  We 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.
