{"paper":{"title":"When can splits be drawn in the plane?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"q-bio.PE","authors_text":"Andreas Spillner, David Bryant, Monika Balvo\\v{c}i\\=ut\\.e","submitted_at":"2015-09-21T03:42:24Z","abstract_excerpt":"Split networks are a popular tool for the analysis and visualization of complex evolutionary histories. Every collection of splits (bipartitions) of a finite set can be represented by a split network. Here we characterize which collection of splits can be represented using a planar split network. Our main theorem links these collections of splits with oriented matroids and arrangements of lines separating points in the plane. As a consequence of our main theorem, we establish a particularly simple characterization of maximal collections of these splits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06104","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"}