{"paper":{"title":"On the Erdos-Ko-Rado Theorem and the Bollobas Theorem for t-intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dong Yeap Kang, Jaehoon Kim, Younjin Kim","submitted_at":"2014-08-14T14:19:13Z","abstract_excerpt":"A family $\\mathcal{F}$ is $t$-$\\it{intersecting}$ if any two members have at least $t$ common elements. Erd\\H os, Ko, and Rado proved that the maximum size of a $t$-intersecting family of subsets of size $k$ is equal to $ {{n-t} \\choose {k-t}}$ if $n\\geq n_0(k,t)$. Alon, Aydinian, and Huang considered families generalizing intersecting families, and proved the same bound. In this paper, we give a strengthening of their result by considering families generalizing $t$-intersecting families for all $t \\geq 1$. In 2004, Talbot generalized Bollob\\'{a}s's Two Families Theorem to $t$-intersecting fam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3292","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"}