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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>1 [1,0,1,0]=>1 [1,1,0,0]=>1 [1,0,1,0,1,0]=>1 [1,0,1,1,0,0]=>1 [1,1,0,0,1,0]=>1 [1,1,0,1,0,0]=>1 [1,1,1,0,0,0]=>1 [1,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,0]=>1 [1,1,0,1,0,1,0,0]=>1 [1,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,1,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,0]=>1 [1,0,1,1,1,0,1,0,0,0]=>1 [1,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,0,0]=>1 [1,1,0,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,1,0,0]=>1 [1,1,0,1,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,1,0,0,0]=>1 [1,1,0,1,1,1,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,0,1,0]=>1 [1,1,1,0,0,1,0,1,0,0]=>1 [1,1,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,0]=>1 [1,1,1,0,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,1,0,0,0]=>1 [1,1,1,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0]=>1 [1,1,1,1,0,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,0,0]=>1 [1,1,1,1,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,1,0,0,0]=>2 [1,0,1,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,0,0,1,0,1,0]=>1 [1,0,1,1,1,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,1,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,1,1,1,0,0,1,0,0,0]=>1 [1,0,1,1,1,1,0,1,0,0,0,0]=>1 [1,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0]=>3 [1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,1,0,0]=>2 [1,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,0,1,1,1,0,1,0,0,0]=>1 [1,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,1,0,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,1,0,1,1,0,1,0,0,0]=>1 [1,1,0,1,0,1,1,1,0,0,0,0]=>1 [1,1,0,1,1,0,0,0,1,0,1,0]=>1 [1,1,0,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,1,1,0,0,1,0,0,1,0]=>1 [1,1,0,1,1,0,0,1,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,0,1,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,0]=>2 [1,1,0,1,1,0,1,0,1,0,0,0]=>1 [1,1,0,1,1,0,1,1,0,0,0,0]=>1 [1,1,0,1,1,1,0,0,0,0,1,0]=>1 [1,1,0,1,1,1,0,0,0,1,0,0]=>1 [1,1,0,1,1,1,0,0,1,0,0,0]=>1 [1,1,0,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,1,1,1,1,0,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0,1,0]=>2 [1,1,1,0,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,1,0,0]=>1 [1,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,1,1,0,0,1,0,0,1,0,1,0]=>1 [1,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,0]=>1 [1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,1,1,0,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,0,1,0]=>1 [1,1,1,0,1,0,0,0,1,1,0,0]=>1 [1,1,1,0,1,0,0,1,0,0,1,0]=>1 [1,1,1,0,1,0,0,1,0,1,0,0]=>1 [1,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,1,0,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,1,0,1,0,0,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,1,0,0,0,0,1,0]=>1 [1,1,1,0,1,1,0,0,0,1,0,0]=>1 [1,1,1,0,1,1,0,0,1,0,0,0]=>1 [1,1,1,0,1,1,0,1,0,0,0,0]=>1 [1,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0,1,0]=>1 [1,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,1,1,1,0,0,0,1,0,1,0,0]=>1 [1,1,1,1,0,0,0,1,1,0,0,0]=>1 [1,1,1,1,0,0,1,0,0,0,1,0]=>1 [1,1,1,1,0,0,1,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,1,0,0,0,0,1,0]=>1 [1,1,1,1,0,1,0,0,0,1,0,0]=>1 [1,1,1,1,0,1,0,0,1,0,0,0]=>1 [1,1,1,1,0,1,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,1,1,1,1,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>1 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>1 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>1 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>1 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>1 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>1 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>1 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
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Description
The number of simple modules of the linear Nakayama algebra corresponding to a Dyck path that are 3-syzygy modules.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
References
[1] http://www.ams.org/notices/200604/what-is.pdf
[2] Auslander, M., Bridger, M. Stable module theory DOI:10.1090/memo/0094
Code
# Pure combinatorial approach: for a linear Nakayama algebra with Kupisch series
# K = [c_0, c_1, ..., c_{n-1}], the indecomposable modules are M(i, l) at vertex i
# with length l (1 <= l <= c_i). The syzygy is:
#   Ω(M(i, l)) = M(i+l, c_i - l)  if l < c_i and i+l < n
#   Ω(M(i, l)) = 0                 if l = c_i (projective) or i+l >= n
#
# S_i = M(i, 1) is a 3-syzygy iff there exists M(j, l) with Ω³(M(j, l)) = M(i, 1).

def kupisch(D):
    DR = D.reverse()
    H = DR.heights()
    return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]

def statistic(D):
    K = kupisch(D)
    n = len(K)

    def omega(i, l):
        """Syzygy of M(i, l). Returns (i', l') or None if zero."""
        if l == K[i]:  # projective
            return None
        ni, nl = i + l, K[i] - l
        if ni >= n or nl <= 0:
            return None
        return (ni, nl)

    # Find all simples that are 3rd syzygies
    syzygy3_simples = set()

    # Projective simples are n-th syzygies for all n by convention
    for i in range(n):
        if K[i] == 1:  # S_i is projective iff K[i] = 1
            syzygy3_simples.add(i)

    # Non-projective simples: S_i is a 3rd syzygy iff ∃ X with Ω³(X) = S_i
    for j in range(n):
        for l in range(1, K[j] + 1):
            cur = (j, l)
            for _ in range(3):
                if cur is None:
                    break
                cur = omega(cur[0], cur[1])
            if cur is not None and cur[1] == 1:
                syzygy3_simples.add(cur[0])

    return ZZ(len(syzygy3_simples))
Created
Dec 30, 2017 at 15:25 by Rene Marczinzik
Updated
Mar 12, 2026 at 15:20 by Nupur Jain