{"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. With an intensive use of the delta-system method, we determine $\\ex_k(n,P^{(k)}_\\ell)$ exactly for all fixed $\\ell\\ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1247","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"}