{"paper":{"title":"An improvement of the general bound on the largest family of subsets avoiding a subposet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","submitted_at":"2014-08-25T14:56:01Z","abstract_excerpt":"Let $La(n,P)$ be the maximum size of a family of subsets of $[n]= \\{1,2, ..., n \\}$ not containing $P$ as a (weak) subposet, and let $h(P)$ be the length of a longest chain in $P$. The best known upper bound for $La(n,P)$ in terms of $|P|$ and $h(P)$ is due to Chen and Li, who showed that $La(n,P) \\le \\frac{1}{m+1} \\left(|P| + \\frac{1}{2}(m^2 +3m-2)(h(P)-1) -1 \\right) {\\binom {n} {\\lfloor n/2 \\rfloor}}$ for any fixed $m \\ge 1$.\n  In this paper we show that $La(n,P) \\le \\frac{1}{2^{k-1}} (|P| + (3k-5)2^{k-2}(h(P)-1) - 1 ) {n \\choose {\\lfloor n/2\\rfloor} }$ for any fixed $k \\ge 2$, improving the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5783","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"}