Geodesic
Matroid inequalities from electrical network theory
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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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.
DOI : 10.37236/1893
Classification : 05B35, 05A20, 05A15
Mots-clés : Aleksandrov-Fenchel inequalities, polynomials, Stanley's theorem 
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     author = {David G. Wagner},
     title = {Matroid inequalities from electrical network theory},
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     doi = {10.37236/1893},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/1893/}
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David G. Wagner. Matroid inequalities from electrical network theory. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1893

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