{"paper":{"title":"Forbidding $K_{2,t}$ traces in triple systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ruth Luo, Sam Spiro","submitted_at":"2020-07-03T17:32:08Z","abstract_excerpt":"Let $H$ and $F$ be hypergraphs. We say $H$ contains $F$ as a trace if there exists some set $S \\subseteq V(H)$ such that $H|_S:=\\{E\\cap S: E \\in E(H)\\}$ contains a subhypergraph isomorphic to $F$. In this paper we give an upper bound on the number of edges in a $3$-uniform hypergraph that does not contain $K_{2,t}$ as a trace when $t$ is large. In particular, we show that $ \\lim_{t\\to \\infty}\\lim_{n\\to \\infty} \\frac{\\mathrm{ex}(n, \\mathrm{Tr}_3(K_{2,t}))}{t^{3/2}n^{3/2}} = \\frac{1}{6}.$\n  Moreover, we show $\\frac{1}{2} n^{3/2} + o(n^{3/2}) \\leq \\mathrm{ex}(n, \\mathrm{Tr}_3(C_4)) \\leq \\frac{5}{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.01827","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/2007.01827/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"}