{"paper":{"title":"Supersaturation and stability for forbidden subposet problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Balazs Patkos","submitted_at":"2014-06-07T11:32:29Z","abstract_excerpt":"We address a supersaturation problem in the context of forbidden subposets. A family $\\mathcal{F}$ of sets is said to contain the poset $P$ if there is an injection $i:P \\rightarrow \\mathcal{F}$ such that $p \\le_P q$ implies $i(p) \\subset i (q)$. The poset on four elements $a,b,c,d$ with $a,b \\le c,d$ is called butterfly. The maximum size of a family $\\mathcal{F} \\subseteq 2^{[n]}$ that does not contain a butterfly is $\\Sigma(n,2)=\\binom{n}{\\lfloor n/2 \\rfloor}+\\binom{n}{\\lfloor n/2 \\rfloor+1}$ as proved by De Bonis, Katona, and Swanepoel. We prove that if $\\mathcal{F} \\subseteq 2^{[n]}$ conta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1887","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"}