{"paper":{"title":"Tur\\'an Number of Generalized Triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liana Yepremyan, Sergey Norin","submitted_at":"2015-01-08T17:47:46Z","abstract_excerpt":"The family $\\Sigma_r$ consists of all $r$-graphs with three edges $D_1,D_2,D_3$ such that $|D_1\\cap D_2|=r-1$ and $D_1 \\triangle D_2 \\subseteq D_3$. A generalized triangle, $\\mathcal{T}_r \\in \\Sigma_r$ is an $r$-graph on $\\{1,2,\\ldots,2r-1\\}$ with three edges $D_1, D_2, D_3$, such that $D_1=\\{1,2,\\dots,r-1, r\\}, D_2= \\{1, 2, \\dots, r-1, r+1 \\}$ and $D_3 = \\{r, r+1, \\dots, 2r-1\\}.$ Frankl and F\\\"{u}redi conjectured that for all $r\\geq 4$, $ex(n,\\Sigma_r) = ex(n,\\mathcal{T}_r )$ for all sufficiently large $n$ and they also proved it for $r=3$. Later, Pikhurko showed that the conjecture holds for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01913","kind":"arxiv","version":2},"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"}