{"paper":{"title":"Intertwining connectivity in matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geoff Whittle, Rong chen","submitted_at":"2014-03-05T03:48:29Z","abstract_excerpt":"Let $M$ be a matroid and let $Q$, $R$, $S$ and $T$ be subsets of the ground set such that the smallest separation that separates $Q$ from $R$ has order $k$ and the smallest separation that separates $S$ from $T$ has order $l$. We prove that if $E(M)-(Q\\cup R\\cup S\\cup T)$ is sufficiently large, then there is an element $e$ of $M$ such that, in one of $M\\backslash e$ or $M/e$, both connectivities are preserved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0997","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"}