From the 1 of 7 linked papers with an AI index.
7 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…
Matroid correspondence
Colin Crowley, Changxin Ding, Haoxi Hu +7
The paper introduces matroid correspondences, a functorial framework linking matroids and polymatroids, and shows how standard matroid operations arise from it while preserving rep…
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…
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 b…
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…
A Consistent Sandpile Torsor Algorithm for Regular Matroids
Changxin Ding, Alex McDonough, Lilla Tóthmérész +1
Every regular matroid is associated with a sandpile group, which acts simply transitively on the set of bases in various ways. Ganguly and the second author introduced the notion o…