{"paper":{"title":"An Erd\\H os--Ko--Rado theorem for cross $t$-intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Siggers, Norihide Tokushige, Peter Frankl, Sang June Lee","submitted_at":"2013-03-04T09:52:13Z","abstract_excerpt":"Two families $\\mathcal{A}$ and $\\mathcal{B}$, of $k$-subsets of an $n$-set, are {\\em cross $t$-intersecting} if for every choice of subsets $A \\in \\mathcal{A}$ and $B \\in \\mathcal{B}$ we have $|A \\cap B| \\geq t$. We address the following conjectured cross $t$-intersecting version of the Erd\\H os--Ko--Rado Theorem: For all $n \\geq (t+1)(k-t+1)$ the maximum value of $|\\mathcal{A}||\\mathcal{B}|$ for two cross $t$-intersecting families $\\mathcal{A}, \\mathcal{B} \\subset\\binom{[n]}{k}$ is $\\binom{n-t}{k-t}^2$. We verify this for all $t \\geq 14$ except finitely many $n$ and $k$ for each fixed $t$. Fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0657","kind":"arxiv","version":4},"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"}