{"paper":{"title":"Using the existence of t-designs to prove Erd\\H{o}s-Ko-Rado","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chris Godsil, Krystal Guo","submitted_at":"2018-02-09T20:39:08Z","abstract_excerpt":"In 1984, Wilson proved the Erd\\H{o}s-Ko-Rado theorem for $t$-intersecting families of $k$-subsets of an $n$-set: he showed that if $n\\ge(t+1)(k-t+1)$ and $\\mathcal{F}$ is a family of $k$-subsets of an $n$-set such that any two members of $\\mathcal{F}$ have at least $t$ elements in common, then $|\\mathcal{F}|\\le\\binom{n-t}{k-t}$. His proof made essential use of a matrix whose origin is not obvious. In this paper we show that this matrix can be derived, in a sense, as a projection of $t$-$(n,k,1)$ design."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03444","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"}