64 citations · 178 across the 18 of their papers we have counts for
16 papers · 1 filter
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…
Answering Two OPAC Problems Involving Banff Quivers
Tucker J. Ervin, Blake Jackson
In a post on the Open Problems in Algebraic Combinatorics (OPAC) blog, E. Bucher and J. Machacek posed three open problems: OPAC-033, OPAC-034, and OPAC-035. These three problems d…
Zero-one Schubert polynomials
Alex Fink, Karola Mészáros, Avery St. Dizier
We prove that if is a pattern of , then we can express the Schubert polynomial as a monomial times (in reindexed variables)…
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…
The Tutte polynomial via lattice point counting
Amanda Cameron, Alex Fink
We recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhart-style polynomial counting lattice points in the Minkowski sum of its base polytope and sc…
Universal Tutte characters via combinatorial coalgebras
Clément Dupont, Alex Fink, Luca Moci
The Tutte polynomial is the most general invariant of matroids and graphs that can be computed recursively by deleting and contracting edges. We generalize this invariant to any cl…