{"paper":{"title":"Subgeometries in the Andr\\'e/Bruck-Bose representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, John Sheekey, Sara Rottey","submitted_at":"2014-09-22T09:19:24Z","abstract_excerpt":"We consider the Andr\\'e/Bruck-Bose representation of the projective plane $\\mathrm{PG}(2,q^n)$ in $\\mathrm{PG}(2n,q)$. We investigate the representation of $\\mathbb{F}_{q^k}$-sublines and $\\mathbb{F}_{q^k}$-subplanes of $\\mathrm{PG}(2,q^n)$, extending the results for $n=3$ of \\cite{BarJack2} and correcting the general result of \\cite{BarJack1}. We characterise the representation of $\\mathbb{F}_{q^k}$-sublines tangent to or contained in the line at infinity, $\\mathbb{F}_q$-sublines external to the line at infinity, $\\mathbb{F}_q$-subplanes tangent to and $\\mathbb{F}_{q^k}$-subplanes secant to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6123","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"}