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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…
Matroid correspondence
Colin Crowley, Changxin Ding, Haoxi Hu +7
Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues.…
Pseudo-orientable ribbon graphs: Matrix--Quasi-tree Theorem and log-concavity
Changxin Ding, Donggyu Kim
One of the most important classes of even -matroids arises from orientable ribbon graphs, which play a role analogous to that of graphic matroids in matroid theory. Motivated by…
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 expressin…