{"paper":{"title":"Turan numbers of extensions of some sparse hypergraphs via Lagrangians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Biao Wu, Tao Jiang, Yuejian Peng","submitted_at":"2016-09-28T16:06:40Z","abstract_excerpt":"Given a positive integer $n$ and an $r$-uniform hypergraph (or $r$-graph for short) $F$, the Turan number $ex(n,F)$ of $F$ is the maximum number of edges in an $r$-graph on $n$ vertices that does not contain $F$ as a subgraph. The extension $H^F $ of $F$ is obtained as follows: For each pair of vertices $v_i,v_j$ in $F$ not contained in an edge of $F$, we add a set $B_{ij}$ of $r-2$ new vertices and the edge $\\{v_i,v_j\\} \\cup B_{ij}$, where the $B_{ij}$ 's are pairwise disjoint over all such pairs $\\{i,j\\}$. Let $K^r_p$ denote the complete $r$-graph on $p$ vertices. For all sufficiently large "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08983","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"}