{"paper":{"title":"Probabilistic Extensions of the Erd\\H os-Ko-Rado Property","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Anant P. Godbole, Anna Celaya, Mandy Rae Schleifer","submitted_at":"2005-09-16T15:31:19Z","abstract_excerpt":"The classical Erd\\H os-Ko-Rado (EKR) Theorem states that if we choose a family of subsets, each of size (k), from a fixed set of size (n (n > 2k)), then the largest possible pairwise intersecting family has size (t ={n-1\\choose k-1}). We consider the probability that a randomly selected family of size (t=t_n) has the EKR property (pairwise nonempty intersection) as $n$ and $k=k_n$ tend to infinity, the latter at a specific rate. As $t$ gets large, the EKR property is less likely to occur, while as $t$ gets smaller, the EKR property is satisfied with high probability. We derive the threshold va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509382","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"}