{"paper":{"title":"Cross-intersecting pairs of hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Howard, Ron Aharoni","submitted_at":"2016-05-20T14:54:12Z","abstract_excerpt":"Two hypergraphs $H_1,\\ H_2$ are called {\\em cross-intersecting} if $e_1 \\cap e_2 \\neq \\emptyset$ for every pair of edges $e_1 \\in H_1,~e_2 \\in H_2$. Each of the hypergraphs is then said to {\\em block} the other. Given parameters $n,r,m$ we determine the maximal size of a sub-hypergraph of $[n]^r$ (meaning that it is $r$-partite, with all sides of size $n$) for which there exists a blocking sub-hypergraph of $[n]^r$ of size $m$. The answer involves a fractal-like (that is, self-similar) sequence, first studied by Knuth. We also study the same question with $\\binom{n}{r}$ replacing $[n]^r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06387","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"}