4 papers
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 Ferro…
Zero-dimensional tropicalizations in OSCAR
Arman Marti-Shahandeh, Yue Ren, Victoria Schleis
We present algorithms for computing zero-dimensional tropical varieties as implemented in OscarZerodimensionalTropicalization.jl. The algorithms include a mathematical workaround f…
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.…