Identifier
Values
=>
Cc0020;cc-rep
[+]=>[1]=>[1]=>([],1)=>1 [-]=>[1]=>[1]=>([],1)=>1 [-,+]=>[2,1]=>[2,1]=>([(0,1)],2)=>1 [-,+,+]=>[2,3,1]=>[3,1,2]=>([(0,2),(1,2)],3)=>1 [-,-,+]=>[3,1,2]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>2 [-,+,+,+]=>[2,3,4,1]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>2 [-,-,+,+]=>[3,4,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)=>1 [-,+,-,+]=>[2,4,1,3]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2 [-,-,-,+]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [-,3,2,+]=>[2,4,1,3]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2 [4,-,+,1]=>[3,1,4,2]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>1 [-,+,+,+,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3 [-,-,+,+,+]=>[3,4,5,1,2]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>1 [-,+,-,+,+]=>[2,4,5,1,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)=>1 [-,+,+,-,+]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 [-,-,-,+,+]=>[4,5,1,2,3]=>[5,3,1,4,2]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>1 [-,-,+,-,+]=>[3,5,1,2,4]=>[3,1,5,4,2]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>1 [-,+,-,-,+]=>[2,5,1,3,4]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,-,-,-,+]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [-,+,4,3,+]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 [-,-,4,3,+]=>[3,5,1,2,4]=>[3,1,5,4,2]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>1 [-,3,2,+,+]=>[2,4,5,1,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)=>1 [-,3,2,-,+]=>[2,5,1,3,4]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,3,4,2,+]=>[2,5,1,3,4]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,4,2,3,+]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 [-,4,+,2,+]=>[3,2,5,1,4]=>[2,5,4,1,3]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>1 [-,4,-,2,+]=>[2,5,1,4,3]=>[4,5,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>2 [-,5,-,2,4]=>[2,4,1,5,3]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 [-,5,-,+,2]=>[4,2,1,5,3]=>[2,5,3,1,4]=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>1 [2,4,+,1,+]=>[3,1,5,2,4]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 [2,5,-,+,1]=>[4,1,2,5,3]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 [4,-,+,1,+]=>[3,1,5,4,2]=>[4,5,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>1 [5,-,+,1,4]=>[3,1,4,5,2]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2 [5,-,+,+,1]=>[3,4,1,5,2]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)=>1 [5,+,-,+,1]=>[2,4,1,5,3]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 [5,-,-,+,1]=>[4,1,5,2,3]=>[4,2,1,5,3]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>1 [5,-,+,-,1]=>[3,1,5,2,4]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 [5,-,4,3,1]=>[3,1,5,2,4]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 [5,3,2,+,1]=>[2,4,1,5,3]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 [-,+,+,+,+,+]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4 [-,-,+,+,+,+]=>[3,4,5,6,1,2]=>[5,1,3,6,2,4]=>([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 [-,+,-,+,+,+]=>[2,4,5,6,1,3]=>[6,3,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,+,+,-,+,+]=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 [-,+,+,+,-,+]=>[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,-,+,+,+]=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1 [-,-,+,-,+,+]=>[3,5,6,1,2,4]=>[5,2,6,4,1,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 [-,-,+,+,-,+]=>[3,4,6,1,2,5]=>[6,5,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,+,-,-,+,+]=>[2,5,6,1,3,4]=>[6,4,1,2,5,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,+,-,+,-,+]=>[2,4,6,1,3,5]=>[4,1,2,6,5,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 [-,+,+,-,-,+]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,-,-,+,+]=>[5,6,1,2,3,4]=>[5,3,1,6,4,2]=>([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,-,-,+,-,+]=>[4,6,1,2,3,5]=>[6,5,3,1,4,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,-,+,-,-,+]=>[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,+,-,-,-,+]=>[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,-,-,-,+]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [-,+,+,5,4,+]=>[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,+,5,4,+]=>[3,4,6,1,2,5]=>[6,5,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,+,-,5,4,+]=>[2,4,6,1,3,5]=>[4,1,2,6,5,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 [-,-,-,5,4,+]=>[4,6,1,2,3,5]=>[6,5,3,1,4,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,+,4,3,+,+]=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 [-,-,4,3,+,+]=>[3,5,6,1,2,4]=>[5,2,6,4,1,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 [-,+,4,3,-,+]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,4,3,-,+]=>[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,+,4,5,3,+]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,4,5,3,+]=>[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,+,5,3,4,+]=>[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,5,3,4,+]=>[3,4,6,1,2,5]=>[6,5,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,+,5,+,3,+]=>[2,4,3,6,1,5]=>[3,6,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,-,5,+,3,+]=>[4,3,6,1,2,5]=>[4,1,6,5,2,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>3 [-,+,5,-,3,+]=>[2,3,6,1,5,4]=>[5,6,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [-,-,5,-,3,+]=>[3,6,1,2,5,4]=>[3,1,5,6,4,2]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1 [-,+,6,-,3,5]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,-,6,-,3,5]=>[3,5,1,2,6,4]=>[3,1,6,4,2,5]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,+,6,-,+,3]=>[2,5,3,1,6,4]=>[3,6,4,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 [-,-,6,-,+,3]=>[5,3,1,2,6,4]=>[6,4,2,3,1,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,3,2,+,+,+]=>[2,4,5,6,1,3]=>[6,3,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,3,2,-,+,+]=>[2,5,6,1,3,4]=>[6,4,1,2,5,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,3,2,+,-,+]=>[2,4,6,1,3,5]=>[4,1,2,6,5,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 [-,3,2,-,-,+]=>[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,3,2,5,4,+]=>[2,4,6,1,3,5]=>[4,1,2,6,5,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 [-,3,4,2,+,+]=>[2,5,6,1,3,4]=>[6,4,1,2,5,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,3,4,2,-,+]=>[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,3,4,5,2,+]=>[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,3,5,2,4,+]=>[2,4,6,1,3,5]=>[4,1,2,6,5,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 [-,3,5,+,2,+]=>[4,2,6,1,3,5]=>[2,4,1,6,5,3]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>1 [-,3,5,-,2,+]=>[2,6,1,3,5,4]=>[5,6,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,3,6,-,2,5]=>[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,3,6,-,+,2]=>[5,2,1,3,6,4]=>[2,6,4,3,1,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,4,2,3,+,+]=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 [-,4,2,3,-,+]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,4,2,5,3,+]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,4,+,2,+,+]=>[3,2,5,6,1,4]=>[2,5,1,3,6,4]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>1 [-,4,-,2,+,+]=>[2,5,6,1,4,3]=>[5,4,1,2,6,3]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,4,+,2,-,+]=>[3,2,6,1,4,5]=>[2,6,5,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,4,-,2,-,+]=>[2,6,1,4,3,5]=>[4,6,5,3,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [-,4,+,5,2,+]=>[3,2,6,1,4,5]=>[2,6,5,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,4,-,5,2,+]=>[2,6,1,4,3,5]=>[4,6,5,3,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [-,4,5,2,3,+]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,4,5,3,2,+]=>[3,2,6,1,4,5]=>[2,6,5,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,5,2,3,4,+]=>[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,5,2,+,3,+]=>[2,4,3,6,1,5]=>[3,6,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,5,2,-,3,+]=>[2,3,6,1,5,4]=>[5,6,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [-,5,+,2,4,+]=>[3,2,4,6,1,5]=>[2,6,5,1,3,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,5,-,2,4,+]=>[2,4,6,1,5,3]=>[4,1,2,5,6,3]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>2 [-,5,+,+,2,+]=>[3,4,2,6,1,5]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,5,-,+,2,+]=>[4,2,6,1,5,3]=>[2,4,1,5,6,3]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1 [-,5,+,-,2,+]=>[3,2,6,1,5,4]=>[2,5,6,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,5,-,-,2,+]=>[2,6,1,5,3,4]=>[6,4,5,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,5,4,2,3,+]=>[2,3,6,1,5,4]=>[5,6,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [-,5,4,3,2,+]=>[3,2,6,1,5,4]=>[2,5,6,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,6,2,-,3,5]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,6,2,-,+,3]=>[2,5,3,1,6,4]=>[3,6,4,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 [-,6,-,2,4,5]=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1 [-,6,-,2,+,4]=>[2,5,4,1,6,3]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [-,6,-,2,-,4]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,6,-,+,2,5]=>[4,2,5,1,6,3]=>[2,4,1,6,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1 [-,6,+,-,2,5]=>[3,2,5,1,6,4]=>[2,6,4,1,3,5]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,6,-,-,2,5]=>[2,5,1,6,3,4]=>[5,3,1,2,6,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1 [-,6,-,+,+,2]=>[4,5,2,1,6,3]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2 [-,6,+,-,+,2]=>[3,5,2,1,6,4]=>[6,4,1,3,2,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,6,-,-,+,2]=>[5,2,1,6,3,4]=>[2,5,3,1,6,4]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,6,-,+,-,2]=>[4,2,1,6,3,5]=>[2,6,5,3,1,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,6,-,5,2,4]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,6,-,5,4,2]=>[4,2,1,6,3,5]=>[2,6,5,3,1,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,6,4,2,3,5]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [-,6,4,2,+,3]=>[2,5,3,1,6,4]=>[3,6,4,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 [-,6,4,3,2,5]=>[3,2,5,1,6,4]=>[2,6,4,1,3,5]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [-,6,4,3,+,2]=>[3,5,2,1,6,4]=>[6,4,1,3,2,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [2,3,5,+,1,+]=>[4,1,6,2,3,5]=>[4,2,1,6,5,3]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>2 [2,3,6,-,+,1]=>[5,1,2,3,6,4]=>[6,4,3,2,1,5]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,4,+,1,+,+]=>[3,1,5,6,2,4]=>[5,2,1,3,6,4]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 [2,4,+,1,-,+]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,4,+,5,1,+]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,4,5,3,1,+]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,5,+,1,4,+]=>[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [2,5,+,+,1,+]=>[3,4,1,6,2,5]=>[3,1,6,5,2,4]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>1 [2,5,-,+,1,+]=>[4,1,6,2,5,3]=>[4,2,1,5,6,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 [2,5,+,-,1,+]=>[3,1,6,2,5,4]=>[5,6,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [2,5,4,3,1,+]=>[3,1,6,2,5,4]=>[5,6,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [2,6,-,+,1,5]=>[4,1,5,2,6,3]=>[4,2,1,6,3,5]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>1 [2,6,+,-,1,5]=>[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [2,6,-,+,+,1]=>[4,5,1,2,6,3]=>[6,3,1,4,2,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 [2,6,+,-,+,1]=>[3,5,1,2,6,4]=>[3,1,6,4,2,5]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1 [2,6,-,-,+,1]=>[5,1,2,6,3,4]=>[5,3,2,1,6,4]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [2,6,-,+,-,1]=>[4,1,2,6,3,5]=>[6,5,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [2,6,-,5,4,1]=>[4,1,2,6,3,5]=>[6,5,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [2,6,4,3,1,5]=>[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [2,6,4,3,+,1]=>[3,5,1,2,6,4]=>[3,1,6,4,2,5]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1 [3,+,5,+,1,+]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [3,-,5,+,1,+]=>[4,1,6,3,2,5]=>[6,5,2,1,4,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [3,+,6,-,+,1]=>[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [3,-,6,-,+,1]=>[5,1,3,2,6,4]=>[3,6,4,2,1,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [3,5,2,+,1,+]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [3,6,2,-,+,1]=>[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [3,6,4,2,+,1]=>[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [4,-,+,1,+,+]=>[3,1,5,6,4,2]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>2 [4,-,+,1,-,+]=>[3,1,6,4,2,5]=>[4,6,5,2,1,3]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [4,-,+,5,1,+]=>[3,1,6,4,2,5]=>[4,6,5,2,1,3]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [4,-,5,3,1,+]=>[3,1,6,4,2,5]=>[4,6,5,2,1,3]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [4,6,-,2,+,1]=>[2,5,1,4,6,3]=>[4,6,3,1,2,5]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [5,-,+,1,4,+]=>[3,1,4,6,5,2]=>[5,6,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2 [5,-,+,+,1,+]=>[3,4,1,6,5,2]=>[3,1,5,6,2,4]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>1 [5,+,-,+,1,+]=>[2,4,1,6,5,3]=>[5,6,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 [5,-,-,+,1,+]=>[4,1,6,5,2,3]=>[5,2,1,4,6,3]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1 [5,-,+,-,1,+]=>[3,1,6,5,2,4]=>[6,4,5,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [5,-,4,3,1,+]=>[3,1,6,5,2,4]=>[6,4,5,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [5,-,6,-,3,1]=>[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [5,3,2,+,1,+]=>[2,4,1,6,5,3]=>[5,6,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 [5,6,-,2,4,1]=>[2,4,1,5,6,3]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [5,6,-,+,1,2]=>[4,1,2,5,6,3]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [5,6,-,+,2,1]=>[4,2,1,5,6,3]=>[2,6,3,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 [6,-,+,1,4,5]=>[3,1,4,5,6,2]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3 [6,-,+,1,+,4]=>[3,1,5,4,6,2]=>[4,6,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 [6,-,+,1,-,4]=>[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,+,+,1,5]=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1 [6,+,-,+,1,5]=>[2,4,1,5,6,3]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,-,+,1,5]=>[4,1,5,6,2,3]=>[6,3,5,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,-,+,-,1,5]=>[3,1,5,6,2,4]=>[5,2,1,3,6,4]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 [6,-,+,+,+,1]=>[3,4,5,1,6,2]=>[6,2,4,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,+,-,+,+,1]=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1 [6,+,+,-,+,1]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,-,+,+,1]=>[4,5,1,6,2,3]=>[5,2,6,3,1,4]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,-,+,-,+,1]=>[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1 [6,-,+,+,-,1]=>[3,4,1,6,2,5]=>[3,1,6,5,2,4]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>1 [6,+,-,-,+,1]=>[2,5,1,6,3,4]=>[5,3,1,2,6,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1 [6,+,-,+,-,1]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,-,-,+,1]=>[5,1,6,2,3,4]=>[6,4,2,1,5,3]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,-,-,+,-,1]=>[4,1,6,2,3,5]=>[4,2,1,6,5,3]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>2 [6,-,+,-,-,1]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [6,-,+,5,1,4]=>[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,+,5,4,1]=>[3,4,1,6,2,5]=>[3,1,6,5,2,4]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>1 [6,+,-,5,4,1]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,-,5,4,1]=>[4,1,6,2,3,5]=>[4,2,1,6,5,3]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>2 [6,-,4,3,1,5]=>[3,1,5,6,2,4]=>[5,2,1,3,6,4]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 [6,+,4,3,+,1]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,4,3,+,1]=>[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1 [6,-,4,3,-,1]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [6,-,4,5,3,1]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [6,-,5,3,1,4]=>[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,5,3,4,1]=>[3,4,1,6,2,5]=>[3,1,6,5,2,4]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>1 [6,-,5,+,1,3]=>[4,1,3,6,2,5]=>[3,6,5,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,5,+,3,1]=>[4,3,1,6,2,5]=>[6,5,2,3,1,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,-,5,-,3,1]=>[3,1,6,2,5,4]=>[5,6,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 [6,3,2,+,1,5]=>[2,4,1,5,6,3]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,3,2,+,+,1]=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1 [6,3,2,-,+,1]=>[2,5,1,6,3,4]=>[5,3,1,2,6,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1 [6,3,2,+,-,1]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,3,2,5,4,1]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,3,4,2,+,1]=>[2,5,1,6,3,4]=>[5,3,1,2,6,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1 [6,3,5,2,4,1]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,3,5,+,1,2]=>[4,1,2,6,3,5]=>[6,5,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,3,5,+,2,1]=>[4,2,1,6,3,5]=>[2,6,5,3,1,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,4,2,3,+,1]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 [6,4,+,1,+,2]=>[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,4,+,2,+,1]=>[3,2,5,1,6,4]=>[2,6,4,1,3,5]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,4,-,2,+,1]=>[2,5,1,6,4,3]=>[6,3,1,2,5,4]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 [6,5,-,2,4,1]=>[2,4,1,6,5,3]=>[5,6,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 [6,5,-,+,1,2]=>[4,1,2,6,5,3]=>[5,6,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2 [6,5,-,+,2,1]=>[4,2,1,6,5,3]=>[2,5,6,3,1,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$
Its eigenvalues are $0,4,4,6$, so the statistic is $2$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
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 $u$.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.