{"paper":{"title":"$\\ell$-degree Tur\\'an density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Allan Lo, Klas Markstr\\\"om","submitted_at":"2012-10-21T13:18:01Z","abstract_excerpt":"Let $H_n$ be a $k$-graph on $n$ vertices. For $0 \\le \\ell <k$ and an $\\ell$-subset $T$ of $V(H_n)$, define the degree $\\deg(T)$ of $T$ to be the number of $(k-\\ell)$-subsets~$S$ such that $S \\cup T$ is an edge in~$H_n$. Let the minimum $\\ell$-degree of $H_n$ be $\\delta_{\\ell}(H_n) = \\min \\{ \\deg(T) : T \\subseteq V(H_n)$ and $|T|=\\ell\\}$. Given a family $\\mathcal{F}$ of $k$-graphs, the $\\ell$-degree Tur\\'an number $\\text{ex}_{\\ell}(n, \\mathcal{F})$ is the largest $\\delta_{\\ell}(H_n)$ over all $\\mathcal{F}$-free $k$-graphs $H_n$ on $n$ vertices. Hence, $\\text{ex}_0(n, \\mathcal{F})$ is the Tur\\'a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5726","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"}