{"paper":{"title":"On the maximum number of distinct intersections in an intersecting family","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Peter Frankl, Sergei Kiselev","submitted_at":"2021-08-01T15:41:56Z","abstract_excerpt":"For $n > 2k \\geq 4$ we consider intersecting families $\\mathcal F$ consisting of $k$-subsets of $\\{1, 2, \\ldots, n\\}$. Let $\\mathcal I(\\mathcal F)$ denote the family of all distinct intersections $F \\cap F'$, $F \\neq F'$ and $F, F'\\in \\mathcal F$. Let $\\mathcal A$ consist of the $k$-sets $A$ satisfying $|A \\cap \\{1, 2, 3\\}| \\geq 2$. We prove that for $n \\geq 50 k^2$ $|\\mathcal I(\\mathcal F)|$ is maximized by $\\mathcal A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.00479","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/2108.00479/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"}