edit this statistic or download as text // json
Identifier
Values
=>
[+]=>0 [-]=>0 [+,+]=>0 [-,+]=>0 [+,-]=>0 [-,-]=>0 [2,1]=>0 [+,+,+]=>0 [-,+,+]=>0 [+,-,+]=>0 [+,+,-]=>0 [-,-,+]=>0 [-,+,-]=>0 [+,-,-]=>0 [-,-,-]=>0 [+,3,2]=>0 [-,3,2]=>0 [2,1,+]=>0 [2,1,-]=>0 [2,3,1]=>0 [3,1,2]=>0 [3,+,1]=>0 [3,-,1]=>0 [+,+,+,+]=>0 [-,+,+,+]=>0 [+,-,+,+]=>0 [+,+,-,+]=>0 [+,+,+,-]=>0 [-,-,+,+]=>0 [-,+,-,+]=>0 [-,+,+,-]=>0 [+,-,-,+]=>0 [+,-,+,-]=>0 [+,+,-,-]=>0 [-,-,-,+]=>0 [-,-,+,-]=>0 [-,+,-,-]=>0 [+,-,-,-]=>0 [-,-,-,-]=>0 [+,+,4,3]=>0 [-,+,4,3]=>0 [+,-,4,3]=>0 [-,-,4,3]=>0 [+,3,2,+]=>0 [-,3,2,+]=>0 [+,3,2,-]=>0 [-,3,2,-]=>0 [+,3,4,2]=>0 [-,3,4,2]=>0 [+,4,2,3]=>0 [-,4,2,3]=>0 [+,4,+,2]=>0 [-,4,+,2]=>0 [+,4,-,2]=>0 [-,4,-,2]=>0 [2,1,+,+]=>0 [2,1,-,+]=>0 [2,1,+,-]=>0 [2,1,-,-]=>0 [2,1,4,3]=>0 [2,3,1,+]=>0 [2,3,1,-]=>0 [2,3,4,1]=>0 [2,4,1,3]=>1 [2,4,+,1]=>0 [2,4,-,1]=>0 [3,1,2,+]=>0 [3,1,2,-]=>0 [3,1,4,2]=>1 [3,+,1,+]=>0 [3,-,1,+]=>0 [3,+,1,-]=>0 [3,-,1,-]=>0 [3,+,4,1]=>0 [3,-,4,1]=>0 [3,4,1,2]=>0 [3,4,2,1]=>1 [4,1,2,3]=>0 [4,1,+,2]=>0 [4,1,-,2]=>0 [4,+,1,3]=>0 [4,-,1,3]=>0 [4,+,+,1]=>0 [4,-,+,1]=>0 [4,+,-,1]=>0 [4,-,-,1]=>0 [4,3,1,2]=>1 [4,3,2,1]=>0 [+,+,+,+,+]=>0 [-,+,+,+,+]=>0 [+,-,+,+,+]=>0 [+,+,-,+,+]=>0 [+,+,+,-,+]=>0 [+,+,+,+,-]=>0 [-,-,+,+,+]=>0 [-,+,-,+,+]=>0 [-,+,+,-,+]=>0 [-,+,+,+,-]=>0 [+,-,-,+,+]=>0 [+,-,+,-,+]=>0 [+,-,+,+,-]=>0 [+,+,-,-,+]=>0 [+,+,-,+,-]=>0 [+,+,+,-,-]=>0 [-,-,-,+,+]=>0 [-,-,+,-,+]=>0 [-,-,+,+,-]=>0 [-,+,-,-,+]=>0 [-,+,-,+,-]=>0 [-,+,+,-,-]=>0 [+,-,-,-,+]=>0 [+,-,-,+,-]=>0 [+,-,+,-,-]=>0 [+,+,-,-,-]=>0 [-,-,-,-,+]=>0 [-,-,-,+,-]=>0 [-,-,+,-,-]=>0 [-,+,-,-,-]=>0 [+,-,-,-,-]=>0 [-,-,-,-,-]=>0 [+,+,+,5,4]=>0 [-,+,+,5,4]=>0 [+,-,+,5,4]=>0 [+,+,-,5,4]=>0 [-,-,+,5,4]=>0 [-,+,-,5,4]=>0 [+,-,-,5,4]=>0 [-,-,-,5,4]=>0 [+,+,4,3,+]=>0 [-,+,4,3,+]=>0 [+,-,4,3,+]=>0 [+,+,4,3,-]=>0 [-,-,4,3,+]=>0 [-,+,4,3,-]=>0 [+,-,4,3,-]=>0 [-,-,4,3,-]=>0 [+,+,4,5,3]=>0 [-,+,4,5,3]=>0 [+,-,4,5,3]=>0 [-,-,4,5,3]=>0 [+,+,5,3,4]=>0 [-,+,5,3,4]=>0 [+,-,5,3,4]=>0 [-,-,5,3,4]=>0 [+,+,5,+,3]=>0 [-,+,5,+,3]=>0 [+,-,5,+,3]=>0 [+,+,5,-,3]=>0 [-,-,5,+,3]=>0 [-,+,5,-,3]=>0 [+,-,5,-,3]=>0 [-,-,5,-,3]=>0 [+,3,2,+,+]=>0 [-,3,2,+,+]=>0 [+,3,2,-,+]=>0 [+,3,2,+,-]=>0 [-,3,2,-,+]=>0 [-,3,2,+,-]=>0 [+,3,2,-,-]=>0 [-,3,2,-,-]=>0 [+,3,2,5,4]=>0 [-,3,2,5,4]=>0 [+,3,4,2,+]=>0 [-,3,4,2,+]=>0 [+,3,4,2,-]=>0 [-,3,4,2,-]=>0 [+,3,4,5,2]=>0 [-,3,4,5,2]=>0 [+,3,5,2,4]=>1 [-,3,5,2,4]=>1 [+,3,5,+,2]=>0 [-,3,5,+,2]=>0 [+,3,5,-,2]=>0 [-,3,5,-,2]=>0 [+,4,2,3,+]=>0 [-,4,2,3,+]=>0 [+,4,2,3,-]=>0 [-,4,2,3,-]=>0 [+,4,2,5,3]=>1 [-,4,2,5,3]=>1 [+,4,+,2,+]=>0 [-,4,+,2,+]=>0 [+,4,-,2,+]=>0 [+,4,+,2,-]=>0 [-,4,-,2,+]=>0 [-,4,+,2,-]=>0 [+,4,-,2,-]=>0 [-,4,-,2,-]=>0 [+,4,+,5,2]=>0 [-,4,+,5,2]=>0 [+,4,-,5,2]=>0 [-,4,-,5,2]=>0 [+,4,5,2,3]=>0 [-,4,5,2,3]=>0 [+,4,5,3,2]=>1 [-,4,5,3,2]=>1 [+,5,2,3,4]=>0 [-,5,2,3,4]=>0 [+,5,2,+,3]=>0 [-,5,2,+,3]=>0 [+,5,2,-,3]=>0 [-,5,2,-,3]=>0 [+,5,+,2,4]=>0 [-,5,+,2,4]=>0 [+,5,-,2,4]=>0 [-,5,-,2,4]=>0 [+,5,+,+,2]=>0 [-,5,+,+,2]=>0 [+,5,-,+,2]=>0 [+,5,+,-,2]=>0 [-,5,-,+,2]=>0 [-,5,+,-,2]=>0 [+,5,-,-,2]=>0 [-,5,-,-,2]=>0 [+,5,4,2,3]=>1 [-,5,4,2,3]=>1 [+,5,4,3,2]=>0 [-,5,4,3,2]=>0 [2,1,+,+,+]=>0 [2,1,-,+,+]=>0 [2,1,+,-,+]=>0 [2,1,+,+,-]=>0 [2,1,-,-,+]=>0 [2,1,-,+,-]=>0 [2,1,+,-,-]=>0 [2,1,-,-,-]=>0 [2,1,+,5,4]=>0 [2,1,-,5,4]=>0 [2,1,4,3,+]=>0 [2,1,4,3,-]=>0 [2,1,4,5,3]=>0 [2,1,5,3,4]=>0 [2,1,5,+,3]=>0 [2,1,5,-,3]=>0 [2,3,1,+,+]=>0 [2,3,1,-,+]=>0 [2,3,1,+,-]=>0 [2,3,1,-,-]=>0 [2,3,1,5,4]=>0 [2,3,4,1,+]=>0 [2,3,4,1,-]=>0 [2,3,4,5,1]=>0 [2,3,5,1,4]=>2 [2,3,5,+,1]=>0 [2,3,5,-,1]=>0 [2,4,1,3,+]=>1 [2,4,1,3,-]=>1 [2,4,1,5,3]=>2 [2,4,+,1,+]=>0 [2,4,-,1,+]=>0 [2,4,+,1,-]=>0 [2,4,-,1,-]=>0 [2,4,+,5,1]=>0 [2,4,-,5,1]=>0 [2,4,5,1,3]=>1 [2,4,5,3,1]=>2 [2,5,1,3,4]=>2 [2,5,1,+,3]=>1 [2,5,1,-,3]=>1 [2,5,+,1,4]=>1 [2,5,-,1,4]=>1 [2,5,+,+,1]=>0 [2,5,-,+,1]=>0 [2,5,+,-,1]=>0 [2,5,-,-,1]=>0 [2,5,4,1,3]=>2 [2,5,4,3,1]=>0 [3,1,2,+,+]=>0 [3,1,2,-,+]=>0 [3,1,2,+,-]=>0 [3,1,2,-,-]=>0 [3,1,2,5,4]=>0 [3,1,4,2,+]=>1 [3,1,4,2,-]=>1 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,+,2]=>1 [3,1,5,-,2]=>1 [3,+,1,+,+]=>0 [3,-,1,+,+]=>0 [3,+,1,-,+]=>0 [3,+,1,+,-]=>0 [3,-,1,-,+]=>0 [3,-,1,+,-]=>0 [3,+,1,-,-]=>0 [3,-,1,-,-]=>0 [3,+,1,5,4]=>0 [3,-,1,5,4]=>0 [3,+,4,1,+]=>0 [3,-,4,1,+]=>0 [3,+,4,1,-]=>0 [3,-,4,1,-]=>0 [3,+,4,5,1]=>0 [3,-,4,5,1]=>0 [3,+,5,1,4]=>1 [3,-,5,1,4]=>1 [3,+,5,+,1]=>0 [3,-,5,+,1]=>0 [3,+,5,-,1]=>0 [3,-,5,-,1]=>0 [3,4,1,2,+]=>0 [3,4,1,2,-]=>0 [3,4,1,5,2]=>1 [3,4,2,1,+]=>1 [3,4,2,1,-]=>1 [3,4,2,5,1]=>2 [3,4,5,1,2]=>0 [3,4,5,2,1]=>1 [3,5,1,2,4]=>1 [3,5,1,+,2]=>0 [3,5,1,-,2]=>0 [3,5,2,1,4]=>2 [3,5,2,+,1]=>1 [3,5,2,-,1]=>1 [3,5,4,1,2]=>1 [3,5,4,2,1]=>2 [4,1,2,3,+]=>0 [4,1,2,3,-]=>0 [4,1,2,5,3]=>2 [4,1,+,2,+]=>0 [4,1,-,2,+]=>0 [4,1,+,2,-]=>0 [4,1,-,2,-]=>0 [4,1,+,5,2]=>1 [4,1,-,5,2]=>1 [4,1,5,2,3]=>1 [4,1,5,3,2]=>2 [4,+,1,3,+]=>0 [4,-,1,3,+]=>0 [4,+,1,3,-]=>0 [4,-,1,3,-]=>0 [4,+,1,5,3]=>1 [4,-,1,5,3]=>1 [4,+,+,1,+]=>0 [4,-,+,1,+]=>0 [4,+,-,1,+]=>0 [4,+,+,1,-]=>0 [4,-,-,1,+]=>0 [4,-,+,1,-]=>0 [4,+,-,1,-]=>0 [4,-,-,1,-]=>0 [4,+,+,5,1]=>0 [4,-,+,5,1]=>0 [4,+,-,5,1]=>0 [4,-,-,5,1]=>0 [4,+,5,1,3]=>0 [4,-,5,1,3]=>0 [4,+,5,3,1]=>1 [4,-,5,3,1]=>1 [4,3,1,2,+]=>1 [4,3,1,2,-]=>1 [4,3,1,5,2]=>2 [4,3,2,1,+]=>0 [4,3,2,1,-]=>0 [4,3,2,5,1]=>0 [4,3,5,1,2]=>1 [4,3,5,2,1]=>2 [4,5,1,2,3]=>0 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>2 [4,5,+,1,2]=>0 [4,5,-,1,2]=>0 [4,5,+,2,1]=>1 [4,5,-,2,1]=>1 [5,1,2,3,4]=>0 [5,1,2,+,3]=>0 [5,1,2,-,3]=>0 [5,1,+,2,4]=>0 [5,1,-,2,4]=>0 [5,1,+,+,2]=>0 [5,1,-,+,2]=>0 [5,1,+,-,2]=>0 [5,1,-,-,2]=>0 [5,1,4,2,3]=>2 [5,1,4,3,2]=>0 [5,+,1,3,4]=>0 [5,-,1,3,4]=>0 [5,+,1,+,3]=>0 [5,-,1,+,3]=>0 [5,+,1,-,3]=>0 [5,-,1,-,3]=>0 [5,+,+,1,4]=>0 [5,-,+,1,4]=>0 [5,+,-,1,4]=>0 [5,-,-,1,4]=>0 [5,+,+,+,1]=>0 [5,-,+,+,1]=>0 [5,+,-,+,1]=>0 [5,+,+,-,1]=>0 [5,-,-,+,1]=>0 [5,-,+,-,1]=>0 [5,+,-,-,1]=>0 [5,-,-,-,1]=>0 [5,+,4,1,3]=>1 [5,-,4,1,3]=>1 [5,+,4,3,1]=>0 [5,-,4,3,1]=>0 [5,3,1,2,4]=>2 [5,3,1,+,2]=>1 [5,3,1,-,2]=>1 [5,3,2,1,4]=>0 [5,3,2,+,1]=>0 [5,3,2,-,1]=>0 [5,3,4,1,2]=>2 [5,3,4,2,1]=>0 [5,4,1,2,3]=>1 [5,4,1,3,2]=>2 [5,4,2,1,3]=>2 [5,4,2,3,1]=>0 [5,4,+,1,2]=>1 [5,4,-,1,2]=>1 [5,4,+,2,1]=>0 [5,4,-,2,1]=>0 [+,+,+,+,+,+]=>0 [-,+,+,+,+,+]=>0 [+,-,+,+,+,+]=>0 [+,+,-,+,+,+]=>0 [+,+,+,-,+,+]=>0 [+,+,+,+,-,+]=>0 [+,+,+,+,+,-]=>0 [-,-,+,+,+,+]=>0 [-,+,-,+,+,+]=>0 [-,+,+,-,+,+]=>0 [-,+,+,+,-,+]=>0 [-,+,+,+,+,-]=>0 [+,-,-,+,+,+]=>0 [+,-,+,-,+,+]=>0 [+,-,+,+,-,+]=>0 [+,-,+,+,+,-]=>0 [+,+,-,-,+,+]=>0 [+,+,-,+,-,+]=>0 [+,+,-,+,+,-]=>0 [+,+,+,-,-,+]=>0 [+,+,+,-,+,-]=>0 [+,+,+,+,-,-]=>0 [-,-,-,+,+,+]=>0 [-,-,+,-,+,+]=>0 [-,-,+,+,-,+]=>0 [-,-,+,+,+,-]=>0 [-,+,-,-,+,+]=>0 [-,+,-,+,-,+]=>0 [-,+,-,+,+,-]=>0 [-,+,+,-,-,+]=>0 [-,+,+,-,+,-]=>0 [-,+,+,+,-,-]=>0 [+,-,-,-,+,+]=>0 [+,-,-,+,-,+]=>0 [+,-,-,+,+,-]=>0 [+,-,+,-,-,+]=>0 [+,-,+,-,+,-]=>0 [+,-,+,+,-,-]=>0 [+,+,-,-,-,+]=>0 [+,+,-,-,+,-]=>0 [+,+,-,+,-,-]=>0 [+,+,+,-,-,-]=>0 [-,-,-,-,+,+]=>0 [-,-,-,+,-,+]=>0 [-,-,-,+,+,-]=>0 [-,-,+,-,-,+]=>0 [-,-,+,-,+,-]=>0 [-,-,+,+,-,-]=>0 [-,+,-,-,-,+]=>0 [-,+,-,-,+,-]=>0 [-,+,-,+,-,-]=>0 [-,+,+,-,-,-]=>0 [+,-,-,-,-,+]=>0 [+,-,-,-,+,-]=>0 [+,-,-,+,-,-]=>0 [+,-,+,-,-,-]=>0 [+,+,-,-,-,-]=>0 [-,-,-,-,-,+]=>0 [-,-,-,-,+,-]=>0 [-,-,-,+,-,-]=>0 [-,-,+,-,-,-]=>0 [-,+,-,-,-,-]=>0 [+,-,-,-,-,-]=>0 [-,-,-,-,-,-]=>0 [+,+,+,+,6,5]=>0 [-,+,+,+,6,5]=>0 [+,-,+,+,6,5]=>0 [+,+,-,+,6,5]=>0 [+,+,+,-,6,5]=>0 [-,-,+,+,6,5]=>0 [-,+,-,+,6,5]=>0 [-,+,+,-,6,5]=>0 [+,-,-,+,6,5]=>0 [+,-,+,-,6,5]=>0 [+,+,-,-,6,5]=>0 [-,-,-,+,6,5]=>0 [-,-,+,-,6,5]=>0 [-,+,-,-,6,5]=>0 [+,-,-,-,6,5]=>0 [-,-,-,-,6,5]=>0 [+,+,+,5,4,+]=>0 [-,+,+,5,4,+]=>0 [+,-,+,5,4,+]=>0 [+,+,-,5,4,+]=>0 [+,+,+,5,4,-]=>0 [-,-,+,5,4,+]=>0 [-,+,-,5,4,+]=>0 [-,+,+,5,4,-]=>0 [+,-,-,5,4,+]=>0 [+,-,+,5,4,-]=>0 [+,+,-,5,4,-]=>0 [-,-,-,5,4,+]=>0 [-,-,+,5,4,-]=>0 [-,+,-,5,4,-]=>0 [+,-,-,5,4,-]=>0 [-,-,-,5,4,-]=>0 [+,+,+,5,6,4]=>0 [-,+,+,5,6,4]=>0 [+,-,+,5,6,4]=>0 [+,+,-,5,6,4]=>0 [-,-,+,5,6,4]=>0 [-,+,-,5,6,4]=>0 [+,-,-,5,6,4]=>0 [-,-,-,5,6,4]=>0 [+,+,+,6,4,5]=>0 [-,+,+,6,4,5]=>0 [+,-,+,6,4,5]=>0 [+,+,-,6,4,5]=>0 [-,-,+,6,4,5]=>0 [-,+,-,6,4,5]=>0 [+,-,-,6,4,5]=>0 [-,-,-,6,4,5]=>0 [+,+,+,6,+,4]=>0 [-,+,+,6,+,4]=>0 [+,-,+,6,+,4]=>0 [+,+,-,6,+,4]=>0 [+,+,+,6,-,4]=>0 [-,-,+,6,+,4]=>0 [-,+,-,6,+,4]=>0 [-,+,+,6,-,4]=>0 [+,-,-,6,+,4]=>0 [+,-,+,6,-,4]=>0 [+,+,-,6,-,4]=>0 [-,-,-,6,+,4]=>0 [-,-,+,6,-,4]=>0 [-,+,-,6,-,4]=>0 [+,-,-,6,-,4]=>0 [-,-,-,6,-,4]=>0 [+,+,4,3,+,+]=>0 [-,+,4,3,+,+]=>0 [+,-,4,3,+,+]=>0 [+,+,4,3,-,+]=>0 [+,+,4,3,+,-]=>0 [-,-,4,3,+,+]=>0 [-,+,4,3,-,+]=>0 [-,+,4,3,+,-]=>0 [+,-,4,3,-,+]=>0 [+,-,4,3,+,-]=>0 [+,+,4,3,-,-]=>0 [-,-,4,3,-,+]=>0 [-,-,4,3,+,-]=>0 [-,+,4,3,-,-]=>0 [+,-,4,3,-,-]=>0 [-,-,4,3,-,-]=>0 [+,+,4,3,6,5]=>0 [-,+,4,3,6,5]=>0 [+,-,4,3,6,5]=>0 [-,-,4,3,6,5]=>0 [+,+,4,5,3,+]=>0 [-,+,4,5,3,+]=>0 [+,-,4,5,3,+]=>0 [+,+,4,5,3,-]=>0 [-,-,4,5,3,+]=>0 [-,+,4,5,3,-]=>0 [+,-,4,5,3,-]=>0 [-,-,4,5,3,-]=>0 [+,+,4,5,6,3]=>0 [-,+,4,5,6,3]=>0 [+,-,4,5,6,3]=>0 [-,-,4,5,6,3]=>0 [+,+,4,6,3,5]=>1 [-,+,4,6,3,5]=>1 [+,-,4,6,3,5]=>1 [-,-,4,6,3,5]=>1 [+,+,4,6,+,3]=>0 [-,+,4,6,+,3]=>0 [+,-,4,6,+,3]=>0 [+,+,4,6,-,3]=>0 [-,-,4,6,+,3]=>0 [-,+,4,6,-,3]=>0 [+,-,4,6,-,3]=>0 [-,-,4,6,-,3]=>0 [+,+,5,3,4,+]=>0 [-,+,5,3,4,+]=>0 [+,-,5,3,4,+]=>0 [+,+,5,3,4,-]=>0 [-,-,5,3,4,+]=>0 [-,+,5,3,4,-]=>0 [+,-,5,3,4,-]=>0 [-,-,5,3,4,-]=>0 [+,+,5,3,6,4]=>1 [-,+,5,3,6,4]=>1 [+,-,5,3,6,4]=>1 [-,-,5,3,6,4]=>1 [+,+,5,+,3,+]=>0 [-,+,5,+,3,+]=>0 [+,-,5,+,3,+]=>0 [+,+,5,-,3,+]=>0 [+,+,5,+,3,-]=>0 [-,-,5,+,3,+]=>0 [-,+,5,-,3,+]=>0 [-,+,5,+,3,-]=>0 [+,-,5,-,3,+]=>0 [+,-,5,+,3,-]=>0 [+,+,5,-,3,-]=>0 [-,-,5,-,3,+]=>0 [-,-,5,+,3,-]=>0 [-,+,5,-,3,-]=>0 [+,-,5,-,3,-]=>0 [-,-,5,-,3,-]=>0 [+,+,5,+,6,3]=>0 [-,+,5,+,6,3]=>0 [+,-,5,+,6,3]=>0 [+,+,5,-,6,3]=>0 [-,-,5,+,6,3]=>0 [-,+,5,-,6,3]=>0 [+,-,5,-,6,3]=>0 [-,-,5,-,6,3]=>0 [+,+,5,6,3,4]=>0 [-,+,5,6,3,4]=>0 [+,-,5,6,3,4]=>0 [-,-,5,6,3,4]=>0 [+,+,5,6,4,3]=>1 [-,+,5,6,4,3]=>1 [+,-,5,6,4,3]=>1 [-,-,5,6,4,3]=>1 [+,+,6,3,4,5]=>0 [-,+,6,3,4,5]=>0 [+,-,6,3,4,5]=>0 [-,-,6,3,4,5]=>0 [+,+,6,3,+,4]=>0 [-,+,6,3,+,4]=>0 [+,-,6,3,+,4]=>0 [+,+,6,3,-,4]=>0 [-,-,6,3,+,4]=>0 [-,+,6,3,-,4]=>0 [+,-,6,3,-,4]=>0 [-,-,6,3,-,4]=>0 [+,+,6,+,3,5]=>0 [-,+,6,+,3,5]=>0 [+,-,6,+,3,5]=>0 [+,+,6,-,3,5]=>0 [-,-,6,+,3,5]=>0 [-,+,6,-,3,5]=>0 [+,-,6,-,3,5]=>0 [-,-,6,-,3,5]=>0 [+,+,6,+,+,3]=>0 [-,+,6,+,+,3]=>0 [+,-,6,+,+,3]=>0 [+,+,6,-,+,3]=>0 [+,+,6,+,-,3]=>0 [-,-,6,+,+,3]=>0 [-,+,6,-,+,3]=>0 [-,+,6,+,-,3]=>0 [+,-,6,-,+,3]=>0 [+,-,6,+,-,3]=>0 [+,+,6,-,-,3]=>0 [-,-,6,-,+,3]=>0 [-,-,6,+,-,3]=>0 [-,+,6,-,-,3]=>0 [+,-,6,-,-,3]=>0 [-,-,6,-,-,3]=>0 [+,+,6,5,3,4]=>1 [-,+,6,5,3,4]=>1 [+,-,6,5,3,4]=>1 [-,-,6,5,3,4]=>1 [+,+,6,5,4,3]=>0 [-,+,6,5,4,3]=>0 [+,-,6,5,4,3]=>0 [-,-,6,5,4,3]=>0 [+,3,2,+,+,+]=>0 [-,3,2,+,+,+]=>0 [+,3,2,-,+,+]=>0 [+,3,2,+,-,+]=>0 [+,3,2,+,+,-]=>0 [-,3,2,-,+,+]=>0 [-,3,2,+,-,+]=>0 [-,3,2,+,+,-]=>0 [+,3,2,-,-,+]=>0 [+,3,2,-,+,-]=>0 [+,3,2,+,-,-]=>0 [-,3,2,-,-,+]=>0 [-,3,2,-,+,-]=>0 [-,3,2,+,-,-]=>0 [+,3,2,-,-,-]=>0 [-,3,2,-,-,-]=>0 [+,3,2,+,6,5]=>0 [-,3,2,+,6,5]=>0 [+,3,2,-,6,5]=>0 [-,3,2,-,6,5]=>0 [+,3,2,5,4,+]=>0 [-,3,2,5,4,+]=>0 [+,3,2,5,4,-]=>0 [-,3,2,5,4,-]=>0 [+,3,2,5,6,4]=>0 [-,3,2,5,6,4]=>0 [+,3,2,6,4,5]=>0 [-,3,2,6,4,5]=>0 [+,3,2,6,+,4]=>0 [-,3,2,6,+,4]=>0 [+,3,2,6,-,4]=>0 [-,3,2,6,-,4]=>0 [+,3,4,2,+,+]=>0 [-,3,4,2,+,+]=>0 [+,3,4,2,-,+]=>0 [+,3,4,2,+,-]=>0 [-,3,4,2,-,+]=>0 [-,3,4,2,+,-]=>0 [+,3,4,2,-,-]=>0 [-,3,4,2,-,-]=>0 [+,3,4,2,6,5]=>0 [-,3,4,2,6,5]=>0 [+,3,4,5,2,+]=>0 [-,3,4,5,2,+]=>0 [+,3,4,5,2,-]=>0 [-,3,4,5,2,-]=>0 [+,3,4,5,6,2]=>0 [-,3,4,5,6,2]=>0 [+,3,4,6,2,5]=>2 [-,3,4,6,2,5]=>2 [+,3,4,6,+,2]=>0 [-,3,4,6,+,2]=>0 [+,3,4,6,-,2]=>0 [-,3,4,6,-,2]=>0 [+,3,5,2,4,+]=>1 [-,3,5,2,4,+]=>1 [+,3,5,2,4,-]=>1 [-,3,5,2,4,-]=>1 [+,3,5,2,6,4]=>2 [-,3,5,2,6,4]=>2 [+,3,5,+,2,+]=>0 [-,3,5,+,2,+]=>0 [+,3,5,-,2,+]=>0 [+,3,5,+,2,-]=>0 [-,3,5,-,2,+]=>0 [-,3,5,+,2,-]=>0 [+,3,5,-,2,-]=>0 [-,3,5,-,2,-]=>0 [+,3,5,+,6,2]=>0 [-,3,5,+,6,2]=>0 [+,3,5,-,6,2]=>0 [-,3,5,-,6,2]=>0 [+,3,5,6,2,4]=>1 [-,3,5,6,2,4]=>1 [+,3,5,6,4,2]=>2 [-,3,5,6,4,2]=>2 [+,3,6,2,4,5]=>2 [-,3,6,2,4,5]=>2 [+,3,6,2,+,4]=>1 [-,3,6,2,+,4]=>1 [+,3,6,2,-,4]=>1 [-,3,6,2,-,4]=>1 [+,3,6,+,2,5]=>1 [-,3,6,+,2,5]=>1 [+,3,6,-,2,5]=>1 [-,3,6,-,2,5]=>1 [+,3,6,+,+,2]=>0 [-,3,6,+,+,2]=>0 [+,3,6,-,+,2]=>0 [+,3,6,+,-,2]=>0 [-,3,6,-,+,2]=>0 [-,3,6,+,-,2]=>0 [+,3,6,-,-,2]=>0 [-,3,6,-,-,2]=>0 [+,3,6,5,2,4]=>2 [-,3,6,5,2,4]=>2 [+,3,6,5,4,2]=>0 [-,3,6,5,4,2]=>0 [+,4,2,3,+,+]=>0 [-,4,2,3,+,+]=>0 [+,4,2,3,-,+]=>0 [+,4,2,3,+,-]=>0 [-,4,2,3,-,+]=>0 [-,4,2,3,+,-]=>0 [+,4,2,3,-,-]=>0 [-,4,2,3,-,-]=>0 [+,4,2,3,6,5]=>0 [-,4,2,3,6,5]=>0 [+,4,2,5,3,+]=>1 [-,4,2,5,3,+]=>1 [+,4,2,5,3,-]=>1 [-,4,2,5,3,-]=>1 [+,4,2,5,6,3]=>2 [-,4,2,5,6,3]=>2 [+,4,2,6,3,5]=>2 [-,4,2,6,3,5]=>2 [+,4,2,6,+,3]=>1 [-,4,2,6,+,3]=>1 [+,4,2,6,-,3]=>1 [-,4,2,6,-,3]=>1 [+,4,+,2,+,+]=>0 [-,4,+,2,+,+]=>0 [+,4,-,2,+,+]=>0 [+,4,+,2,-,+]=>0 [+,4,+,2,+,-]=>0 [-,4,-,2,+,+]=>0 [-,4,+,2,-,+]=>0 [-,4,+,2,+,-]=>0 [+,4,-,2,-,+]=>0 [+,4,-,2,+,-]=>0 [+,4,+,2,-,-]=>0 [-,4,-,2,-,+]=>0 [-,4,-,2,+,-]=>0 [-,4,+,2,-,-]=>0 [+,4,-,2,-,-]=>0 [-,4,-,2,-,-]=>0 [+,4,+,2,6,5]=>0 [-,4,+,2,6,5]=>0 [+,4,-,2,6,5]=>0 [-,4,-,2,6,5]=>0 [+,4,+,5,2,+]=>0 [-,4,+,5,2,+]=>0 [+,4,-,5,2,+]=>0 [+,4,+,5,2,-]=>0 [-,4,-,5,2,+]=>0 [-,4,+,5,2,-]=>0 [+,4,-,5,2,-]=>0 [-,4,-,5,2,-]=>0 [+,4,+,5,6,2]=>0 [-,4,+,5,6,2]=>0 [+,4,-,5,6,2]=>0 [-,4,-,5,6,2]=>0 [+,4,+,6,2,5]=>1 [-,4,+,6,2,5]=>1 [+,4,-,6,2,5]=>1 [-,4,-,6,2,5]=>1 [+,4,+,6,+,2]=>0 [-,4,+,6,+,2]=>0 [+,4,-,6,+,2]=>0 [+,4,+,6,-,2]=>0 [-,4,-,6,+,2]=>0 [-,4,+,6,-,2]=>0 [+,4,-,6,-,2]=>0 [-,4,-,6,-,2]=>0 [+,4,5,2,3,+]=>0 [-,4,5,2,3,+]=>0 [+,4,5,2,3,-]=>0 [-,4,5,2,3,-]=>0 [+,4,5,2,6,3]=>1 [-,4,5,2,6,3]=>1 [+,4,5,3,2,+]=>1 [-,4,5,3,2,+]=>1 [+,4,5,3,2,-]=>1 [-,4,5,3,2,-]=>1 [+,4,5,3,6,2]=>2 [-,4,5,3,6,2]=>2 [+,4,5,6,2,3]=>0 [-,4,5,6,2,3]=>0 [+,4,5,6,3,2]=>1 [-,4,5,6,3,2]=>1 [+,4,6,2,3,5]=>1 [-,4,6,2,3,5]=>1 [+,4,6,2,+,3]=>0 [-,4,6,2,+,3]=>0 [+,4,6,2,-,3]=>0 [-,4,6,2,-,3]=>0 [+,4,6,3,2,5]=>2 [-,4,6,3,2,5]=>2 [+,4,6,3,+,2]=>1 [-,4,6,3,+,2]=>1 [+,4,6,3,-,2]=>1 [-,4,6,3,-,2]=>1 [+,4,6,5,2,3]=>1 [-,4,6,5,2,3]=>1 [+,4,6,5,3,2]=>2 [-,4,6,5,3,2]=>2 [+,5,2,3,4,+]=>0 [-,5,2,3,4,+]=>0 [+,5,2,3,4,-]=>0 [-,5,2,3,4,-]=>0 [+,5,2,3,6,4]=>2 [-,5,2,3,6,4]=>2 [+,5,2,+,3,+]=>0 [-,5,2,+,3,+]=>0 [+,5,2,-,3,+]=>0 [+,5,2,+,3,-]=>0 [-,5,2,-,3,+]=>0 [-,5,2,+,3,-]=>0 [+,5,2,-,3,-]=>0 [-,5,2,-,3,-]=>0 [+,5,2,+,6,3]=>1 [-,5,2,+,6,3]=>1 [+,5,2,-,6,3]=>1 [-,5,2,-,6,3]=>1 [+,5,2,6,3,4]=>1 [-,5,2,6,3,4]=>1 [+,5,2,6,4,3]=>2 [-,5,2,6,4,3]=>2 [+,5,+,2,4,+]=>0 [-,5,+,2,4,+]=>0 [+,5,-,2,4,+]=>0 [+,5,+,2,4,-]=>0 [-,5,-,2,4,+]=>0 [-,5,+,2,4,-]=>0 [+,5,-,2,4,-]=>0 [-,5,-,2,4,-]=>0 [+,5,+,2,6,4]=>1 [-,5,+,2,6,4]=>1 [+,5,-,2,6,4]=>1 [-,5,-,2,6,4]=>1 [+,5,+,+,2,+]=>0 [-,5,+,+,2,+]=>0 [+,5,-,+,2,+]=>0 [+,5,+,-,2,+]=>0 [+,5,+,+,2,-]=>0 [-,5,-,+,2,+]=>0 [-,5,+,-,2,+]=>0 [-,5,+,+,2,-]=>0 [+,5,-,-,2,+]=>0 [+,5,-,+,2,-]=>0 [+,5,+,-,2,-]=>0 [-,5,-,-,2,+]=>0 [-,5,-,+,2,-]=>0 [-,5,+,-,2,-]=>0 [+,5,-,-,2,-]=>0 [-,5,-,-,2,-]=>0 [+,5,+,+,6,2]=>0 [-,5,+,+,6,2]=>0 [+,5,-,+,6,2]=>0 [+,5,+,-,6,2]=>0 [-,5,-,+,6,2]=>0 [-,5,+,-,6,2]=>0 [+,5,-,-,6,2]=>0 [-,5,-,-,6,2]=>0 [+,5,+,6,2,4]=>0 [-,5,+,6,2,4]=>0 [+,5,-,6,2,4]=>0 [-,5,-,6,2,4]=>0 [+,5,+,6,4,2]=>1 [-,5,+,6,4,2]=>1 [+,5,-,6,4,2]=>1 [-,5,-,6,4,2]=>1 [+,5,4,2,3,+]=>1 [-,5,4,2,3,+]=>1 [+,5,4,2,3,-]=>1 [-,5,4,2,3,-]=>1 [+,5,4,2,6,3]=>2 [-,5,4,2,6,3]=>2 [+,5,4,3,2,+]=>0 [-,5,4,3,2,+]=>0 [+,5,4,3,2,-]=>0 [-,5,4,3,2,-]=>0 [+,5,4,3,6,2]=>0 [-,5,4,3,6,2]=>0 [+,5,4,6,2,3]=>1 [-,5,4,6,2,3]=>1 [+,5,4,6,3,2]=>2 [-,5,4,6,3,2]=>2 [+,5,6,2,3,4]=>0 [-,5,6,2,3,4]=>0 [+,5,6,2,4,3]=>1 [-,5,6,2,4,3]=>1 [+,5,6,3,2,4]=>1 [-,5,6,3,2,4]=>1 [+,5,6,3,4,2]=>2 [-,5,6,3,4,2]=>2 [+,5,6,+,2,3]=>0 [-,5,6,+,2,3]=>0 [+,5,6,-,2,3]=>0 [-,5,6,-,2,3]=>0 [+,5,6,+,3,2]=>1 [-,5,6,+,3,2]=>1 [+,5,6,-,3,2]=>1 [-,5,6,-,3,2]=>1 [+,6,2,3,4,5]=>0 [-,6,2,3,4,5]=>0 [+,6,2,3,+,4]=>0 [-,6,2,3,+,4]=>0 [+,6,2,3,-,4]=>0 [-,6,2,3,-,4]=>0 [+,6,2,+,3,5]=>0 [-,6,2,+,3,5]=>0 [+,6,2,-,3,5]=>0 [-,6,2,-,3,5]=>0 [+,6,2,+,+,3]=>0 [-,6,2,+,+,3]=>0 [+,6,2,-,+,3]=>0 [+,6,2,+,-,3]=>0 [-,6,2,-,+,3]=>0 [-,6,2,+,-,3]=>0 [+,6,2,-,-,3]=>0 [-,6,2,-,-,3]=>0 [+,6,2,5,3,4]=>2 [-,6,2,5,3,4]=>2 [+,6,2,5,4,3]=>0 [-,6,2,5,4,3]=>0 [+,6,+,2,4,5]=>0 [-,6,+,2,4,5]=>0 [+,6,-,2,4,5]=>0 [-,6,-,2,4,5]=>0 [+,6,+,2,+,4]=>0 [-,6,+,2,+,4]=>0 [+,6,-,2,+,4]=>0 [+,6,+,2,-,4]=>0 [-,6,-,2,+,4]=>0 [-,6,+,2,-,4]=>0 [+,6,-,2,-,4]=>0 [-,6,-,2,-,4]=>0 [+,6,+,+,2,5]=>0 [-,6,+,+,2,5]=>0 [+,6,-,+,2,5]=>0 [+,6,+,-,2,5]=>0 [-,6,-,+,2,5]=>0 [-,6,+,-,2,5]=>0 [+,6,-,-,2,5]=>0 [-,6,-,-,2,5]=>0 [+,6,+,+,+,2]=>0 [-,6,+,+,+,2]=>0 [+,6,-,+,+,2]=>0 [+,6,+,-,+,2]=>0 [+,6,+,+,-,2]=>0 [-,6,-,+,+,2]=>0 [-,6,+,-,+,2]=>0 [-,6,+,+,-,2]=>0 [+,6,-,-,+,2]=>0 [+,6,-,+,-,2]=>0 [+,6,+,-,-,2]=>0 [-,6,-,-,+,2]=>0 [-,6,-,+,-,2]=>0 [-,6,+,-,-,2]=>0 [+,6,-,-,-,2]=>0 [-,6,-,-,-,2]=>0 [+,6,+,5,2,4]=>1 [-,6,+,5,2,4]=>1 [+,6,-,5,2,4]=>1 [-,6,-,5,2,4]=>1 [+,6,+,5,4,2]=>0 [-,6,+,5,4,2]=>0 [+,6,-,5,4,2]=>0 [-,6,-,5,4,2]=>0 [+,6,4,2,3,5]=>2 [-,6,4,2,3,5]=>2 [+,6,4,2,+,3]=>1 [-,6,4,2,+,3]=>1 [+,6,4,2,-,3]=>1 [-,6,4,2,-,3]=>1 [+,6,4,3,2,5]=>0 [-,6,4,3,2,5]=>0 [+,6,4,3,+,2]=>0 [-,6,4,3,+,2]=>0 [+,6,4,3,-,2]=>0 [-,6,4,3,-,2]=>0 [+,6,4,5,2,3]=>2 [-,6,4,5,2,3]=>2 [+,6,4,5,3,2]=>0 [-,6,4,5,3,2]=>0 [+,6,5,2,3,4]=>1 [-,6,5,2,3,4]=>1 [+,6,5,2,4,3]=>2 [-,6,5,2,4,3]=>2 [+,6,5,3,2,4]=>2 [-,6,5,3,2,4]=>2 [+,6,5,3,4,2]=>0 [-,6,5,3,4,2]=>0 [+,6,5,+,2,3]=>1 [-,6,5,+,2,3]=>1 [+,6,5,-,2,3]=>1 [-,6,5,-,2,3]=>1 [+,6,5,+,3,2]=>0 [-,6,5,+,3,2]=>0 [+,6,5,-,3,2]=>0 [-,6,5,-,3,2]=>0 [2,1,+,+,+,+]=>0 [2,1,-,+,+,+]=>0 [2,1,+,-,+,+]=>0 [2,1,+,+,-,+]=>0 [2,1,+,+,+,-]=>0 [2,1,-,-,+,+]=>0 [2,1,-,+,-,+]=>0 [2,1,-,+,+,-]=>0 [2,1,+,-,-,+]=>0 [2,1,+,-,+,-]=>0 [2,1,+,+,-,-]=>0 [2,1,-,-,-,+]=>0 [2,1,-,-,+,-]=>0 [2,1,-,+,-,-]=>0 [2,1,+,-,-,-]=>0 [2,1,-,-,-,-]=>0 [2,1,+,+,6,5]=>0 [2,1,-,+,6,5]=>0 [2,1,+,-,6,5]=>0 [2,1,-,-,6,5]=>0 [2,1,+,5,4,+]=>0 [2,1,-,5,4,+]=>0 [2,1,+,5,4,-]=>0 [2,1,-,5,4,-]=>0 [2,1,+,5,6,4]=>0 [2,1,-,5,6,4]=>0 [2,1,+,6,4,5]=>0 [2,1,-,6,4,5]=>0 [2,1,+,6,+,4]=>0 [2,1,-,6,+,4]=>0 [2,1,+,6,-,4]=>0 [2,1,-,6,-,4]=>0 [2,1,4,3,+,+]=>0 [2,1,4,3,-,+]=>0 [2,1,4,3,+,-]=>0 [2,1,4,3,-,-]=>0 [2,1,4,3,6,5]=>0 [2,1,4,5,3,+]=>0 [2,1,4,5,3,-]=>0 [2,1,4,5,6,3]=>0 [2,1,4,6,3,5]=>1 [2,1,4,6,+,3]=>0 [2,1,4,6,-,3]=>0 [2,1,5,3,4,+]=>0 [2,1,5,3,4,-]=>0 [2,1,5,3,6,4]=>1 [2,1,5,+,3,+]=>0 [2,1,5,-,3,+]=>0 [2,1,5,+,3,-]=>0 [2,1,5,-,3,-]=>0 [2,1,5,+,6,3]=>0 [2,1,5,-,6,3]=>0 [2,1,5,6,3,4]=>0 [2,1,5,6,4,3]=>1 [2,1,6,3,4,5]=>0 [2,1,6,3,+,4]=>0 [2,1,6,3,-,4]=>0 [2,1,6,+,3,5]=>0 [2,1,6,-,3,5]=>0 [2,1,6,+,+,3]=>0 [2,1,6,-,+,3]=>0 [2,1,6,+,-,3]=>0 [2,1,6,-,-,3]=>0 [2,1,6,5,3,4]=>1 [2,1,6,5,4,3]=>0 [2,3,1,+,+,+]=>0 [2,3,1,-,+,+]=>0 [2,3,1,+,-,+]=>0 [2,3,1,+,+,-]=>0 [2,3,1,-,-,+]=>0 [2,3,1,-,+,-]=>0 [2,3,1,+,-,-]=>0 [2,3,1,-,-,-]=>0 [2,3,1,+,6,5]=>0 [2,3,1,-,6,5]=>0 [2,3,1,5,4,+]=>0 [2,3,1,5,4,-]=>0 [2,3,1,5,6,4]=>0 [2,3,1,6,4,5]=>0 [2,3,1,6,+,4]=>0 [2,3,1,6,-,4]=>0 [2,3,4,1,+,+]=>0 [2,3,4,1,-,+]=>0 [2,3,4,1,+,-]=>0 [2,3,4,1,-,-]=>0 [2,3,4,1,6,5]=>0 [2,3,4,5,1,+]=>0 [2,3,4,5,1,-]=>0 [2,3,4,5,6,1]=>0 [2,3,4,6,1,5]=>2 [2,3,4,6,+,1]=>0 [2,3,4,6,-,1]=>0 [2,3,5,1,4,+]=>2 [2,3,5,1,4,-]=>2 [2,3,5,1,6,4]=>3 [2,3,5,+,1,+]=>0 [2,3,5,-,1,+]=>0 [2,3,5,+,1,-]=>0 [2,3,5,-,1,-]=>0 [2,3,5,+,6,1]=>0 [2,3,5,-,6,1]=>0 [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,+,4]=>2 [2,3,6,1,-,4]=>2 [2,3,6,+,1,5]=>2 [2,3,6,-,1,5]=>2 [2,3,6,+,+,1]=>0 [2,3,6,-,+,1]=>0 [2,3,6,+,-,1]=>0 [2,3,6,-,-,1]=>0 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>0 [2,4,1,3,+,+]=>1 [2,4,1,3,-,+]=>1 [2,4,1,3,+,-]=>1 [2,4,1,3,-,-]=>1 [2,4,1,3,6,5]=>1 [2,4,1,5,3,+]=>2 [2,4,1,5,3,-]=>2 [2,4,1,5,6,3]=>3 [2,4,1,6,3,5]=>3 [2,4,1,6,+,3]=>2 [2,4,1,6,-,3]=>2 [2,4,+,1,+,+]=>0 [2,4,-,1,+,+]=>0 [2,4,+,1,-,+]=>0 [2,4,+,1,+,-]=>0 [2,4,-,1,-,+]=>0 [2,4,-,1,+,-]=>0 [2,4,+,1,-,-]=>0 [2,4,-,1,-,-]=>0 [2,4,+,1,6,5]=>0
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Description
The number of crossed alignments in a decorated permutation.
Let $w$ be a decorated permutation.
An alignment $(i \mapsto w(i), j \mapsto w(j))$ is crossed if there exists a third arc $(h \mapsto w(h))$ which forms a crossing with both arcs in the alignment.
References
[1] Billey, S. C., Weaver, J. E. Criteria for smoothness of Positroid varieties via pattern avoidance, Johnson graphs, and spirographs arXiv:2207.06508
Code
def cyclic_interval(a, b, n):
    if a <= b:
        return list(range(a, b+1))
    return list(range(a, n+1)) + list(range(1, b+1))

def alignments(x):
    """
    sage: x = DecoratedPermutation([8,9,5,-4,7,6,1,3,2])
    sage: (3, 5, 6, 6) in alignments(x)
    True    
    sage: len(alignments(x))
    13

    sage: x = DecoratedPermutation([8,9,5,4,7,-6,1,3,2])
    sage: (3, 5, 6, 6) in alignments(x)
    False
    """
    pi = x.to_signed_permutation().permutation()
    n = len(pi)
    al = []
    for i, e in enumerate(pi, 1):
        for j, f in enumerate(pi, 1):
            if i == j:
                continue
            a, b = sorted([i, e])
            c, d = sorted([j, f])
            if a <= c <= b <= d or c <= a <= d <= b:
                continue
            if (e not in cyclic_interval(i, f-1, n)
                or f not in cyclic_interval(e+1, j, n)):
                continue
            if j == f and x[j-1] < 0:
                continue
            if i == e and x[i-1] > 0:
                continue
            al.append((i, e, j, f))

    return al

def statistic(x):
    A = alignments(x)
    pi = x.to_signed_permutation().permutation()    
    n = len(pi)
    cal = []
    for i, e, j, f in A:
        a, b = sorted([i, e])
        c, d = sorted([j, f])            
        for k, g in enumerate(pi, 1):
            r, s = sorted([k, g])
            if ((a <= r <= b <= s or r <= a <= s <= b) and
                (c <= r <= d <= s or r <= c <= s <= d)):
                cal.append((i, e, j, f, r, k))
                break
    return len(cal)

Created
Jul 22, 2022 at 12:07 by Martin Rubey
Updated
Jul 22, 2022 at 12:07 by Martin Rubey