{"paper":{"title":"On cross-2-intersecting families","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anshui Li, Biao Wu, Huajun Zhang, Yanhong Chen","submitted_at":"2025-03-20T09:14:13Z","abstract_excerpt":"Two families $\\mathcal A\\subseteq\\binom{[n]}{k}$ and $\\mathcal B\\subseteq\\binom{[n]}{\\ell}$ are called cross-$t$-intersecting if $|A\\cap B|\\geq t$ for all $A\\in\\mathcal A$, $B\\in\\mathcal B$. Let $n$, $k$ and $\\ell$ be positive integers such that $n\\geq 3.38\\ell$ and $\\ell\\geq k\\geq 2$. In this paper, we will determine the upper bound of $|\\mathcal A||\\mathcal B|$ for cross-$2$-intersecting families $\\mathcal A\\subseteq\\binom{[n]}{k}$ and $\\mathcal B\\subseteq\\binom{[n]}{\\ell}$. The structures of the extremal families attaining the upper bound are also characterized. The similar result obtained "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.15971","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.15971/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"}