For a finite (multi-) graph G=(V,E) and functions f,g: V ---> N and natural number j, consider the number of (f,g)-factors of G with exactly j edges. We investigate logarithmic concavity properties of such sequences (as j varies with f and g fixed) by considering the location of zeros of their generating functions. The case f==0 and g==1 is that of the Heilmann-Lieb theorem on matching polynomials. The more general case f
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