{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DF3HZ7C5DXW5H3LZOJXYUIIIZS","short_pith_number":"pith:DF3HZ7C5","schema_version":"1.0","canonical_sha256":"19767cfc5d1dedd3ed79726f8a2108cc827db374eba2ee654908e86135ea8e1e","source":{"kind":"arxiv","id":"1611.01078","version":3},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.01078","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-11-03T16:15:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"69e56ff636506fa670991651428570040f141e1714993f02ce68b08c3312d635","abstract_canon_sha256":"80b423932da0b8a352a2d3b0e884027dff8b8b8e49ce6683a3f19b8660389bc3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.968437Z","signature_b64":"6RgNA4NbJ0OjwfVAzug7D5Kp3OjuOc62AnLwvMoiZ/CEaM92iKaOFYs5hrOHUJ7FtQg4g4jmKMNPVwDZKjS6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19767cfc5d1dedd3ed79726f8a2108cc827db374eba2ee654908e86135ea8e1e","last_reissued_at":"2026-05-18T00:40:53.967956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.967956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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