{"paper":{"title":"Subspaces intersecting each element of a regulus in one point, Andr\\'e-Bruck-Bose representation and clubs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Corrado Zanella, Michel Lavrauw","submitted_at":"2014-09-03T13:33:04Z","abstract_excerpt":"In this paper results are proved with applications to the orbits of $(n-1)$-dimensional subspaces disjoint from a regulus $\\cR$ of $(n-1)$-subspaces in $\\PG(2n-1,q)$, with respect to the subgroup of $\\PGL(2n,q)$ fixing $\\cR$. Such results have consequences on several aspects of finite geometry. First of all, a necessary condition for an $(n-1)$-subspace $U$ and a regulus $\\cR$ of $(n-1)$-subspaces to be extendable to a Desarguesian spread is given. The description also allows to improve results in \\cite{BaJa12} on the Andr\\'e-Bruck-Bose representation of a $q$-subline in $\\PG(2,q^n)$. Furtherm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1081","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"}