{"paper":{"title":"Colorful theorems for strong convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Andreas F. Holmsen, Roman Karasev","submitted_at":"2015-09-29T14:53:51Z","abstract_excerpt":"We prove two colorful Carath\\'eodory theorems for strongly convex hulls, generalizing the colorful Carat\\'eodory theorem for ordinary convexity by Imre B\\'ar\\'any, the non-colorful Carath\\'eodory theorem for strongly convex hulls by the second author, and the \"very colorful theorems\" by the first author and others. We also investigate if the assumption of a \"generating convex set\" is really needed in such results and try to give a topological criterion for one convex body to be a Minkowski summand of another."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08783","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"}