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arXiv · 2609.37778

Weighted coloop splittings in rank six

James Dylan Douthitt·Lee Kennard·Josef Komissar
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Abstract

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 matroid has a cocircuit whose deletion yields two coloops unless the matroid takes a particular form. In the latter case, one can split off any element of the ground set as a coloop. We reprove this using Seymour's structure theorem for regular matroids and prove an extension to matroids of ranks five and six. As an application to Riemannian geometry, we prove that the torus symmetry assumption in a recent result of Mouillé, Nienhaus, and the second author can be relaxed from rank ten to rank nine.

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James Dylan Douthitt, Lee Kennard, Josef Komissar. 2026-09-29. Weighted coloop splittings in rank six. https://arxiv.org/abs/2609.37778

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