{"paper":{"title":"The structure of $\\{U_{2,5}, U_{3,5}\\}$-fragile matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Clark, Dillon Mayhew, Geoff Whittle, Stefan van Zwam","submitted_at":"2015-11-09T20:48:29Z","abstract_excerpt":"Let $\\mathcal{N}$ be a set of matroids. A matroid $M$ is strictly $\\mathcal{N}$-fragile if $M$ has a member of $\\mathcal{N}$ as minor and, for all $e \\in E(M)$, at least one of $M\\backslash e$ and $M/e$ has no minor in $\\mathcal{N}$. In this paper we give a structural description of the strictly $\\{U_{2,5},U_{3,5}\\}$-fragile matroids that have six inequivalent representations over $\\mathrm{GF}(5)$. Roughly speaking, these matroids fall into two classes. The matroids without an $\\{X_8, Y_8, Y_8^{*}\\}$-minor are constructed, up to duality, from one of two matroids by gluing wheels onto specified"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02840","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}