{"paper":{"title":"An Erd\\H{o}s-Ko-Rado theorem in general linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun Guo, Kaishun Wang","submitted_at":"2011-07-15T23:01:22Z","abstract_excerpt":"Let $S_n$ be the symmetric group on $n$ points. Deza and Frankl [M. Deza and P. Frankl, On the maximum number of permutations with given maximal or minimal distance, J. Combin. Theory Ser. A 22 (1977) 352--360] proved that if ${\\cal F}$ is an intersecting set in $S_n$ then $|{\\cal F}|\\leq(n-1)!$. In this paper we consider the $q$-analogue version of this result. Let $\\mathbb{F}_q^n$ be the $n$-dimensional row vector space over a finite field $\\mathbb{F}_q$ and $GL_n(\\mathbb{F}_q)$ the general linear group of degree $n$. A set ${\\cal F}_q\\subseteq GL_n(\\mathbb{F}_q)$ is {\\it intersecting} if fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3178","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":""},"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"}