{"paper":{"title":"Linear representations of subgeometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, Sara Rottey, Stefaan De Winter","submitted_at":"2014-07-15T11:58:28Z","abstract_excerpt":"The linear representation $T_n^*(\\mathcal{K})$ of a point set $\\mathcal{K}$ in a hyperplane of $\\mathrm{PG}(n+1,q)$ is a point-line geometry embedded in this projective space. In this paper, we will determine the isomorphisms between two linear representations $T_n^*(\\mathcal{K})$ and $T_n^*(\\mathcal{K}')$, under a few conditions on $\\mathcal{K}$ and $\\mathcal{K}'$. First, we prove that an isomorphism between $T_n^*(\\mathcal{K})$ and $T_n^*(\\mathcal{K}')$ is induced by an isomorphism between the two linear representations $T_n^*(\\overline{\\mathcal{K}})$ and $T_n^*(\\overline{\\mathcal{K}'})$ of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3953","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"}