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Matroids and their Dressians

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arxiv 1902.05592 v2 pith:B62LPXDF submitted 2019-02-14 math.CO

Madeline Brandt , David E Speyer This is my paper · ORCID
classification math.CO
keywords matroidsdressiansmatroidsubdivisionsalgorithmappliedcellscomputing
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We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its implementation is applied to a range of interesting matroids. We give counterexamples to a few plausible statements about matroid subdivisions.

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  1. Perfect matroids over hyperfields

    math.CO 2019-08 conditional novelty 7.0 of 10

    Stringent skew hyperfields are perfect: over them every vector of a matroid is orthogonal to every covector, and weak matroids coincide with strong matroids.

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