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With an intensive use of the delta-system method, we determine $\\ex_k(n,P^{(k)}_\\ell)$ exactly for all fixed $\\ell\\ge"},"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":"1108.1247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-05T04:17:17Z","cross_cats_sorted":[],"title_canon_sha256":"c63e61b31acbc74b536b78e649ad542ebe922442d10ec6c9face47e81a08acc9","abstract_canon_sha256":"cfd60bb79b16150d3ec39ec611b7f240629e961dbb06e10089c0a50ce141d21b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:11.332422Z","signature_b64":"rDh/y1xjGbZRg6lQVHb3NC9XzD33TjHkDmpHVwVJSCrGpEbBdGab+gDQrSXr8Y52Yuou0PYkigmmzL8IjpJgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8839975738ba5c44ddc099fbd549767b739124e4f985af18a905b0e1aee290c","last_reissued_at":"2026-05-18T04:16:11.331778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:11.331778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact solution of the hypergraph Tur\\'an problem for $k$-uniform linear paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Robert Seiver, Tao Jiang, Zoltan Furedi","submitted_at":"2011-08-05T04:17:17Z","abstract_excerpt":"A $k$-uniform linear path of length $\\ell$, denoted by $P^{(k)}_\\ell$, is a family of $k$-sets $\\{F_1,..., F_\\ell\\}$ such that $|F_i\\cap F_{i+1}|=1$ for each $i$ and $F_i\\cap F_j=\\emptyset$ whenever $|i-j|>1$.\n  Given a $k$-uniform hypergraph $H$ and a positive integer $n$, the {\\it $k$-uniform hypergraph Tur\\'an number} of $H$, denoted by $\\ex_k(n,H)$, is the maximum number of edges in a $k$-uniform hypergraph $\\cF$ on $n$ vertices that does not contain $H$ as a subhypergraph. 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