11 citations · 43 across the 9 of their papers we have counts for
11 papers
Extensions of transversal valuated matroids
Alex Fink, Jorge Alberto Olarte
Following up on our previous work, we study single-element extensions of transversal valuated matroids. We show that tropical presentations of valuated matroids with a minimal set…
Positivity for partial tropical flag varieties
Jorge Alberto Olarte
We study positivity notions for the tropicalization of type A flag varieties and the flag Dressian. We focus on the hollow case, where we have one constituent of rank 1 and another…
Initial degenerations of flag varieties
Daniel Corey, Jorge Alberto Olarte
We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal…
Generalized permutahedra and positive flag Dressians
Michael Joswig, Georg Loho, Dante Luber +1
We study valuated matroids, their tropical incidence relations, flag matroids and total positivity. This leads to a characterization of permutahedral subdivisions, namely subdivisi…
The tropical symplectic Grassmannian
George Balla, Jorge Alberto Olarte
We launch the study of the tropicalization of the symplectic Grassmannian, that is, the space of all linear subspaces that are isotropic with respect to a fixed symplectic form. We…
Hypersimplicial subdivisions
Jorge Alberto Olarte, Francisco Santos
Let be any linear projection, let be the image of the standard basis. Motivated by Postnikov's study of postitive Grassmannians via plabic g…
Presentations of Transversal Valuated Matroids
Alex Fink, Jorge Alberto Olarte
Given row vectors of tropical numbers, , the tropical Stiefel map constructs a version of their row space, whose Plücker coordinates are tropical determinants. We expl…
On local Dressians of matroids
Jorge Alberto Olarte, Marta Panizzut, Benjamin Schröter
We study the fan structure of Dressians $\Dr(d,n)$ and local Dressians $\Dr(\cM)$ for a given matroid $\cM$. In particular we show that the fan structure on $\Dr(\cM)$ given by the…
Short proof of two cases of Chvátal's conjecture
Jorge Olarte, Francisco Santos, Jonathan Spreer
In 1974 Chvátal conjectured that no intersecting family in a downset can be larger than the largest star. In the same year Kleitman and Magnanti proved the conjecture…
The EKR property for flag pure simplicial complexes without boundary
Jorge Olarte, Francisco Santos, Jonathan Spreer +1
We prove that the family of facets of a pure simplicial complex of dimension up to three satisfies the Erdős-Ko-Rado property whenever it is flag and has no boundary ridges. We con…
Gammoids, Pseudomodularity and Flatness Degree
Jorge Alberto Olarte
We study weaker variations of the property of flatness in matroid theory. We show that these variations form a chain of increasingly stronger properties all implying pseudomodulari…