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Identifier
Values
=>
Cc0020;cc-rep
([],1)=>0 ([],2)=>0 ([(0,1)],2)=>1 ([],3)=>0 ([(1,2)],3)=>0 ([(0,2),(1,2)],3)=>0 ([(0,1),(0,2),(1,2)],3)=>0 ([],4)=>0 ([(2,3)],4)=>0 ([(1,3),(2,3)],4)=>0 ([(0,3),(1,3),(2,3)],4)=>0 ([(0,3),(1,2)],4)=>1 ([(0,3),(1,2),(2,3)],4)=>1 ([(1,2),(1,3),(2,3)],4)=>0 ([(0,3),(1,2),(1,3),(2,3)],4)=>1 ([(0,2),(0,3),(1,2),(1,3)],4)=>2 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 ([],5)=>0 ([(3,4)],5)=>0 ([(2,4),(3,4)],5)=>0 ([(1,4),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,4),(3,4)],5)=>0 ([(1,4),(2,3)],5)=>0 ([(1,4),(2,3),(3,4)],5)=>0 ([(0,1),(2,4),(3,4)],5)=>0 ([(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,3),(3,4)],5)=>0 ([(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(2,3),(2,4)],5)=>0 ([(0,1),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>0 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([],6)=>0 ([(4,5)],6)=>0 ([(3,5),(4,5)],6)=>0 ([(2,5),(3,5),(4,5)],6)=>0 ([(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(2,5),(3,4)],6)=>0 ([(2,5),(3,4),(4,5)],6)=>0 ([(1,2),(3,5),(4,5)],6)=>0 ([(3,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,5),(3,4),(4,5)],6)=>0 ([(0,1),(2,5),(3,5),(4,5)],6)=>0 ([(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>0 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,5),(2,4),(3,4)],6)=>0 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>0 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,4),(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 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(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),(4,5)],6)=>0 ([(0,5),(1,4),(2,3)],6)=>1 ([(1,5),(2,4),(3,4),(3,5)],6)=>0 ([(0,1),(2,5),(3,4),(4,5)],6)=>1 ([(1,2),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>1 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>0 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>1 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>0 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>2 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>1 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>2 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>2 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>2 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>2 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>3 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>2 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>6 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>6 ([(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)=>6 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>0 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>2 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>1 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>3 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>3 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>5 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>4 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(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)=>7 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>6 ([(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)=>9 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(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)=>8 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>8 ([(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)=>10 ([(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)=>12 ([(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)=>15
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Description
The number of perfect matchings of a graph.
A matching of a graph $G$ is a subset $F \subset E(G)$ such that no two edges in $F$ share a vertex in common. A perfect matching $F'$ is then a matching such that every vertex in $V(G)$ is incident with exactly one edge in $F'$.
Code
def statistic(g):
    return abs(g.matching_polynomial()(0))

Created
Jul 28, 2015 at 18:52 by Martin Rubey
Updated
Dec 17, 2015 at 22:58 by Matthew Donahue