{"paper":{"title":"Some remarks on the extremal function for uniformly two-path dense hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Reiher, Mathias Schacht, Vojt\\v{e}ch R\\\"odl","submitted_at":"2016-02-06T19:47:38Z","abstract_excerpt":"We investigate extremal problems for hypergraphs satisfying the following density condition. A $3$-uniform hypergraph $H=(V, E)$ is $(d, \\eta,P_2)$-dense if for any two subsets of pairs $P$, $Q\\subseteq V\\times V$ the number of pairs $((x,y),(x,z))\\in P\\times Q$ with $\\{x,y,z\\}\\in E$ is at least $d|\\mathcal{K}_{P_2}(P,Q)|-\\eta|V|^3,$ where $\\mathcal{K}_{P_2}(P,Q)$ denotes the set of pairs in $P\\times Q$ of the form $((x,y),(x,z))$. For a given $3$-uniform hypergraph $F$ we are interested in the infimum $d\\geq 0$ such that for sufficiently small $\\eta$ every sufficiently large $(d, \\eta,P_2)$-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02299","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"}