{"paper":{"title":"A rainbow $r$-partite version of the Erd\\H{o}s-Ko-Rado theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Howard, Ron Aharoni","submitted_at":"2016-05-22T08:03:07Z","abstract_excerpt":"Let $f(n,r,k)$ be the minimal number such that every hypergraph larger than $f(n,r,k)$ contained in $\\binom{[n]}{r}$ contains a matching of size $k$, and let $g(n,r,k)$ be the minimal number such that every hypergraph larger than $g(n,r,k)$ contained in the $r$-partite $r$-graph $[n]^{r}$ contains a matching of size $k$. The Erd\\H{o}s-Ko-Rado theorem states that $f(n,r,2)=\\binom{n-1}{r-1}$~~($r \\le \\frac{n}{2}$) and it is easy to show that $g(n,r,k)=(k-1)n^{r-1}$.\n  The conjecture inspiring this paper is that if $F_1,F_2,\\ldots,F_k\\subseteq \\binom{[n]}{r}$ are of size larger than $f(n,r,k)$ or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06752","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"}