{"paper":{"title":"The structure of claw-free binary matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kazuhiro Nomoto, Peter Nelson","submitted_at":"2018-07-30T19:37:23Z","abstract_excerpt":"A simple binary matroid is called claw-free if none of its rank-3 flats are independent sets. These objects can be equivalently defined as the sets $E$ of points in $\\mathrm{PG}(n-1,2)$ for which $|E \\cap P|$ is not a basis of $P$ for any plane $P$, or as the subsets $X$ of $\\mathbb{F}_2^n$ containing no linearly independent triple $x,y,z$ for which $x+y,y+z,x+z,x+y+z \\notin X$.\n  We prove a decomposition theorem that exactly determines the structure of all claw-free matroids. The theorem states that claw-free matroids either belong to one of three particular basic classes of claw-free matroid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11543","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"}