{"paper":{"title":"On local Tur\\'an density problems of hypergraphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunqiu Fang, Ge Song, Guorong Gao, Jie Ma","submitted_at":"2023-03-01T11:31:28Z","abstract_excerpt":"For integers $q\\ge p\\ge r\\ge2$, we say that an $r$-uniform hypergraph $H$ has property $(q,p)$, if for any $q$-vertex subset $Q$ of $V(H)$, there exists a $p$-vertex subset $P$ of $Q$ spanning a clique in $H$. Let $T_{r}(n,q,p)=\\min\\{ e(H): H\\subset \\binom{[n]}{r}, H \\text{~has property~} (q,p)\\}$. The local Tur\\'an density about property $(q,p)$ in $r$-uniform hypergraphs is defined as $t_{r}(q,p)=\\lim_{n\\to \\infty}T_{r}(n,q,p)/\\binom{n}{r}$. Frankl, Huang and R\\\"odl [J. Comb. Theory, Ser. A, 177 (2021)] showed that $\\lim_{p\\to\\infty}t_{r}(ap+1,p+1)=\\frac{1}{a^{r-1}}$ for positive integer $a$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.00427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.00427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}