{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:X3CQRJJV6RQ4KN3ZMK4AQWADF5","short_pith_number":"pith:X3CQRJJV","schema_version":"1.0","canonical_sha256":"bec508a535f461c5377962b80858032f4ff7de089401ae1fbf61d05e8fd18bef","source":{"kind":"arxiv","id":"1611.01735","version":1},"attestation_state":"computed","paper":{"title":"On rainbow matchings for hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Xingxing Yu","submitted_at":"2016-11-06T07:29:29Z","abstract_excerpt":"For any posotive integer $m$, let $[m]:=\\{1,\\ldots,m\\}$. Let $n,k,t$ be positive integers. Aharoni and Howard conjectured that if, for $i\\in [t]$, $\\mathcal{F}_i\\subset[n]^k:= \\{(a_1,\\ldots,a_k): a_j\\in [n] \\mbox{ for } j\\in [k]\\}$ and $|\\mathcal{F}_i|>(t-1)n^{k-1}$, then there exist $M\\subseteq [n]^k$ such that $|M|=t$ and $|M\\cap \\mathcal{F}_i|=1$ for $i\\in [t]$ We show that this conjecture holds when $n\\geq 3(k-1)(t-1)$.\n  Let $n, t, k_1\\ge k_2\\geq \\ldots\\geq k_t $ be positive integers. Huang, Loh and Sudakov asked for the maximum $\\Pi_{i=1}^t |{\\cal\n  R}_i|$ over all ${\\cal R}=\\{{\\cal R}_1"},"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":"1611.01735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-06T07:29:29Z","cross_cats_sorted":[],"title_canon_sha256":"e8add51a17076ae70776388c9c15306e58781a8b5ca4aa05710116722cdcc5ca","abstract_canon_sha256":"8ce1a8c1876ee19fdbc45e4cdfd2b283663533ff3ee7380d123d93375e5ecc19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:04.568530Z","signature_b64":"h+KugFe72kB7IAt86wrU6sGzi4zFS9JCcJTpBwIb8b2q5NWWCmY/OAzeW5HSdahqkY7DCNCndJZ/EcExzmuSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bec508a535f461c5377962b80858032f4ff7de089401ae1fbf61d05e8fd18bef","last_reissued_at":"2026-05-18T01:00:04.567737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:04.567737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On rainbow matchings for hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Xingxing Yu","submitted_at":"2016-11-06T07:29:29Z","abstract_excerpt":"For any posotive integer $m$, let $[m]:=\\{1,\\ldots,m\\}$. Let $n,k,t$ be positive integers. Aharoni and Howard conjectured that if, for $i\\in [t]$, $\\mathcal{F}_i\\subset[n]^k:= \\{(a_1,\\ldots,a_k): a_j\\in [n] \\mbox{ for } j\\in [k]\\}$ and $|\\mathcal{F}_i|>(t-1)n^{k-1}$, then there exist $M\\subseteq [n]^k$ such that $|M|=t$ and $|M\\cap \\mathcal{F}_i|=1$ for $i\\in [t]$ We show that this conjecture holds when $n\\geq 3(k-1)(t-1)$.\n  Let $n, t, k_1\\ge k_2\\geq \\ldots\\geq k_t $ be positive integers. Huang, Loh and Sudakov asked for the maximum $\\Pi_{i=1}^t |{\\cal\n  R}_i|$ over all ${\\cal R}=\\{{\\cal R}_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01735","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.01735","created_at":"2026-05-18T01:00:04.567886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.01735v1","created_at":"2026-05-18T01:00:04.567886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01735","created_at":"2026-05-18T01:00:04.567886+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3CQRJJV6RQ4","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3CQRJJV6RQ4KN3Z","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3CQRJJV","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5","json":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5.json","graph_json":"https://pith.science/api/pith-number/X3CQRJJV6RQ4KN3ZMK4AQWADF5/graph.json","events_json":"https://pith.science/api/pith-number/X3CQRJJV6RQ4KN3ZMK4AQWADF5/events.json","paper":"https://pith.science/paper/X3CQRJJV"},"agent_actions":{"view_html":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5","download_json":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5.json","view_paper":"https://pith.science/paper/X3CQRJJV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.01735&json=true","fetch_graph":"https://pith.science/api/pith-number/X3CQRJJV6RQ4KN3ZMK4AQWADF5/graph.json","fetch_events":"https://pith.science/api/pith-number/X3CQRJJV6RQ4KN3ZMK4AQWADF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5/action/storage_attestation","attest_author":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5/action/author_attestation","sign_citation":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5/action/citation_signature","submit_replication":"https://pith.science/pith/X3CQRJJV6RQ4KN3ZMK4AQWADF5/action/replication_record"}},"created_at":"2026-05-18T01:00:04.567886+00:00","updated_at":"2026-05-18T01:00:04.567886+00:00"}