9=2 graph G=(V,E) Boolean symmetric f:10,1dC f=[6,f,,jf where fi=x)for∑xi=i counting perfect matchings: at every vertex veV, =[0,1,0,0,0] the exact-one function holant ∑I[0,1,0,0,,0(oE()) o∈{0,1}Ev∈Vf : {0, 1} Boolean symmetric d ! C at every vertex v∈V, fv = [0, 1, 0, 0..., 0] counting perfect matchings: the exact-one function q=2 holant = X 2{0,1}E Y v2V [0, 1, 0, 0,..., 0] |E(v) f = [f0, f1 ,..., fd] where fi = f(x) for Σjxj = i graph G=(V,E) fv