2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73465For a finite undirected multigraph G=(V,E) and functions f,g:V-->\NN, let N_f^g(G,j) denote the number of (f,g)-factors of G with exactly j edges. The Heilmann-Lieb Theorem implies that \sum_j N_0^1(G,j) t^j is a polynomial with only real (negative) zeros, and hence that the sequence {N_0^1(G,j)} is strictly logarithmically concave. Separate generalizations of this theorem were obtained by Ruelle and by the author. We unify, simplify, and generalize these results by means of the Grace-Szegö-Walsh Coincidence Theorem.15 pages. minor corrections and a new resultCombinatorics05A20; 05C30, 26C10, 30C15text