{"paper":{"title":"Classifying unavoidable Tverberg partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Boris Bukh, Gabriel Nivasch, Po-Shen Loh","submitted_at":"2016-11-03T16:15:59Z","abstract_excerpt":"Let $T(d,r) = (r-1)(d+1)+1$ be the parameter in Tverberg's theorem, and call a partition $\\mathcal I$ of $\\{1,2,\\ldots,T(d,r)\\}$ into $r$ parts a \"Tverberg type\". We say that $\\mathcal I$ \"occurs\" in an ordered point sequence $P$ if $P$ contains a subsequence $P'$ of $T(d,r)$ points such that the partition of $P'$ that is order-isomorphic to $\\mathcal I$ is a Tverberg partition. We say that $\\mathcal I$ is \"unavoidable\" if it occurs in every sufficiently long point sequence.\n  In this paper we study the problem of determining which Tverberg types are unavoidable. We conjecture a complete chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01078","kind":"arxiv","version":3},"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"}