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We show that if $a_1, a_2\\ge \\epsilon n$, then $H$ contains a matching of size $\\min\\{n-1, \\sum_{i\\in [k]}a_i\\}$. In particular, $H$ contains a matching of size $n-1$ if each crossing $(k-1)$-set lies in at least $\\lceil n/k \\rceil$ edges, or each crossing $(k-1)$-set lies in at least $\\lfloor n/"},"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":"1611.00290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-01T16:42:06Z","cross_cats_sorted":[],"title_canon_sha256":"69a61f2c17955b092e15e0ae8c41d4cb9449825f6a4674966650f3f82f21ce12","abstract_canon_sha256":"ddc26638f4603feb74b666152fb1996c5a1ecf041a6a391f8fb407532d585e0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.285314Z","signature_b64":"ETDSxNc9NQfhY6DME5yZLJpgU5RfQGj8DXqNMMOzukvcsuXoSEG94UJdPY4butNSSE6YslArH3skqhpFDCocBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42b2a3039cddbac4f42f00544ad994d886542490e14f543b9fe591764fa68b2e","last_reissued_at":"2026-05-18T00:23:09.284648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.284648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matchings in $k$-partite $k$-uniform Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chuanyun Zang, Jie Han, Yi Zhao","submitted_at":"2016-11-01T16:42:06Z","abstract_excerpt":"For $k\\ge 3$ and $\\epsilon>0$, let $H$ be a $k$-partite $k$-graph with parts $V_1,\\dots, V_k$ each of size $n$, where $n$ is sufficiently large. 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