2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71588In 1981, Stanley applied the Aleksandrov-Fenchel inequalities to prove a logarithmic concavity theorem for regular matroids. Using ideas from electrical network theory we prove a generalization of this for the wider class of matroids with the ``half-plane property''. Then we explore a nest of inequalities for weighted basis-generating polynomials that are related to these ideas. As a first result from this investigation we find that every matroid of rank three or corank three satisfies a condition only slightly weaker than the conclusion of Stanley's theorem.18 pages, one figure, two tables. Minor typos and references fixedCombinatorics05B35; 05A20, 05A15text