{"paper":{"title":"Tur\\'an H-densities for 3-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emil R. Vaughan, Victor Falgas-Ravry","submitted_at":"2012-01-20T16:02:34Z","abstract_excerpt":"Given an $r$-graph $H$ on $h$ vertices, and a family $\\mathcal{F}$ of forbidden subgraphs, we define $\\ex_{H}(n, \\mathcal{F})$ to be the maximum number of induced copies of $H$ in an $\\mathcal{F}$-free $r$-graph on $n$ vertices.\n  Then the \\emph{Tur\\'an $H$-density} of $\\mathcal{F}$ is the limit \\[\\pi_{H}(\\mathcal{F})= \\lim_{n\\rightarrow \\infty}\\ex_{H}(n, \\mathcal{F})/\\binom{n}{h}. \\]\n  This generalises the notions of \\emph{Tur\\'an density} (when $H$ is an $r$-edge), and \\emph{inducibility} (when $\\mathcal{F}$ is empty). Although problems of this kind have received some attention, very few res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4326","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"}