{"paper":{"title":"On extremal cross $t$-intersecting families with $t$-covering number conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjian Lv, Kaishun Wang, Yu Zhu","submitted_at":"2026-05-19T06:23:26Z","abstract_excerpt":"Let $n$, $k$ and $t$ be positive integers, and let $\\mathcal{F}$ be a collection of $k$-subsets of $[n]=\\{1,2,\\dots,n\\}$. The $t$-covering number $\\tau_t(\\mathcal{F})$ of $\\mathcal{F}$ is defined as the minimum size of a set $T$ such that $|F\\cap T|\\geq t$ for all $F\\in \\mathcal{F}$. For positive integers $k_1$ and $k_2$, let $\\mathcal{F}_i$ be a collection of $k_i$-subsets of $[n]$ for $i\\in \\{1,2\\}$. The families $\\mathcal{F}_1$ and $\\mathcal{F}_2$ are said to be cross $t$-intersecting if $|F_1\\cap F_2|\\geq t$ for all $F_1\\in\\mathcal{F}_1$ and $F_2\\in \\mathcal{F}_2$. When $\\mathcal{F}_1=\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19424","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/2605.19424/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"}