{"paper":{"title":"Set families with a forbidden induced subposet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edward Boehnlein, Tao Jiang","submitted_at":"2011-06-12T14:48:37Z","abstract_excerpt":"For each poset $H$ whose Hasse diagram is a tree of height $k$, we show that the largest size of a family $\\cF$ of subsets of $[n]=\\{1,..., n\\}$ not containing $H$ as an induced subposet is asymptotic to $(k-1){n\\choose \\fl{n/2}}$. This extends the result of Bukh \\cite{bukh}, which in turn generalizes several known results including Sperner's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2315","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":""},"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"}