,-5,2,-4]=>2 [-1,3,-5,-2,4]=>2 [-1,3,-5,-2,-4]=>3 [-1,-3,5,2,4]=>1 [-1,-3,5,2,-4]=>2 [-1,-3,5,-2,4]=>2 [-1,-3,5,-2,-4]=>3 [-1,-3,-5,2,4]=>1 [-1,-3,-5,2,-4]=>2 [-1,-3,-5,-2,4]=>2 [-1,-3,-5,-2,-4]=>3 [1,3,5,4,2]=>1 [1,3,5,4,-2]=>2 [1,3,5,-4,2]=>3 [1,3,5,-4,-2]=>4 [1,3,-5,4,2]=>1 [1,3,-5,4,-2]=>2 [1,3,-5,-4,2]=>3 [1,3,-5,-4,-2]=>4 [1,-3,5,4,2]=>1 [1,-3,5,4,-2]=>2 [1,-3,5,-4,2]=>3 [1,-3,5,-4,-2]=>4 [1,-3,-5,4,2]=>1 [1,-3,-5,4,-2]=>2 [1,-3,-5,-4,2]=>3 [1,-3,-5,-4,-2]=>4 [-1,3,5,4,2]=>1 [-1,3,5,4,-2]=>2 [-1,3,5,-4,2]=>3 [-1,3,5,-4,-2]=>4 [-1,3,-5,4,2]=>1 [-1,3,-5,4,-2]=>2 [-1,3,-5,-4,2]=>3 [-1,3,-5,-4,-2]=>4 [-1,-3,5,4,2]=>1 [-1,-3,5,4,-2]=>2 [-1,-3,5,-4,2]=>3 [-1,-3,5,-4,-2]=>4 [-1,-3,-5,4,2]=>1 [-1,-3,-5,4,-2]=>2 [-1,-3,-5,-4,2]=>3 [-1,-3,-5,-4,-2]=>4 [1,4,2,3,5]=>0 [1,4,2,3,-5]=>0 [1,4,2,-3,5]=>1 [1,4,2,-3,-5]=>1 [1,4,-2,3,5]=>1 [1,4,-2,3,-5]=>1 [1,4,-2,-3,5]=>2 [1,4,-2,-3,-5]=>2 [1,-4,2,3,5]=>0 [1,-4,2,3,-5]=>0 [1,-4,2,-3,5]=>1 [1,-4,2,-3,-5]=>1 [1,-4,-2,3,5]=>1 [1,-4,-2,3,-5]=>1 [1,-4,-2,-3,5]=>2 [1,-4,-2,-3,-5]=>2 [-1,4,2,3,5]=>0 [-1,4,2,3,-5]=>0 [-1,4,2,-3,5]=>1 [-1,4,2,-3,-5]=>1 [-1,4,-2,3,5]=>1 [-1,4,-2,3,-5]=>1 [-1,4,-2,-3,5]=>2 [-1,4,-2,-3,-5]=>2 [-1,-4,2,3,5]=>0 [-1,-4,2,3,-5]=>0 [-1,-4,2,-3,5]=>1 [-1,-4,2,-3,-5]=>1 [-1,-4,-2,3,5]=>1 [-1,-4,-2,3,-5]=>1 [-1,-4,-2,-3,5]=>2 [-1,-4,-2,-3,-5]=>2 [1,4,2,5,3]=>1 [1,4,2,5,-3]=>2 [1,4,2,-5,3]=>1 [1,4,2,-5,-3]=>2 [1,4,-2,5,3]=>2 [1,4,-2,5,-3]=>3 [1,4,-2,-5,3]=>2 [1,4,-2,-5,-3]=>3 [1,-4,2,5,3]=>1 [1,-4,2,5,-3]=>2 [1,-4,2,-5,3]=>1 [1,-4,2,-5,-3]=>2 [1,-4,-2,5,3]=>2 [1,-4,-2,5,-3]=>3 [1,-4,-2,-5,3]=>2 [1,-4,-2,-5,-3]=>3 [-1,4,2,5,3]=>1 [-1,4,2,5,-3]=>2 [-1,4,2,-5,3]=>1 [-1,4,2,-5,-3]=>2 [-1,4,-2,5,3]=>2 [-1,4,-2,5,-3]=>3 [-1,4,-2,-5,3]=>2 [-1,4,-2,-5,-3]=>3 [-1,-4,2,5,3]=>1 [-1,-4,2,5,-3]=>2 [-1,-4,2,-5,3]=>1 [-1,-4,2,-5,-3]=>2 [-1,-4,-2,5,3]=>2 [-1,-4,-2,5,-3]=>3 [-1,-4,-2,-5,3]=>2 [-1,-4,-2,-5,-3]=>3 [1,4,3,2,5]=>0 [1,4,3,2,-5]=>0 [1,4,3,-2,5]=>1 [1,4,3,-2,-5]=>1 [1,4,-3,2,5]=>2 [1,4,-3,2,-5]=>2 [1,4,-3,-2,5]=>3 [1,4,-3,-2,-5]=>3 [1,-4,3,2,5]=>0 [1,-4,3,2,-5]=>0 [1,-4,3,-2,5]=>1 [1,-4,3,-2,-5]=>1 [1,-4,-3,2,5]=>2 [1,-4,-3,2,-5]=>2 [1,-4,-3,-2,5]=>3 [1,-4,-3,-2,-5]=>3 [-1,4,3,2,5]=>0 [-1,4,3,2,-5]=>0 [-1,4,3,-2,5]=>1 [-1,4,3,-2,-5]=>1 [-1,4,-3,2,5]=>2 [-1,4,-3,2,-5]=>2 [-1,4,-3,-2,5]=>3 [-1,4,-3,-2,-5]=>3 [-1,-4,3,2,5]=>0 [-1,-4,3,2,-5]=>0 [-1,-4,3,-2,5]=>1 [-1,-4,3,-2,-5]=>1 [-1,-4,-3,2,5]=>2 [-1,-4,-3,2,-5]=>2 [-1,-4,-3,-2,5]=>3 [-1,-4,-3,-2,-5]=>3 [1,4,3,5,2]=>1 [1,4,3,5,-2]=>2 [1,4,3,-5,2]=>1 [1,4,3,-5,-2]=>2 [1,4,-3,5,2]=>3 [1,4,-3,5,-2]=>4 [1,4,-3,-5,2]=>3 [1,4,-3,-5,-2]=>4 [1,-4,3,5,2]=>1 [1,-4,3,5,-2]=>2 [1,-4,3,-5,2]=>1 [1,-4,3,-5,-2]=>2 [1,-4,-3,5,2]=>3 [1,-4,-3,5,-2]=>4 [1,-4,-3,-5,2]=>3 [1,-4,-3,-5,-2]=>4 [-1,4,3,5,2]=>1 [-1,4,3,5,-2]=>2 [-1,4,3,-5,2]=>1 [-1,4,3,-5,-2]=>2 [-1,4,-3,5,2]=>3 [-1,4,-3,5,-2]=>4 [-1,4,-3,-5,2]=>3 [-1,4,-3,-5,-2]=>4 [-1,-4,3,5,2]=>1 [-1,-4,3,5,-2]=>2 [-1,-4,3,-5,2]=>1 [-1,-4,3,-5,-2]=>2 [-1,-4,-3,5,2]=>3 [-1,-4,-3,5,-2]=>4 [-1,-4,-3,-5,2]=>3 [-1,-4,-3,-5,-2]=>4 [1,4,5,2,3]=>2 [1,4,5,2,-3]=>3 [1,4,5,-2,3]=>3 [1,4,5,-2,-3]=>4 [1,4,-5,2,3]=>2 [1,4,-5,2,-3]=>3 [1,4,-5,-2,3]=>3 [1,4,-5,-2,-3]=>4 [1,-4,5,2,3]=>2 [1,-4,5,2,-3]=>3 [1,-4,5,-2,3]=>3 [1,-4,5,-2,-3]=>4 [1,-4,-5,2,3]=>2 [1,-4,-5,2,-3]=>3 [1,-4,-5,-2,3]=>3 [1,-4,-5,-2,-3]=>4 [-1,4,5,2,3]=>2 [-1,4,5,2,-3]=>3 [-1,4,5,-2,3]=>3 [-1,4,5,-2,-3]=>4 [-1,4,-5,2,3]=>2 [-1,4,-5,2,-3]=>3 [-1,4,-5,-2,3]=>3 [-1,4,-5,-2,-3]=>4 [-1,-4,5,2,3]=>2 [-1,-4,5,2,-3]=>3 [-1,-4,5,-2,3]=>3 [-1,-4,5,-2,-3]=>4 [-1,-4,-5,2,3]=>2 [-1,-4,-5,2,-3]=>3 [-1,-4,-5,-2,3]=>3 [-1,-4,-5,-2,-3]=>4 [1,4,5,3,2]=>1 [1,4,5,3,-2]=>2 [1,4,5,-3,2]=>4 [1,4,5,-3,-2]=>5 [1,4,-5,3,2]=>1 [1,4,-5,3,-2]=>2 [1,4,-5,-3,2]=>4 [1,4,-5,-3,-2]=>5 [1,-4,5,3,2]=>1 [1,-4,5,3,-2]=>2 [1,-4,5,-3,2]=>4 [1,-4,5,-3,-2]=>5 [1,-4,-5,3,2]=>1 [1,-4,-5,3,-2]=>2 [1,-4,-5,-3,2]=>4 [1,-4,-5,-3,-2]=>5 [-1,4,5,3,2]=>1 [-1,4,5,3,-2]=>2 [-1,4,5,-3,2]=>4 [-1,4,5,-3,-2]=>5 [-1,4,-5,3,2]=>1 [-1,4,-5,3,-2]=>2 [-1,4,-5,-3,2]=>4 [-1,4,-5,-3,-2]=>5 [-1,-4,5,3,2]=>1 [-1,-4,5,3,-2]=>2 [-1,-4,5,-3,2]=>4 [-1,-4,5,-3,-2]=>5 [-1,-4,-5,3,2]=>1 [-1,-4,-5,3,-2]=>2 [-1,-4,-5,-3,2]=>4 [-1,-4,-5,-3,-2]=>5 [1,5,2,3,4]=>0 [1,5,2,3,-4]=>1 [1,5,2,-3,4]=>1 [1,5,2,-3,-4]=>2 [1,5,-2,3,4]=>1 [1,5,-2,3,-4]=>2 [1,5,-2,-3,4]=>2 [1,5,-2,-3,-4]=>3 [1,-5,2,3,4]=>0 [1,-5,2,3,-4]=>1 [1,-5,2,-3,4]=>1 [1,-5,2,-3,-4]=>2 [1,-5,-2,3,4]=>1 [1,-5,-2,3,-4]=>2 [1,-5,-2,-3,4]=>2 [1,-5,-2,-3,-4]=>3 [-1,5,2,3,4]=>0 [-1,5,2,3,-4]=>1 [-1,5,2,-3,4]=>1 [-1,5,2,-3,-4]=>2 [-1,5,-2,3,4]=>1 [-1,5,-2,3,-4]=>2 [-1,5,-2,-3,4]=>2 [-1,5,-2,-3,-4]=>3 [-1,-5,2,3,4]=>0 [-1,-5,2,3,-4]=>1 [-1,-5,2,-3,4]=>1 [-1,-5,2,-3,-4]=>2 [-1,-5,-2,3,4]=>1 [-1,-5,-2,3,-4]=>2 [-1,-5,-2,-3,4]=>2 [-1,-5,-2,-3,-4]=>3 [1,5,2,4,3]=>0 [1,5,2,4,-3]=>1 [1,5,2,-4,3]=>2 [1,5,2,-4,-3]=>3 [1,5,-2,4,3]=>1 [1,5,-2,4,-3]=>2 [1,5,-2,-4,3]=>3 [1,5,-2,-4,-3]=>4 [1,-5,2,4,3]=>0 [1,-5,2,4,-3]=>1 [1,-5,2,-4,3]=>2 [1,-5,2,-4,-3]=>3 [1,-5,-2,4,3]=>1 [1,-5,-2,4,-3]=>2 [1,-5,-2,-4,3]=>3 [1,-5,-2,-4,-3]=>4 [-1,5,2,4,3]=>0 [-1,5,2,4,-3]=>1 [-1,5,2,-4,3]=>2 [-1,5,2,-4,-3]=>3 [-1,5,-2,4,3]=>1 [-1,5,-2,4,-3]=>2 [-1,5,-2,-4,3]=>3 [-1,5,-2,-4,-3]=>4 [-1,-5,2,4,3]=>0 [-1,-5,2,4,-3]=>1 [-1,-5,2,-4,3]=>2 [-1,-5,2,-4,-3]=>3 [-1,-5,-2,4,3]=>1 [-1,-5,-2,4,-3]=>2 [-1,-5,-2,-4,3]=>3 [-1,-5,-2,-4,-3]=>4 [1,5,3,2,4]=>0 [1,5,3,2,-4]=>1 [1,5,3,-2,4]=>1 [1,5,3,-2,-4]=>2 [1,5,-3,2,4]=>2 [1,5,-3,2,-4]=>3 [1,5,-3,-2,4]=>3 [1,5,-3,-2,-4]=>4 [1,-5,3,2,4]=>0 [1,-5,3,2,-4]=>1 [1,-5,3,-2,4]=>1 [1,-5,3,-2,-4]=>2 [1,-5,-3,2,4]=>2 [1,-5,-3,2,-4]=>3 [1,-5,-3,-2,4]=>3 [1,-5,-3,-2,-4]=>4 [-1,5,3,2,4]=>0 [-1,5,3,2,-4]=>1 [-1,5,3,-2,4]=>1 [-1,5,3,-2,-4]=>2 [-1,5,-3,2,4]=>2 [-1,5,-3,2,-4]=>3 [-1,5,-3,-2,4]=>3 [-1,5,-3,-2,-4]=>4 [-1,-5,3,2,4]=>0 [-1,-5,3,2,-4]=>1 [-1,-5,3,-2,4]=>1 [-1,-5,3,-2,-4]=>2 [-1,-5,-3,2,4]=>2 [-1,-5,-3,2,-4]=>3 [-1,-5,-3,-2,4]=>3 [-1,-5,-3,-2,-4]=>4 [1,5,3,4,2]=>0 [1,5,3,4,-2]=>1 [1,5,3,-4,2]=>2 [1,5,3,-4,-2]=>3 [1,5,-3,4,2]=>2 [1,5,-3,4,-2]=>3 [1,5,-3,-4,2]=>4 [1,5,-3,-4,-2]=>5 [1,-5,3,4,2]=>0 [1,-5,3,4,-2]=>1 [1,-5,3,-4,2]=>2 [1,-5,3,-4,-2]=>3 [1,-5,-3,4,2]=>2 [1,-5,-3,4,-2]=>3 [1,-5,-3,-4,2]=>4 [1,-5,-3,-4,-2]=>5 [-1,5,3,4,2]=>0 [-1,5,3,4,-2]=>1 [-1,5,3,-4,2]=>2 [-1,5,3,-4,-2]=>3 [-1,5,-3,4,2]=>2 [-1,5,-3,4,-2]=>3 [-1,5,-3,-4,2]=>4 [-1,5,-3,-4,-2]=>5 [-1,-5,3,4,2]=>0 [-1,-5,3,4,-2]=>1 [-1,-5,3,-4,2]=>2 [-1,-5,3,-4,-2]=>3 [-1,-5,-3,4,2]=>2 [-1,-5,-3,4,-2]=>3 [-1,-5,-3,-4,2]=>4 [-1,-5,-3,-4,-2]=>5 [1,5,4,2,3]=>1 [1,5,4,2,-3]=>2 [1,5,4,-2,3]=>2 [1,5,4,-2,-3]=>3 [1,5,-4,2,3]=>3 [1,5,-4,2,-3]=>4 [1,5,-4,-2,3]=>4 [1,5,-4,-2,-3]=>5 [1,-5,4,2,3]=>1 [1,-5,4,2,-3]=>2 [1,-5,4,-2,3]=>2 [1,-5,4,-2,-3]=>3 [1,-5,-4,2,3]=>3 [1,-5,-4,2,-3]=>4 [1,-5,-4,-2,3]=>4 [1,-5,-4,-2,-3]=>5 [-1,5,4,2,3]=>1 [-1,5,4,2,-3]=>2 [-1,5,4,-2,3]=>2 [-1,5,4,-2,-3]=>3 [-1,5,-4,2,3]=>3 [-1,5,-4,2,-3]=>4 [-1,5,-4,-2,3]=>4 [-1,5,-4,-2,-3]=>5 [-1,-5,4,2,3]=>1 [-1,-5,4,2,-3]=>2 [-1,-5,4,-2,3]=>2 [-1,-5,4,-2,-3]=>3 [-1,-5,-4,2,3]=>3 [-1,-5,-4,2,-3]=>4 [-1,-5,-4,-2,3]=>4 [-1,-5,-4,-2,-3]=>5 [1,5,4,3,2]=>0 [1,5,4,3,-2]=>1 [1,5,4,-3,2]=>3 [1,5,4,-3,-2]=>4 [1,5,-4,3,2]=>2 [1,5,-4,3,-2]=>3 [1,5,-4,-3,2]=>5 [1,5,-4,-3,-2]=>6 [1,-5,4,3,2]=>0 [1,-5,4,3,-2]=>1 [1,-5,4,-3,2]=>3 [1,-5,4,-3,-2]=>4 [1,-5,-4,3,2]=>2 [1,-5,-4,3,-2]=>3 [1,-5,-4,-3,2]=>5 [1,-5,-4,-3,-2]=>6 [-1,5,4,3,2]=>0 [-1,5,4,3,-2]=>1 [-1,5,4,-3,2]=>3 [-1,5,4,-3,-2]=>4 [-1,5,-4,3,2]=>2 [-1,5,-4,3,-2]=>3
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Description
The number of crossings of a signed permutation.
A crossing of a signed permutation $\pi$ is a pair $(i, j)$ of indices such that
  • $i < j \leq \pi(i) < \pi(j)$, or
  • $-i < j \leq -\pi(i) < \pi(j)$, or
  • $i > j > \pi(i) > \pi(j)$.
References
[1] Corteel, S., Josuat-Vergès, M., Williams, L. K. The Matrix Ansatz, Orthogonal Polynomials, and Permutations arXiv:1005.2696
[2] Corteel, S., Josuat-Vergès, M., Kim, J. S. Crossings of signed permutations and $q$-Eulerian numbers of type $B$ MathSciNet:3096133
Code
def statistic(pi):
    n = len(pi)
    cr1 = sum(1 for j in range(n) for i in range(j) if j + 1 <= pi[i] < pi[j])
    cr2 = sum(1 for j in range(n) for i in range(n) if j + 1 <= -pi[i] < pi[j])
    cr3 = sum(1 for i in range(n) for j in range(i) if j + 1 > pi[i] > pi[j])
    return cr1 + cr2 + cr3
Created
Nov 30, 2022 at 23:44 by Martin Rubey
Updated
Nov 30, 2022 at 23:44 by Martin Rubey