{"paper":{"title":"A Tverberg type theorem for matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gil Kalai, Imre B\\'ar\\'any, Roy Meshulam","submitted_at":"2016-07-06T12:54:24Z","abstract_excerpt":"Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \\geq \\sqrt{b(M)}/4 disjoint independent sets \\sigma_1,\\ldots,\\sigma_t \\in M such that \\bigcap_{i=1}^t f(\\sigma_i) \\neq \\emptyset."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01599","kind":"arxiv","version":2},"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"}