{"paper":{"title":"Uniform s-cross-intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Peter Frankl","submitted_at":"2016-11-22T11:41:00Z","abstract_excerpt":"In this paper we study a question related to the classical Erd\\H{o}s-Ko-Rado theorem, which states that any family of $k$-element subsets of the set $[n] = \\{1,\\ldots,n\\}$ in which any two sets intersect, has cardinality at most ${n-1\\choose k-1}$.\n  We say that two non-empty families are $\\mathcal A, \\mathcal B\\subset {[n]\\choose k}$ are {\\it $s$-cross-intersecting}, if for any $A\\in\\mathcal A,B\\in \\mathcal B$ we have $|A\\cap B|\\ge s$. In this paper we determine the maximum of $|\\mathcal A|+|\\mathcal B|$ for all $n$. This generalizes a result of Hilton and Milner, who determined the maximum o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07258","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"}