Transversal Valuated Matroids

Abstract: Transversal matroids are a class of matroids that arises from matchings in bipartite graphs. This has a generalization to valuated matroids which arise from tropical minors of a matrix. This is the so-called tropical Stiefel map. Brualdi and Dinolt gave a construction that characterizes all bipartite graphs that represent a given transversal matroid. We show a valuated analogue of this result. In other words, we characterize all matrices with fixed maximal tropical minors. This has several geometric interpretations, such as characterizing tropical hyperplanes with fixed stable intersections.This is joint work with Alex Fink.

commutative algebraalgebraic geometrycombinatorics

Audience: researchers in the topic

Matroids - Combinatorics, Algebra and Geometry Seminar