{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NRDWSNAQJX5V5HSR5D5ATBSGXP","short_pith_number":"pith:NRDWSNAQ","schema_version":"1.0","canonical_sha256":"6c476934104dfb5e9e51e8fa098646bbe387533404161d269dfca44e39516bf9","source":{"kind":"arxiv","id":"1605.06752","version":1},"attestation_state":"computed","paper":{"title":"A rainbow $r$-partite version of the Erd\\H{o}s-Ko-Rado theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Howard, Ron Aharoni","submitted_at":"2016-05-22T08:03:07Z","abstract_excerpt":"Let $f(n,r,k)$ be the minimal number such that every hypergraph larger than $f(n,r,k)$ contained in $\\binom{[n]}{r}$ contains a matching of size $k$, and let $g(n,r,k)$ be the minimal number such that every hypergraph larger than $g(n,r,k)$ contained in the $r$-partite $r$-graph $[n]^{r}$ contains a matching of size $k$. The Erd\\H{o}s-Ko-Rado theorem states that $f(n,r,2)=\\binom{n-1}{r-1}$~~($r \\le \\frac{n}{2}$) and it is easy to show that $g(n,r,k)=(k-1)n^{r-1}$.\n  The conjecture inspiring this paper is that if $F_1,F_2,\\ldots,F_k\\subseteq \\binom{[n]}{r}$ are of size larger than $f(n,r,k)$ or"},"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":"1605.06752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-22T08:03:07Z","cross_cats_sorted":[],"title_canon_sha256":"f6e3f6889cc336294edbdc86352a57698ae6e1c7eb13abd190fc90a0a161e503","abstract_canon_sha256":"2a2578d21f2719ce12c228c762a1abdde1cbf402f0192e251b22d4e3777cc0d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:11.349007Z","signature_b64":"a+5+xPQBr4SRqpB19xlQ+/ZGqu1AeHGotOmFb1Q/qs+gfvgdHzT4+ndZel4ayBKAiiWB/3GHaCcQ8oVaavsKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c476934104dfb5e9e51e8fa098646bbe387533404161d269dfca44e39516bf9","last_reissued_at":"2026-05-18T01:14:11.348356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:11.348356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rainbow $r$-partite version of the Erd\\H{o}s-Ko-Rado theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Howard, Ron Aharoni","submitted_at":"2016-05-22T08:03:07Z","abstract_excerpt":"Let $f(n,r,k)$ be the minimal number such that every hypergraph larger than $f(n,r,k)$ contained in $\\binom{[n]}{r}$ contains a matching of size $k$, and let $g(n,r,k)$ be the minimal number such that every hypergraph larger than $g(n,r,k)$ contained in the $r$-partite $r$-graph $[n]^{r}$ contains a matching of size $k$. The Erd\\H{o}s-Ko-Rado theorem states that $f(n,r,2)=\\binom{n-1}{r-1}$~~($r \\le \\frac{n}{2}$) and it is easy to show that $g(n,r,k)=(k-1)n^{r-1}$.\n  The conjecture inspiring this paper is that if $F_1,F_2,\\ldots,F_k\\subseteq \\binom{[n]}{r}$ are of size larger than $f(n,r,k)$ or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06752","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":"1605.06752","created_at":"2026-05-18T01:14:11.348450+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.06752v1","created_at":"2026-05-18T01:14:11.348450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06752","created_at":"2026-05-18T01:14:11.348450+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRDWSNAQJX5V","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRDWSNAQJX5V5HSR","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRDWSNAQ","created_at":"2026-05-18T12:30:36.002864+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/NRDWSNAQJX5V5HSR5D5ATBSGXP","json":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP.json","graph_json":"https://pith.science/api/pith-number/NRDWSNAQJX5V5HSR5D5ATBSGXP/graph.json","events_json":"https://pith.science/api/pith-number/NRDWSNAQJX5V5HSR5D5ATBSGXP/events.json","paper":"https://pith.science/paper/NRDWSNAQ"},"agent_actions":{"view_html":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP","download_json":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP.json","view_paper":"https://pith.science/paper/NRDWSNAQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.06752&json=true","fetch_graph":"https://pith.science/api/pith-number/NRDWSNAQJX5V5HSR5D5ATBSGXP/graph.json","fetch_events":"https://pith.science/api/pith-number/NRDWSNAQJX5V5HSR5D5ATBSGXP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP/action/storage_attestation","attest_author":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP/action/author_attestation","sign_citation":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP/action/citation_signature","submit_replication":"https://pith.science/pith/NRDWSNAQJX5V5HSR5D5ATBSGXP/action/replication_record"}},"created_at":"2026-05-18T01:14:11.348450+00:00","updated_at":"2026-05-18T01:14:11.348450+00:00"}