{"paper":{"title":"Partial covering arrays and a generalized Erdos-Ko-Rado property","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anant P. Godbole, Patricia A. Carey","submitted_at":"2005-12-06T21:51:47Z","abstract_excerpt":"The classical Erd\\H os-Ko-Rado theorem states that if $k\\le\\floor{n/2}$ then the largest family of pairwise intersecting $k$-subsets of $[n]=\\{0,1,...,n\\}$ is of size ${{n-1}\\choose{k-1}}$. A family of $k$ subsets satisfying this pairwise intersecting property is called an EKR family. We generalize the EKR property and provide asymptotic lower bounds on the size of the largest family ${\\cal A}$ of $k$-subsets of $[n]$ that satisfies the following property: For each $A,B,C\\in{\\cal A}$, each of the four sets $A\\cap B\\cap C;A\\cap B\\cap C^C; A\\cap B^C\\cap C; A^C\\cap B\\cap C$ are non-empty. This ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512139","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"}