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We provide new evidence that spanning forests of graphs satisfy the samenegative correlation properties as spanning trees, derived from Lord Rayleigh'smonotonicity property for electrical networks. The main result of this paper isthat the Rayleigh difference for the spanning forest generating polynomial of aseries parallel graph can be expressed as a certain positive sum of monomialstimes squares of polynomials. We also show that every regular matroid isindependent-set-Rayleigh if and only if every basis-Rayleigh binary matroid isalso independent-set-Rayleigh.

Sums of squares and negative correlation for spanning forests of series parallel graphs