{"paper":{"title":"More on $r$-cross $t$-intersecting families for vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dehai Liu, Kaishun Wang, Tian Yao","submitted_at":"2023-10-29T08:56:04Z","abstract_excerpt":"Let $V$ be a finite dimensional vector space over a finite field. Suppose that $\\mathscr{F}_1$, $\\mathscr{F}_2$, $\\dots$, $\\mathscr{F}_r$ are $r$-cross $t$-intersecting families of $k$-subspaces of $V$. In this paper, we determine the extremal structure when $\\prod_{i=1}^r|\\mathscr{F}_i|$ is maximum under the condition that $\\dim(\\bigcap_{F\\in\\mathscr{F}_i}F)<t$ for each $i$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.18939","kind":"arxiv","version":2},"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/2310.18939/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"}