5 papers
A polyhedral approach to homotopy theorems in matroid theory
Changxin Ding, Donggyu Kim
We give a new proof of Maurer's homotopy theorem for matroids using polyhedral methods, in contrast to Maurer's original combinatorial proof. The same polyhedral approach yields a…
The Jacobian of a regular orthogonal matroid and torsor structures on spanning quasi-trees of ribbon graphs
Matthew Baker, Changxin Ding, Donggyu Kim
Previous work of Chan--Church--Grochow and Baker--Wang shows that the set of spanning trees in a plane graph is naturally a torsor for the Jacobian group of . Informally, th…
Grassmann--Plücker functions for orthogonal matroids
Changxin Ding, Donggyu Kim
We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann--Plücker functions. The equivalence is motivated by Cayley's identities expressi…
Baker--Bowler theory for Lagrangian Grassmannians
Donggyu Kim
Baker and Bowler showed that the Grassmannian can be defined over a tract, a field-like structure generalizing both partial fields and hyperfields. This notion unifies theories of…
Representation theory for polymatroids
Matthew Baker, June Huh, Donggyu Kim +2
We develop a theory of representations of (discrete) polymatroids over tracts in terms of Plücker coordinates and suitable Plücker relations. As special cases, we recover polymat…