{"paper":{"title":"Non-trivial $t$-intersecting families for the distance-regular graphs of bilinear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjian Lv, Kaishun Wang, Mengyu Cao","submitted_at":"2021-03-20T07:02:50Z","abstract_excerpt":"Let $V$ be an $(n+\\ell)$-dimensional vector space over a finite field, and $W$ a fixed $\\ell$-dimensional subspace of $V$. Write ${V\\brack n,0}$ to be the set of all $n$-dimensional subspaces $U$ of $V$ satisfying $\\dim(U\\cap W)=0$. A family $\\mathcal{F}\\subseteq{V\\brack n,0}$ is $t$-intersecting if $\\dim(A\\cap B)\\geq t$ for all $A,B\\in\\mathcal{F}$. A $t$-intersecting family $\\mathcal{F}\\subseteq{V\\brack n,0}$ is called non-trivial if $\\dim(\\cap_{F\\in\\mathcal{F}}F)<t$. In this paper, we describe the structure of non-trivial $t$-intersecting families of ${V\\brack n,0}$ with large size. In parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.11117","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/2103.11117/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"}