{"paper":{"title":"Embedding tetrahedra into quasirandom 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":"2016-02-06T18:49:40Z","abstract_excerpt":"We investigate extremal problems for quasirandom hypergraphs. We say that a $3$-uniform hypergraph $H=(V,E)$ is $(d,\\eta)$-quasirandom if for any subset $X\\subseteq V$ and every set of pairs $P\\subseteq V\\times V$ the number of pairs $(x,(y,z))\\in X\\times P$ with $\\{x,y,z\\}$ being a hyperedge of $H$ is in the interval $d|X||P|\\pm\\eta|V|^3$. We show that for any $\\varepsilon>0$ there exists $\\eta>0$ such that every sufficiently large $(1/2+\\varepsilon,\\eta)$-quasirandom hypergraph contains a tetrahedron, i.e., four vertices spanning all four hyperedges. A known random construction shows that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02289","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"}