{"paper":{"title":"Sidorenko Hypergraphs and Random Tur\\'an Numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiaxi Nie, Sam Spiro","submitted_at":"2023-09-22T13:55:12Z","abstract_excerpt":"Let $\\mathrm{ex}(G_{n,p}^r,F)$ denote the maximum number of edges in an $F$-free subgraph of the random $r$-uniform hypergraph $G_{n,p}^r$, and let $s(F):=\\sup\\{s: \\exists H,\\ t_F(H)=t_{K_r^r}(H)^{s+e(F)}>0\\}$. Following recent work of Conlon, Lee, and Sidorenko, we prove non-trivial lower bounds on $\\mathrm{ex}(G_{n,p}^r,F)$ whenever $s(F)>0$, i.e. $F$ is not Sidorenko. This connection between Sidorenko's conjecture and random Tur\\'an problems gives new lower bounds on $\\mathrm{ex}(G_{n,p}^r,F)$ whenever $s(F)>0$, and further allows us to establish upper bounds for $s(F)$ whenever upper bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.12873","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.12873/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"}