{"paper":{"title":"Clonal cores and flexipaths in matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charles Semple, Geoff Whittle, James Oxley, Nick Brettell","submitted_at":"2024-05-24T04:30:21Z","abstract_excerpt":"A partitioned matroid $(M, \\{X_1,X_2,\\dots,X_n\\})$ consists of a matroid $M$ and a partition $\\{X_1,X_2,\\dots,X_n\\}$ of its ground set. As such structures arise frequently in structural matroid theory, this paper introduces a general technique for analyzing those special properties of partitioned matroids that depend solely on the values of the connectivities $\\lambda(X_i)$, the local connectivities $\\sqcap(\\cup_{j\\in J}X_j, \\cup_{k\\in K}X_k,)$, and the dual local connectivities $\\sqcap^*(\\cup_{h\\in H}X_h, \\cup_{g\\in G}X_g)$. In particular, we consider those partitioned matroids in which each "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15207","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.15207/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}