{"paper":{"title":"Matroids representable over fields with a common subfield","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Nelson, Stefan H.M. van Zwam","submitted_at":"2014-01-27T22:30:35Z","abstract_excerpt":"A matroid is $\\text{GF}(q)$-regular if it is representable over all proper superfields of the field $\\text{GF}(q)$. We show that, for highly connected matroids having a large projective geometry over $\\text{GF}(q)$ as a minor, the property of $\\text{GF}(q)$-regularity is equivalent to representability over both $\\text{GF}(q^2)$ and $\\text{GF}(q^t)$ for some odd integer $t \\geq 3$. We do this by means of an exact structural description of all such matroids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7040","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"}