PreprintCC BY 4.0arXiv
Weighted coloop splittings in rank six
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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BibTeX
@misc{douthitt2026weighted,
title = {{Weighted coloop splittings in rank six}},
author = {James Dylan Douthitt and Lee Kennard and Josef Komissar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37778},
eprint = {2609.37778},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37778},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weighted coloop splittings in rank six
AU - James Dylan Douthitt
AU - Lee Kennard
AU - Josef Komissar
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37778
UR - https://arxiv.org/abs/2609.37778
AB - 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.
ER -