{"paper":{"title":"Extremal cross $t$-intersecting families under $t$-covering number constraints for vector spaces","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":"2026-08-01T07:56:42Z","abstract_excerpt":"Let $V$ be an $n$-dimensional vector space over the finite field $\\mathbb{F}_q$, and ${V\\brack k}$ denote the family of all $k$-dimensional subspaces of $V$. The families $\\mathcal{F}\\subseteq {V\\brack k}$ and $\\mathcal{G}\\subseteq {V\\brack \\ell}$ are said to be cross $t$-intersecting if $\\dim(F\\cap G)\\geq t$ for all $F\\in\\mathcal{F}$ and $G\\in \\mathcal{G}$. In this paper, we determine the extremal structures when $|\\mathcal{F}||\\mathcal{G}|$ attains the maximum value under the conditions $\\dim\\left(\\cap_{F\\in \\mathcal{F}}F\\right)<t$ and $\\dim\\left(\\cap_{G\\in \\mathcal{G}}G\\right)<t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00505","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/2608.00505/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"}