{"paper":{"title":"Repeated columns and an old chestnut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Linyuan Lu, Richard P. Anstee","submitted_at":"2013-05-03T00:48:20Z","abstract_excerpt":"Let $t\\ge 1$ be a given integer. Let ${\\cal F}$ be a family of subsets of $[m]=\\{1,2,\\ldots,m\\}$. Assume that for every pair of disjoint sets $S,T\\subset [m]$ with $|S|=|T|=k$, there do not exist $2t$ sets in ${\\cal F}$ where $t$ subsets of ${\\cal F}$ contain $S$ and are disjoint from $T$ and $t$ subsets of ${\\cal F}$ contain $T$ and are disjoint from $S$. We show that $|{\\cal F}|$ is $O(m^{k})$.\n  Our main new ingredient is allowing, during the inductive proof, multisets of subsets of $[m]$ where the multiplicity of a given set is bounded by $t-1$. We use a strong stability result of Anstee a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0603","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"}