{"paper":{"title":"A geometric proof of the colored Tverberg theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ji\\v{r}\\'i Matou\\v{s}ek, Martin Tancer, Uli Wagner","submitted_at":"2010-08-31T10:26:24Z","abstract_excerpt":"The colored Tverberg theorem asserts that for every d and r there exists t=t(d,r) such that for every set C in R^d of cardinality (d+1)t, partitioned into t-point subsets C_1,C_2,...,C_{d+1} (which we think of as color classes; e.g., the points of C_1 are red, the points of C_2 blue, etc.), there exist r disjoint sets R_1,R_2,...,R_r \\subseteq C that are \"rainbow\", meaning that |R_i \\cap C_j| < 2 for every i,j, and whose convex hulls all have a common point.\n  All known proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojevi\\'c, Matschke,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.5275","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"}