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Identifier
Values
=>
Cc0014;cc-rep
([],1)=>0 ([],2)=>0 ([(0,1)],2)=>1 ([],3)=>0 ([(1,2)],3)=>1 ([(0,1),(0,2)],3)=>0 ([(0,2),(2,1)],3)=>2 ([(0,2),(1,2)],3)=>0 ([],4)=>0 ([(2,3)],4)=>1 ([(1,2),(1,3)],4)=>0 ([(0,1),(0,2),(0,3)],4)=>0 ([(0,2),(0,3),(3,1)],4)=>1 ([(0,1),(0,2),(1,3),(2,3)],4)=>0 ([(1,2),(2,3)],4)=>2 ([(0,3),(3,1),(3,2)],4)=>1 ([(1,3),(2,3)],4)=>0 ([(0,3),(1,3),(3,2)],4)=>1 ([(0,3),(1,3),(2,3)],4)=>0 ([(0,3),(1,2)],4)=>2 ([(0,3),(1,2),(1,3)],4)=>0 ([(0,2),(0,3),(1,2),(1,3)],4)=>0 ([(0,3),(2,1),(3,2)],4)=>3 ([(0,3),(1,2),(2,3)],4)=>1 ([],5)=>0 ([(3,4)],5)=>1 ([(2,3),(2,4)],5)=>0 ([(1,2),(1,3),(1,4)],5)=>0 ([(0,1),(0,2),(0,3),(0,4)],5)=>0 ([(0,2),(0,3),(0,4),(4,1)],5)=>1 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>0 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(4,2)],5)=>1 ([(0,3),(0,4),(4,1),(4,2)],5)=>0 ([(1,2),(1,3),(2,4),(3,4)],5)=>0 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>1 ([(0,3),(0,4),(3,2),(4,1)],5)=>2 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>0 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(2,3),(3,4)],5)=>2 ([(1,4),(4,2),(4,3)],5)=>1 ([(0,4),(4,1),(4,2),(4,3)],5)=>1 ([(2,4),(3,4)],5)=>0 ([(1,4),(2,4),(4,3)],5)=>1 ([(0,4),(1,4),(4,2),(4,3)],5)=>0 ([(1,4),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,4),(4,3)],5)=>1 ([(0,4),(1,4),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,3)],5)=>1 ([(0,4),(1,3),(2,3),(2,4)],5)=>0 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,4),(1,4),(2,3),(4,2)],5)=>2 ([(0,4),(1,3),(2,3),(3,4)],5)=>0 ([(0,4),(1,4),(2,3),(2,4)],5)=>0 ([(0,4),(1,4),(2,3),(3,4)],5)=>1 ([(1,4),(2,3)],5)=>2 ([(1,4),(2,3),(2,4)],5)=>0 ([(0,4),(1,2),(1,4),(2,3)],5)=>1 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>1 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>2 ([(0,4),(1,2),(1,4),(4,3)],5)=>1 ([(0,4),(1,2),(1,3)],5)=>1 ([(0,4),(1,2),(1,3),(1,4)],5)=>0 ([(0,2),(0,4),(3,1),(4,3)],5)=>2 ([(0,4),(1,2),(1,3),(3,4)],5)=>0 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>1 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>0 ([(0,3),(1,2),(1,4),(3,4)],5)=>1 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>1 ([(1,4),(3,2),(4,3)],5)=>3 ([(0,3),(3,4),(4,1),(4,2)],5)=>2 ([(1,4),(2,3),(3,4)],5)=>1 ([(0,4),(1,2),(2,4),(4,3)],5)=>2 ([(0,3),(1,4),(4,2)],5)=>3 ([(0,4),(3,2),(4,1),(4,3)],5)=>2 ([(0,4),(1,2),(2,3),(2,4)],5)=>1 ([(0,4),(2,3),(3,1),(4,2)],5)=>4 ([(0,3),(1,2),(2,4),(3,4)],5)=>2 ([(0,4),(1,2),(2,3),(3,4)],5)=>2 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>1 ([],6)=>0 ([(4,5)],6)=>1 ([(3,4),(3,5)],6)=>0 ([(2,3),(2,4),(2,5)],6)=>0 ([(1,2),(1,3),(1,4),(1,5)],6)=>0 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>0 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>1 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(1,3),(1,4),(1,5),(5,2)],6)=>1 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>0 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>0 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>1 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)=>1 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)=>0 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)=>0 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>0 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)=>1 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)=>2 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)=>0 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(2,3),(2,4),(4,5)],6)=>1 ([(1,4),(1,5),(5,2),(5,3)],6)=>0 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>0 ([(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>1 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>0 ([(1,4),(1,5),(4,3),(5,2)],6)=>2 ([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>0 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>1 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>2 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)=>1 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)=>1 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)=>0 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>0 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)=>0 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(3,4),(4,5)],6)=>2 ([(2,3),(3,4),(3,5)],6)=>1 ([(1,5),(5,2),(5,3),(5,4)],6)=>1 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>1 ([(2,3),(3,5),(5,4)],6)=>3 ([(1,4),(4,5),(5,2),(5,3)],6)=>2 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>2 ([(3,5),(4,5)],6)=>0 ([(2,5),(3,5),(5,4)],6)=>1 ([(1,5),(2,5),(5,3),(5,4)],6)=>0 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>0 ([(2,5),(3,5),(4,5)],6)=>0 ([(1,5),(2,5),(3,5),(5,4)],6)=>1 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>0 ([(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>1 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,4)],6)=>1 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>2 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>0 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>1 ([(1,5),(2,5),(3,4)],6)=>1 ([(1,5),(2,4),(3,4),(3,5)],6)=>0 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)=>1 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)=>1 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>2 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>1 ([(1,5),(2,5),(3,4),(5,3)],6)=>2 ([(1,5),(2,4),(3,4),(4,5)],6)=>0 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>1 ([(0,5),(1,5),(2,3),(5,4)],6)=>2 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>1 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6)=>0 ([(1,5),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6)=>1 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6)=>1 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>0 ([(0,5),(1,5),(2,3),(2,4)],6)=>0 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>1 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6)=>0 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6)=>1 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)=>0 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>2 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>1 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,5),(3,4),(4,5)],6)=>1 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>2 ([(0,5),(1,5),(2,3),(3,4)],6)=>2 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>3 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6)=>1 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>1 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6)=>1 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>1 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>1 ([(0,5),(1,5),(2,4),(3,4)],6)=>0 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6)=>0 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>1 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>0 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>0 ([(2,5),(3,4)],6)=>2 ([(2,5),(3,4),(3,5)],6)=>0 ([(1,5),(2,3),(2,5),(3,4)],6)=>1 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6)=>0 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>0 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>1 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)=>2 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>0 ([(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)=>0 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>3 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>3 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>1 ([(1,5),(2,3),(2,5),(5,4)],6)=>1 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6)=>0 ([(1,5),(2,3),(2,4)],6)=>1 ([(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6)=>1 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>0 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6)=>1 ([(0,5),(1,2),(1,3),(1,4)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>0 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>2 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6)=>0 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>0 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6)=>1 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6)=>1 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>1 ([(1,3),(1,5),(4,2),(5,4)],6)=>2 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)=>1 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>3 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>1 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>0 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)=>1 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>0 ([(1,5),(2,3),(2,4),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6)=>1 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>1 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>2 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>1 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6)=>1 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)=>0 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)=>0 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>0 ([(0,4),(1,3),(1,5),(5,2)],6)=>2 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>1 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6)=>0 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6)=>1 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>2 ([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>1 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>0 ([(1,4),(1,5),(2,3),(2,5)],6)=>0 ([(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>1 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)=>1 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>1 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6)=>1 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6)=>1 ([(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)=>1 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>1 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>1 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)=>1 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)=>0 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>0 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>0 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)=>0 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)=>0 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>1 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)=>0 ([(1,4),(2,3),(2,5),(4,5)],6)=>1 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)=>2 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>1 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>2 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>2 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>2 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>1 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,5),(1,3),(1,4),(5,2)],6)=>2 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>3 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>1 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)=>1 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>1 ([(2,5),(3,4),(4,5)],6)=>1 ([(1,5),(2,3),(3,5),(5,4)],6)=>2 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>1 ([(1,3),(2,4),(4,5)],6)=>3 ([(1,5),(4,3),(5,2),(5,4)],6)=>2 ([(1,5),(2,3),(3,4),(3,5)],6)=>1 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>2 ([(0,4),(1,5),(5,2),(5,3)],6)=>2 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>2 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6)=>1 ([(1,5),(3,4),(4,2),(5,3)],6)=>4 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>3 ([(1,4),(2,3),(3,5),(4,5)],6)=>2 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>3 ([(0,5),(1,4),(4,2),(5,3)],6)=>4 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>3 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)=>2 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>1 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>2 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>3 ([(0,5),(1,4),(2,3)],6)=>3 ([(0,5),(1,3),(2,4),(2,5)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6)=>0 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)=>2 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>0 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>2 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6)=>0 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)=>0 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>0 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>1 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>2 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>2 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>1 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>1 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6)=>1 ([(0,5),(1,3),(4,2),(5,4)],6)=>4 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6)=>3 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6)=>2 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)=>1 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>3 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>2 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5 ([(0,5),(1,3),(2,4),(4,5)],6)=>2 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6)=>1 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>3 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>1 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>3 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>2 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>3 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>2 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>2 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>0 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>1 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>0 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>0 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>0 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>1 ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)=>2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>0 ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>0 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>0 ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>0 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>1 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>0 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>0 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>1 ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>1 ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>3 ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>1 ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>2 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)=>1 ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>0 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)=>1 ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)=>2 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)=>0 ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)=>1 ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>2 ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>1 ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>3 ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>1 ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>3 ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>3 ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>1 ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>1 ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>1 ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>2 ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>3 ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>1 ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>3 ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>1 ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>1 ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>3 ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>0 ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>1 ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>3 ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6 ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>2 ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>3 ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>3 ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>1 ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>3 ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>3 ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>3
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Description
The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset.
Code
gap('LoadPackage("QPA");')
    
def incidence_algebra_gap(P):
    P = P.relabel()
    return gap("PosetAlgebra(GF(3), Poset(%s, %s))" % (list(P), P.cover_relations()))
    
def statistic(P):
    A = incidence_algebra_gap(P)
    simples = A.SimpleModules()
    projective = A.IndecProjectiveModules().DirectSumOfQPAModules()
    return sum(1 for M in simples if M.ExtOverAlgebra(projective)[2].Size().sage() == 1)
Created
Oct 03, 2020 at 21:07 by Rene Marczinzik
Updated
Nov 13, 2022 at 12:11 by Martin Rubey