6 papers · 1 filter
Canonical forms of oriented matroids
Christopher Eur, Thomas Lam
Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full-dimensional projecti…
The Universal Valuation of Coxeter Matroids
Christopher Eur, Mario Sanchez, Mariel Supina
Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to su…
Tropical flag varieties
Madeline Brandt, Christopher Eur, Leon Zhang
Flag matroids are combinatorial abstractions of flags of linear subspaces, just as matroids are of linear subspaces. We introduce the flag Dressian as a tropical analogue of the pa…
K-theoretic Tutte polynomials of morphisms of matroids
Rodica Dinu, Christopher Eur, Tim Seynnaeve
We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We introduce two different generalizations, and demonstrate that each…
Logarithmic concavity for morphisms of matroids
Christopher Eur, June Huh
Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of basis for morphisms of matroids, and show that its generatin…
Divisors on matroids and their volumes
Christopher Eur
The classical volume polynomial in algebraic geometry measures the degrees of ample (and nef) divisors on a smooth projective variety. We introduce an analogous volume polynomial f…