{"paper":{"title":"Some intersection theorems for finite sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjian Lv, Kaishun Wang, Mei Lu, Mengyu Cao","submitted_at":"2022-05-22T10:05:40Z","abstract_excerpt":"Let $n$, $r$, $k_1,\\ldots,k_r$ and $t$ be positive integers with $r\\geq 2$, and $\\mathcal{F}_i\\ (1\\leq i\\leq r)$ a family of $k_i$-subsets of an $n$-set $V$. The families $\\mathcal{F}_1,\\ \\mathcal{F}_2,\\ldots,\\mathcal{F}_r$ are said to be $r$-cross $t$-intersecting if $|F_1\\cap F_2\\cap\\cdots\\cap F_r|\\geq t$ for all $F_i\\in\\mathcal{F}_i\\ (1\\leq i\\leq r),$ and said to be non-trivial if $|\\cap_{1\\leq i\\leq r}\\cap_{F\\in\\mathcal{F}_i}F|<t$. If the $r$-cross $t$-intersecting families $\\mathcal{F}_1,\\ldots,\\mathcal{F}_r$ satisfy $\\mathcal{F}_1=\\cdots=\\mathcal{F}_r=\\mathcal{F}$, then $\\mathcal{F}$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.10789","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/2205.10789/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"}