2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110232We derive here the Friedland-Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in $r$-regular bipartite graphs. It is shown that some of these bounds are asymptotically sharp. We improve the known lower bound for the three dimensional monomer-dimer entropy. We present Ryser-like formulas for computations of matchings in bipartite and general graphs. Additional algorithmic applications are given.21 pages, 2 figuresCombinatoricsMathematical Physics05A15, 05A16, 05C70, 05C80, 82B20text