{"paper":{"title":"On the representability of the bi-uniform matroid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carles Padr\\'o, Chaoping Xing, Simeon Ball, Zsuzsa Weiner","submitted_at":"2014-07-27T20:55:15Z","abstract_excerpt":"Every bi-uniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given bi-uniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all bi-uniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of bi-uniform matroids, while the known genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7283","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"}