Matroids and their Dressians
Madeline Brandt, David E Speyer

TL;DR
This paper explores the structure of Dressians of matroids through initial matroids, introduces an efficient algorithm for their computation, and provides counterexamples to certain assumptions about matroid subdivisions.
Contribution
It presents a new algorithm for computing Dressians of matroids and applies it to various cases, advancing understanding of matroid subdivisions.
Findings
Algorithm for Dressian computation implemented and tested
Counterexamples to some conjectures about matroid subdivisions
Application to a range of interesting matroids
Abstract
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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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Commutative Algebra and Its Applications
