{"paper":{"title":"A Product Version of the Hilton-Milner-Frankl Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jian Wang, Peter Frankl","submitted_at":"2022-06-15T00:13:43Z","abstract_excerpt":"Two families $\\mathcal{F},\\mathcal{G}$ of $k$-subsets of $\\{1,2,\\ldots,n\\}$ are called non-trivial cross $t$-intersecting if $|F\\cap G|\\geq t$ for all $F\\in \\mathcal{F}, G\\in \\mathcal{G}$ and $|\\cap \\{F\\colon F\\in \\mathcal{F}\\}|<t$, $|\\cap \\{G\\colon G\\in\\mathcal{G}\\}|<t$. In the present paper, we determine the maximum product of the sizes of two non-trivial cross $t$-intersecting families of $k$-subsets of $\\{1,2,\\ldots,n\\}$ for $n\\geq 4(t+2)^2k^2$, $k\\geq 5$, which is a product version of the Hilton-Milner-Frankl Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.07217","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.07217/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}