2004/06/17 by David G. Wagner, Wagner, David G.
Mathematics · #05A15 #05A20 #05B35 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Mathematical Inequalities and Applications #Point processes and geometric inequalities #math.CO #msc:05A15 #msc:05A20 #msc:05B35
paper · pdf · doi:10.48550/arxiv.math/0406339
18 pages, one figure, two tables. Minor typos and references fixed
openalex publication_date 2004/06/17 · arxiv created 2004/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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.