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Weighted coloop splittings in rank six
James Dylan Douthitt, Lee Kennard, Josef Komissar
With a view toward applications in Riemannian geometry, we explore coloop splitting properties of regular matroids. Nienhaus showed by classification in rank four that a regular ma…
Degeneracy: From Graphs to Matroids
Allan Bickle, James Dylan Douthitt, Wayne Ge +1
A graph is -degenerate if every subgraph has a vertex of degree at most . We extend this notion to matroids, defining a loopless matroid to be -degenerate if every res…
Higher cosystoles of matroids
James Dylan Douthitt, Elana Israel, Lee Kennard
We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class…