发表机构
Syracuse University（雪城大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用 Seymour 结构定理重新证明并推广了正则拟阵的余圈分裂性质至秩五、六，并将黎曼几何中环面对称性假设从秩十放宽至秩九。
AI 中文摘要
着眼于黎曼几何中的应用，我们探讨正则拟阵的余圈分裂性质。Nienhaus 通过秩四分类表明，一个正则拟阵具有一个余圈，其删除后产生两个余圈，除非该拟阵具有特定形式。在后一种情况下，可以将基集的任意元素分裂为一个余圈。我们使用 Seymour 的正则拟阵结构定理重新证明这一结果，并将其推广到秩五和秩六的拟阵。作为在黎曼几何中的应用，我们证明 Mouillé、Nienhaus 和第二作者最近结果中的环面对称性假设可以从秩十放宽到秩九。
英文摘要
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.
Comments17 pages, 2 figures
