{"paper":{"title":"On the Tur\\'an number of blow-ups of $\\mathcal{F}_5$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D\\'aniel Gerbner, Hilal Hama Karim, Junpeng Zhou, Shujing Miao, Xiamiao Zhao, Xin Cheng, Yichen Wang","submitted_at":"2026-05-21T12:30:55Z","abstract_excerpt":"Let $\\mathcal{F}_5$ denote the $3$-uniform hypergraph on the vertex set $\\{f_1,f_2,\\dots,f_5\\}$ with hyperedges $\\{f_1f_2f_3,f_1f_2f_4,f_3f_4f_5\\}$. Recently, Balogh, Clemen and Luo determined the Tur\\'an number of a one-vertex blow-up of $\\mathcal{F}_5$, more specifically, they blow up the vertex $f_5$ to $t$ vertices, the resulting hypergraph is denoted by $\\mathcal{F}_5(f_5;t)$. They show that for infinitely many $t$, $\\mathcal{F}_5(f_5;t)$ has exponentially many extremal constructions and positive Tur\\'an density.\n  In this paper, we determine the exact Tur\\'an number of the hypergraph obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22397","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/2605.22397/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"}