Identifier
Values
=>
[+,+]=>[1,2]=>0 [-,+]=>[2,1]=>1 [+,-]=>[1,2]=>0 [-,-]=>[1,2]=>0 [2,1]=>[1,2]=>0 [+,+,+]=>[1,2,3]=>0 [-,+,+]=>[2,3,1]=>1 [+,-,+]=>[1,3,2]=>1 [+,+,-]=>[1,2,3]=>0 [-,-,+]=>[3,1,2]=>1 [-,+,-]=>[2,1,3]=>1 [+,-,-]=>[1,2,3]=>0 [-,-,-]=>[1,2,3]=>0 [+,3,2]=>[1,2,3]=>0 [-,3,2]=>[2,1,3]=>1 [2,1,+]=>[1,3,2]=>1 [2,1,-]=>[1,2,3]=>0 [2,3,1]=>[1,2,3]=>0 [3,1,2]=>[1,2,3]=>0 [3,+,1]=>[2,1,3]=>1 [3,-,1]=>[1,3,2]=>1 [+,+,+,+]=>[1,2,3,4]=>0 [-,+,+,+]=>[2,3,4,1]=>1 [+,-,+,+]=>[1,3,4,2]=>2 [+,+,-,+]=>[1,2,4,3]=>1 [+,+,+,-]=>[1,2,3,4]=>0 [-,-,+,+]=>[3,4,1,2]=>2 [-,+,-,+]=>[2,4,1,3]=>2 [-,+,+,-]=>[2,3,1,4]=>2 [+,-,-,+]=>[1,4,2,3]=>2 [+,-,+,-]=>[1,3,2,4]=>1 [+,+,-,-]=>[1,2,3,4]=>0 [-,-,-,+]=>[4,1,2,3]=>1 [-,-,+,-]=>[3,1,2,4]=>2 [-,+,-,-]=>[2,1,3,4]=>1 [+,-,-,-]=>[1,2,3,4]=>0 [-,-,-,-]=>[1,2,3,4]=>0 [+,+,4,3]=>[1,2,3,4]=>0 [-,+,4,3]=>[2,3,1,4]=>2 [+,-,4,3]=>[1,3,2,4]=>1 [-,-,4,3]=>[3,1,2,4]=>2 [+,3,2,+]=>[1,2,4,3]=>1 [-,3,2,+]=>[2,4,1,3]=>2 [+,3,2,-]=>[1,2,3,4]=>0 [-,3,2,-]=>[2,1,3,4]=>1 [+,3,4,2]=>[1,2,3,4]=>0 [-,3,4,2]=>[2,1,3,4]=>1 [+,4,2,3]=>[1,2,3,4]=>0 [-,4,2,3]=>[2,3,1,4]=>2 [+,4,+,2]=>[1,3,2,4]=>1 [-,4,+,2]=>[3,2,1,4]=>2 [+,4,-,2]=>[1,2,4,3]=>1 [-,4,-,2]=>[2,1,4,3]=>1 [2,1,+,+]=>[1,3,4,2]=>2 [2,1,-,+]=>[1,4,2,3]=>2 [2,1,+,-]=>[1,3,2,4]=>1 [2,1,-,-]=>[1,2,3,4]=>0 [2,1,4,3]=>[1,3,2,4]=>1 [2,3,1,+]=>[1,4,2,3]=>2 [2,3,1,-]=>[1,2,3,4]=>0 [2,3,4,1]=>[1,2,3,4]=>0 [2,4,1,3]=>[1,3,2,4]=>1 [2,4,+,1]=>[3,1,2,4]=>2 [2,4,-,1]=>[1,2,4,3]=>1 [3,1,2,+]=>[1,2,4,3]=>1 [3,1,2,-]=>[1,2,3,4]=>0 [3,1,4,2]=>[1,2,3,4]=>0 [3,+,1,+]=>[2,1,4,3]=>1 [3,-,1,+]=>[1,4,3,2]=>2 [3,+,1,-]=>[2,1,3,4]=>1 [3,-,1,-]=>[1,3,2,4]=>1 [3,+,4,1]=>[2,1,3,4]=>1 [3,-,4,1]=>[1,3,2,4]=>1 [3,4,1,2]=>[1,2,3,4]=>0 [3,4,2,1]=>[2,1,3,4]=>1 [4,1,2,3]=>[1,2,3,4]=>0 [4,1,+,2]=>[1,3,2,4]=>1 [4,1,-,2]=>[1,2,4,3]=>1 [4,+,1,3]=>[2,1,3,4]=>1 [4,-,1,3]=>[1,3,4,2]=>2 [4,+,+,1]=>[2,3,1,4]=>2 [4,-,+,1]=>[3,1,4,2]=>2 [4,+,-,1]=>[2,1,4,3]=>1 [4,-,-,1]=>[1,4,2,3]=>2 [4,3,1,2]=>[1,2,4,3]=>1 [4,3,2,1]=>[2,1,4,3]=>1 [+,+,+,+,+]=>[1,2,3,4,5]=>0 [-,+,+,+,+]=>[2,3,4,5,1]=>1 [+,-,+,+,+]=>[1,3,4,5,2]=>2 [+,+,-,+,+]=>[1,2,4,5,3]=>2 [+,+,+,-,+]=>[1,2,3,5,4]=>1 [+,+,+,+,-]=>[1,2,3,4,5]=>0 [-,-,+,+,+]=>[3,4,5,1,2]=>2 [-,+,-,+,+]=>[2,4,5,1,3]=>2 [-,+,+,-,+]=>[2,3,5,1,4]=>2 [-,+,+,+,-]=>[2,3,4,1,5]=>2 [+,-,-,+,+]=>[1,4,5,2,3]=>2 [+,-,+,-,+]=>[1,3,5,2,4]=>2 [+,-,+,+,-]=>[1,3,4,2,5]=>2 [+,+,-,-,+]=>[1,2,5,3,4]=>2 [+,+,-,+,-]=>[1,2,4,3,5]=>1 [+,+,+,-,-]=>[1,2,3,4,5]=>0 [-,-,-,+,+]=>[4,5,1,2,3]=>2 [-,-,+,-,+]=>[3,5,1,2,4]=>2 [-,-,+,+,-]=>[3,4,1,2,5]=>2 [-,+,-,-,+]=>[2,5,1,3,4]=>2 [-,+,-,+,-]=>[2,4,1,3,5]=>2 [-,+,+,-,-]=>[2,3,1,4,5]=>2 [+,-,-,-,+]=>[1,5,2,3,4]=>2 [+,-,-,+,-]=>[1,4,2,3,5]=>2 [+,-,+,-,-]=>[1,3,2,4,5]=>1 [+,+,-,-,-]=>[1,2,3,4,5]=>0 [-,-,-,-,+]=>[5,1,2,3,4]=>1 [-,-,-,+,-]=>[4,1,2,3,5]=>2 [-,-,+,-,-]=>[3,1,2,4,5]=>2 [-,+,-,-,-]=>[2,1,3,4,5]=>1 [+,-,-,-,-]=>[1,2,3,4,5]=>0 [-,-,-,-,-]=>[1,2,3,4,5]=>0 [+,+,+,5,4]=>[1,2,3,4,5]=>0 [-,+,+,5,4]=>[2,3,4,1,5]=>2 [+,-,+,5,4]=>[1,3,4,2,5]=>2 [+,+,-,5,4]=>[1,2,4,3,5]=>1 [-,-,+,5,4]=>[3,4,1,2,5]=>2 [-,+,-,5,4]=>[2,4,1,3,5]=>2 [+,-,-,5,4]=>[1,4,2,3,5]=>2 [-,-,-,5,4]=>[4,1,2,3,5]=>2 [+,+,4,3,+]=>[1,2,3,5,4]=>1 [-,+,4,3,+]=>[2,3,5,1,4]=>2 [+,-,4,3,+]=>[1,3,5,2,4]=>2 [+,+,4,3,-]=>[1,2,3,4,5]=>0 [-,-,4,3,+]=>[3,5,1,2,4]=>2 [-,+,4,3,-]=>[2,3,1,4,5]=>2 [+,-,4,3,-]=>[1,3,2,4,5]=>1 [-,-,4,3,-]=>[3,1,2,4,5]=>2 [+,+,4,5,3]=>[1,2,3,4,5]=>0 [-,+,4,5,3]=>[2,3,1,4,5]=>2 [+,-,4,5,3]=>[1,3,2,4,5]=>1 [-,-,4,5,3]=>[3,1,2,4,5]=>2 [+,+,5,3,4]=>[1,2,3,4,5]=>0 [-,+,5,3,4]=>[2,3,4,1,5]=>2 [+,-,5,3,4]=>[1,3,4,2,5]=>2 [-,-,5,3,4]=>[3,4,1,2,5]=>2 [+,+,5,+,3]=>[1,2,4,3,5]=>1 [-,+,5,+,3]=>[2,4,3,1,5]=>2 [+,-,5,+,3]=>[1,4,3,2,5]=>2 [+,+,5,-,3]=>[1,2,3,5,4]=>1 [-,-,5,+,3]=>[4,3,1,2,5]=>2 [-,+,5,-,3]=>[2,3,1,5,4]=>2 [+,-,5,-,3]=>[1,3,2,5,4]=>1 [-,-,5,-,3]=>[3,1,2,5,4]=>2 [+,3,2,+,+]=>[1,2,4,5,3]=>2 [-,3,2,+,+]=>[2,4,5,1,3]=>2 [+,3,2,-,+]=>[1,2,5,3,4]=>2 [+,3,2,+,-]=>[1,2,4,3,5]=>1 [-,3,2,-,+]=>[2,5,1,3,4]=>2 [-,3,2,+,-]=>[2,4,1,3,5]=>2 [+,3,2,-,-]=>[1,2,3,4,5]=>0 [-,3,2,-,-]=>[2,1,3,4,5]=>1 [+,3,2,5,4]=>[1,2,4,3,5]=>1 [-,3,2,5,4]=>[2,4,1,3,5]=>2 [+,3,4,2,+]=>[1,2,5,3,4]=>2 [-,3,4,2,+]=>[2,5,1,3,4]=>2 [+,3,4,2,-]=>[1,2,3,4,5]=>0 [-,3,4,2,-]=>[2,1,3,4,5]=>1 [+,3,4,5,2]=>[1,2,3,4,5]=>0 [-,3,4,5,2]=>[2,1,3,4,5]=>1 [+,3,5,2,4]=>[1,2,4,3,5]=>1 [-,3,5,2,4]=>[2,4,1,3,5]=>2 [+,3,5,+,2]=>[1,4,2,3,5]=>2 [-,3,5,+,2]=>[4,2,1,3,5]=>2 [+,3,5,-,2]=>[1,2,3,5,4]=>1 [-,3,5,-,2]=>[2,1,3,5,4]=>1 [+,4,2,3,+]=>[1,2,3,5,4]=>1 [-,4,2,3,+]=>[2,3,5,1,4]=>2 [+,4,2,3,-]=>[1,2,3,4,5]=>0 [-,4,2,3,-]=>[2,3,1,4,5]=>2 [+,4,2,5,3]=>[1,2,3,4,5]=>0 [-,4,2,5,3]=>[2,3,1,4,5]=>2 [+,4,+,2,+]=>[1,3,2,5,4]=>1 [-,4,+,2,+]=>[3,2,5,1,4]=>2 [+,4,-,2,+]=>[1,2,5,4,3]=>2 [+,4,+,2,-]=>[1,3,2,4,5]=>1 [-,4,-,2,+]=>[2,5,1,4,3]=>2 [-,4,+,2,-]=>[3,2,1,4,5]=>2 [+,4,-,2,-]=>[1,2,4,3,5]=>1 [-,4,-,2,-]=>[2,1,4,3,5]=>1 [+,4,+,5,2]=>[1,3,2,4,5]=>1 [-,4,+,5,2]=>[3,2,1,4,5]=>2 [+,4,-,5,2]=>[1,2,4,3,5]=>1 [-,4,-,5,2]=>[2,1,4,3,5]=>1 [+,4,5,2,3]=>[1,2,3,4,5]=>0 [-,4,5,2,3]=>[2,3,1,4,5]=>2 [+,4,5,3,2]=>[1,3,2,4,5]=>1 [-,4,5,3,2]=>[3,2,1,4,5]=>2 [+,5,2,3,4]=>[1,2,3,4,5]=>0 [-,5,2,3,4]=>[2,3,4,1,5]=>2 [+,5,2,+,3]=>[1,2,4,3,5]=>1 [-,5,2,+,3]=>[2,4,3,1,5]=>2 [+,5,2,-,3]=>[1,2,3,5,4]=>1 [-,5,2,-,3]=>[2,3,1,5,4]=>2 [+,5,+,2,4]=>[1,3,2,4,5]=>1 [-,5,+,2,4]=>[3,2,4,1,5]=>2 [+,5,-,2,4]=>[1,2,4,5,3]=>2 [-,5,-,2,4]=>[2,4,1,5,3]=>2 [+,5,+,+,2]=>[1,3,4,2,5]=>2 [-,5,+,+,2]=>[3,4,2,1,5]=>2 [+,5,-,+,2]=>[1,4,2,5,3]=>2 [+,5,+,-,2]=>[1,3,2,5,4]=>1 [-,5,-,+,2]=>[4,2,1,5,3]=>2 [-,5,+,-,2]=>[3,2,1,5,4]=>2 [+,5,-,-,2]=>[1,2,5,3,4]=>2 [-,5,-,-,2]=>[2,1,5,3,4]=>2 [+,5,4,2,3]=>[1,2,3,5,4]=>1 [-,5,4,2,3]=>[2,3,1,5,4]=>2 [+,5,4,3,2]=>[1,3,2,5,4]=>1 [-,5,4,3,2]=>[3,2,1,5,4]=>2 [2,1,+,+,+]=>[1,3,4,5,2]=>2 [2,1,-,+,+]=>[1,4,5,2,3]=>2 [2,1,+,-,+]=>[1,3,5,2,4]=>2 [2,1,+,+,-]=>[1,3,4,2,5]=>2 [2,1,-,-,+]=>[1,5,2,3,4]=>2 [2,1,-,+,-]=>[1,4,2,3,5]=>2 [2,1,+,-,-]=>[1,3,2,4,5]=>1 [2,1,-,-,-]=>[1,2,3,4,5]=>0 [2,1,+,5,4]=>[1,3,4,2,5]=>2 [2,1,-,5,4]=>[1,4,2,3,5]=>2 [2,1,4,3,+]=>[1,3,5,2,4]=>2 [2,1,4,3,-]=>[1,3,2,4,5]=>1 [2,1,4,5,3]=>[1,3,2,4,5]=>1 [2,1,5,3,4]=>[1,3,4,2,5]=>2 [2,1,5,+,3]=>[1,4,3,2,5]=>2 [2,1,5,-,3]=>[1,3,2,5,4]=>1 [2,3,1,+,+]=>[1,4,5,2,3]=>2 [2,3,1,-,+]=>[1,5,2,3,4]=>2 [2,3,1,+,-]=>[1,4,2,3,5]=>2 [2,3,1,-,-]=>[1,2,3,4,5]=>0 [2,3,1,5,4]=>[1,4,2,3,5]=>2 [2,3,4,1,+]=>[1,5,2,3,4]=>2 [2,3,4,1,-]=>[1,2,3,4,5]=>0 [2,3,4,5,1]=>[1,2,3,4,5]=>0 [2,3,5,1,4]=>[1,4,2,3,5]=>2 [2,3,5,+,1]=>[4,1,2,3,5]=>2 [2,3,5,-,1]=>[1,2,3,5,4]=>1 [2,4,1,3,+]=>[1,3,5,2,4]=>2 [2,4,1,3,-]=>[1,3,2,4,5]=>1 [2,4,1,5,3]=>[1,3,2,4,5]=>1 [2,4,+,1,+]=>[3,1,5,2,4]=>2 [2,4,-,1,+]=>[1,5,2,4,3]=>2 [2,4,+,1,-]=>[3,1,2,4,5]=>2 [2,4,-,1,-]=>[1,2,4,3,5]=>1 [2,4,+,5,1]=>[3,1,2,4,5]=>2 [2,4,-,5,1]=>[1,2,4,3,5]=>1 [2,4,5,1,3]=>[1,3,2,4,5]=>1 [2,4,5,3,1]=>[3,1,2,4,5]=>2 [2,5,1,3,4]=>[1,3,4,2,5]=>2 [2,5,1,+,3]=>[1,4,3,2,5]=>2 [2,5,1,-,3]=>[1,3,2,5,4]=>1 [2,5,+,1,4]=>[3,1,4,2,5]=>2 [2,5,-,1,4]=>[1,4,2,5,3]=>2 [2,5,+,+,1]=>[3,4,1,2,5]=>2 [2,5,-,+,1]=>[4,1,2,5,3]=>2 [2,5,+,-,1]=>[3,1,2,5,4]=>2 [2,5,-,-,1]=>[1,2,5,3,4]=>2 [2,5,4,1,3]=>[1,3,2,5,4]=>1 [2,5,4,3,1]=>[3,1,2,5,4]=>2 [3,1,2,+,+]=>[1,2,4,5,3]=>2 [3,1,2,-,+]=>[1,2,5,3,4]=>2 [3,1,2,+,-]=>[1,2,4,3,5]=>1 [3,1,2,-,-]=>[1,2,3,4,5]=>0 [3,1,2,5,4]=>[1,2,4,3,5]=>1 [3,1,4,2,+]=>[1,2,5,3,4]=>2 [3,1,4,2,-]=>[1,2,3,4,5]=>0 [3,1,4,5,2]=>[1,2,3,4,5]=>0 [3,1,5,2,4]=>[1,2,4,3,5]=>1 [3,1,5,+,2]=>[1,4,2,3,5]=>2 [3,1,5,-,2]=>[1,2,3,5,4]=>1 [3,+,1,+,+]=>[2,1,4,5,3]=>2 [3,-,1,+,+]=>[1,4,5,3,2]=>2 [3,+,1,-,+]=>[2,1,5,3,4]=>2 [3,+,1,+,-]=>[2,1,4,3,5]=>1 [3,-,1,-,+]=>[1,5,3,2,4]=>2 [3,-,1,+,-]=>[1,4,3,2,5]=>2 [3,+,1,-,-]=>[2,1,3,4,5]=>1 [3,-,1,-,-]=>[1,3,2,4,5]=>1 [3,+,1,5,4]=>[2,1,4,3,5]=>1 [3,-,1,5,4]=>[1,4,3,2,5]=>2 [3,+,4,1,+]=>[2,1,5,3,4]=>2 [3,-,4,1,+]=>[1,5,3,2,4]=>2 [3,+,4,1,-]=>[2,1,3,4,5]=>1 [3,-,4,1,-]=>[1,3,2,4,5]=>1 [3,+,4,5,1]=>[2,1,3,4,5]=>1 [3,-,4,5,1]=>[1,3,2,4,5]=>1 [3,+,5,1,4]=>[2,1,4,3,5]=>1 [3,-,5,1,4]=>[1,4,3,2,5]=>2 [3,+,5,+,1]=>[2,4,1,3,5]=>2 [3,-,5,+,1]=>[4,1,3,2,5]=>2 [3,+,5,-,1]=>[2,1,3,5,4]=>1 [3,-,5,-,1]=>[1,3,2,5,4]=>1 [3,4,1,2,+]=>[1,2,5,3,4]=>2 [3,4,1,2,-]=>[1,2,3,4,5]=>0 [3,4,1,5,2]=>[1,2,3,4,5]=>0 [3,4,2,1,+]=>[2,1,5,3,4]=>2 [3,4,2,1,-]=>[2,1,3,4,5]=>1 [3,4,2,5,1]=>[2,1,3,4,5]=>1 [3,4,5,1,2]=>[1,2,3,4,5]=>0 [3,4,5,2,1]=>[2,1,3,4,5]=>1 [3,5,1,2,4]=>[1,2,4,3,5]=>1 [3,5,1,+,2]=>[1,4,2,3,5]=>2 [3,5,1,-,2]=>[1,2,3,5,4]=>1 [3,5,2,1,4]=>[2,1,4,3,5]=>1 [3,5,2,+,1]=>[2,4,1,3,5]=>2 [3,5,2,-,1]=>[2,1,3,5,4]=>1 [3,5,4,1,2]=>[1,2,3,5,4]=>1 [3,5,4,2,1]=>[2,1,3,5,4]=>1 [4,1,2,3,+]=>[1,2,3,5,4]=>1 [4,1,2,3,-]=>[1,2,3,4,5]=>0 [4,1,2,5,3]=>[1,2,3,4,5]=>0 [4,1,+,2,+]=>[1,3,2,5,4]=>1 [4,1,-,2,+]=>[1,2,5,4,3]=>2 [4,1,+,2,-]=>[1,3,2,4,5]=>1 [4,1,-,2,-]=>[1,2,4,3,5]=>1 [4,1,+,5,2]=>[1,3,2,4,5]=>1 [4,1,-,5,2]=>[1,2,4,3,5]=>1 [4,1,5,2,3]=>[1,2,3,4,5]=>0 [4,1,5,3,2]=>[1,3,2,4,5]=>1 [4,+,1,3,+]=>[2,1,3,5,4]=>1 [4,-,1,3,+]=>[1,3,5,4,2]=>2 [4,+,1,3,-]=>[2,1,3,4,5]=>1 [4,-,1,3,-]=>[1,3,4,2,5]=>2 [4,+,1,5,3]=>[2,1,3,4,5]=>1 [4,-,1,5,3]=>[1,3,4,2,5]=>2 [4,+,+,1,+]=>[2,3,1,5,4]=>2 [4,-,+,1,+]=>[3,1,5,4,2]=>2 [4,+,-,1,+]=>[2,1,5,4,3]=>2 [4,+,+,1,-]=>[2,3,1,4,5]=>2 [4,-,-,1,+]=>[1,5,4,2,3]=>2 [4,-,+,1,-]=>[3,1,4,2,5]=>2 [4,+,-,1,-]=>[2,1,4,3,5]=>1 [4,-,-,1,-]=>[1,4,2,3,5]=>2 [4,+,+,5,1]=>[2,3,1,4,5]=>2 [4,-,+,5,1]=>[3,1,4,2,5]=>2 [4,+,-,5,1]=>[2,1,4,3,5]=>1 [4,-,-,5,1]=>[1,4,2,3,5]=>2 [4,+,5,1,3]=>[2,1,3,4,5]=>1 [4,-,5,1,3]=>[1,3,4,2,5]=>2 [4,+,5,3,1]=>[2,3,1,4,5]=>2 [4,-,5,3,1]=>[3,1,4,2,5]=>2 [4,3,1,2,+]=>[1,2,5,4,3]=>2 [4,3,1,2,-]=>[1,2,4,3,5]=>1 [4,3,1,5,2]=>[1,2,4,3,5]=>1 [4,3,2,1,+]=>[2,1,5,4,3]=>2 [4,3,2,1,-]=>[2,1,4,3,5]=>1 [4,3,2,5,1]=>[2,1,4,3,5]=>1 [4,3,5,1,2]=>[1,2,4,3,5]=>1 [4,3,5,2,1]=>[2,1,4,3,5]=>1 [4,5,1,2,3]=>[1,2,3,4,5]=>0 [4,5,1,3,2]=>[1,3,2,4,5]=>1 [4,5,2,1,3]=>[2,1,3,4,5]=>1 [4,5,2,3,1]=>[2,3,1,4,5]=>2 [4,5,+,1,2]=>[3,1,2,4,5]=>2 [4,5,-,1,2]=>[1,2,4,5,3]=>2 [4,5,+,2,1]=>[3,2,1,4,5]=>2 [4,5,-,2,1]=>[2,1,4,5,3]=>2 [5,1,2,3,4]=>[1,2,3,4,5]=>0 [5,1,2,+,3]=>[1,2,4,3,5]=>1 [5,1,2,-,3]=>[1,2,3,5,4]=>1 [5,1,+,2,4]=>[1,3,2,4,5]=>1 [5,1,-,2,4]=>[1,2,4,5,3]=>2 [5,1,+,+,2]=>[1,3,4,2,5]=>2 [5,1,-,+,2]=>[1,4,2,5,3]=>2 [5,1,+,-,2]=>[1,3,2,5,4]=>1 [5,1,-,-,2]=>[1,2,5,3,4]=>2 [5,1,4,2,3]=>[1,2,3,5,4]=>1 [5,1,4,3,2]=>[1,3,2,5,4]=>1 [5,+,1,3,4]=>[2,1,3,4,5]=>1 [5,-,1,3,4]=>[1,3,4,5,2]=>2 [5,+,1,+,3]=>[2,1,4,3,5]=>1 [5,-,1,+,3]=>[1,4,3,5,2]=>2 [5,+,1,-,3]=>[2,1,3,5,4]=>1 [5,-,1,-,3]=>[1,3,5,2,4]=>2 [5,+,+,1,4]=>[2,3,1,4,5]=>2 [5,-,+,1,4]=>[3,1,4,5,2]=>2 [5,+,-,1,4]=>[2,1,4,5,3]=>2 [5,-,-,1,4]=>[1,4,5,2,3]=>2 [5,+,+,+,1]=>[2,3,4,1,5]=>2 [5,-,+,+,1]=>[3,4,1,5,2]=>2 [5,+,-,+,1]=>[2,4,1,5,3]=>2 [5,+,+,-,1]=>[2,3,1,5,4]=>2 [5,-,-,+,1]=>[4,1,5,2,3]=>2 [5,-,+,-,1]=>[3,1,5,2,4]=>2 [5,+,-,-,1]=>[2,1,5,3,4]=>2 [5,-,-,-,1]=>[1,5,2,3,4]=>2 [5,+,4,1,3]=>[2,1,3,5,4]=>1 [5,-,4,1,3]=>[1,3,5,2,4]=>2 [5,+,4,3,1]=>[2,3,1,5,4]=>2 [5,-,4,3,1]=>[3,1,5,2,4]=>2 [5,3,1,2,4]=>[1,2,4,5,3]=>2 [5,3,1,+,2]=>[1,4,2,5,3]=>2 [5,3,1,-,2]=>[1,2,5,3,4]=>2 [5,3,2,1,4]=>[2,1,4,5,3]=>2 [5,3,2,+,1]=>[2,4,1,5,3]=>2 [5,3,2,-,1]=>[2,1,5,3,4]=>2 [5,3,4,1,2]=>[1,2,5,3,4]=>2 [5,3,4,2,1]=>[2,1,5,3,4]=>2 [5,4,1,2,3]=>[1,2,3,5,4]=>1 [5,4,1,3,2]=>[1,3,2,5,4]=>1 [5,4,2,1,3]=>[2,1,3,5,4]=>1 [5,4,2,3,1]=>[2,3,1,5,4]=>2 [5,4,+,1,2]=>[3,1,2,5,4]=>2 [5,4,-,1,2]=>[1,2,5,4,3]=>2 [5,4,+,2,1]=>[3,2,1,5,4]=>2 [5,4,-,2,1]=>[2,1,5,4,3]=>2
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Description
The maximal modular displacement of a permutation.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
Map
lower permutation
Description
The lower bound in the Grassmann interval corresponding to the decorated permutation.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $u$.