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We prove that there exists an absolute constant $n_0$ such that this rainbow version holds for $k=3$ and $n\\geq n_0$. We convert this rainbow matching problem to a match"},"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":"2011.14363","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-11-29T13:03:33Z","cross_cats_sorted":[],"title_canon_sha256":"59b8d28e08da8d7fd90bc73d629847dc8bcc061abb7222b2fcfc6cc6214aab13","abstract_canon_sha256":"38b00d1bb603351f4985016d8710d2074f2f22b2eb8ec25fb5bb152b6e651380"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:18:25.597359Z","signature_b64":"HvNnMeDD+Fd5tFKrqlVnV/2Pho/8tIhzSrgDFF77uo9kiCG3/j7INwg+Tx2fSCV06wRCqgVG+RO3q14JTgoSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25cf201e2cfd40fb476a8f8bbc24867ad3b09ae0e9ef861a43119b3ad894968f","last_reissued_at":"2026-07-05T03:18:25.596865Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:18:25.596865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the rainbow matching conjecture for 3-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Jie Ma, Jun Gao, Xingxing Yu","submitted_at":"2020-11-29T13:03:33Z","abstract_excerpt":"Aharoni and Howard, and, independently, Huang, Loh, and Sudakov proposed the following rainbow version of Erd\\H{o}s matching conjecture: For positive integers $n,k,m$ with $n\\ge km$, if each of the families $F_1,\\ldots, F_m\\subseteq {[n]\\choose k}$ has size more than $\\max\\{\\binom{n}{k} - \\binom{n-m+1}{k}, \\binom{km-1}{k}\\}$, then there exist pairwise disjoint subsets $e_1,\\dots, e_m$ such that $e_i\\in F_i$ for all $i\\in [m]$. We prove that there exists an absolute constant $n_0$ such that this rainbow version holds for $k=3$ and $n\\geq n_0$. 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