{"paper":{"title":"Ramsey-type results on singletons, co-singletons and monotone sequences in large collections of sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Maffray, J\\'er\\^ome Renault, Nicolas Trotignon, Sylvain Gravier","submitted_at":"2013-08-27T12:51:24Z","abstract_excerpt":"We say that a 0-1 matrix $N$ of size $a\\times b$ can be found in a collection of sets $\\mathcal{H}$ if we can find sets $H_{1}, H_{2}, \\dots, H_{a}$ in $\\mathcal{H}$ and elements $e_1, e_2, \\dots, e_b$ in $\\cup_{H \\in \\mathcal{H}} H$ such that $N$ is the incidence matrix of the sets $H_{1}, H_{2}, \\dots, H_{a}$ over the elements $e_1, e_2, \\dots, e_b$. We prove the following Ramsey-type result: for every $n\\in \\N$, there exists a number S(n) such that in any collection of at least S(n) sets, one can find either the incidence matrix of a collection of $n$ singletons, or its complementary matrix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5849","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"}