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The polytope of all matroids in ranks 2 and 3
Narayan Collins, Victoria Schleis
We give explicit recursive constructions for the polytope of all matroids in ranks 2 and 3 for all ground set sizes. This polytope was introduced in recent work by Ferron…
Regular subdivisions, bounds on initial ideals, and categorical limits
George Balla, Daniel Corey, Igor Makhlin +1
Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a ge…
Log-concavity for independent sets of valuated matroids
Jeffrey Giansiracusa, Felipe Rincón, Victoria Schleis +1
Recently, several proofs of the Mason--Welsh conjecture for matroids have been found, which asserts the log-concavity of the sequence that counts independent sets of a given size.…
Tropical Quiver Grassmannians
Giulia Iezzi, Victoria Schleis
We introduce quivers of valuated matroids and study their tropical parameter spaces. We define quiver Dressians, which parametrize containment of tropical linear spaces after tropi…
Linear Degenerate Tropical Flag Varieties
Alessio Borzì, Victoria Schleis
We study linear degenerations of flag varieties from the point of view of tropical geometry. We define the linear degenerate flag Dressian and prove a correspondence between: …