{"paper":{"title":"Geometry of the inversion in a finite field and partitions of ${\\mathrm{PG}}(2^k-1,q)$ in normal rational curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Corrado Zanella, Michel Lavrauw","submitted_at":"2013-11-18T09:45:11Z","abstract_excerpt":"Let $L=\\mathbb F_{q^n}$ be a finite field and let $F=\\mathbb F_q$ be a subfield of $L$.\n  Consider $L$ as a vector space over $F$ and the associated projective space that is isomorphic to ${\\mathrm{PG}}(n-1,q)$.\n  The properties of the projective mapping induced by $x\\mapsto x^{-1}$ have been studied in \\cite{Cs13,Fa02,Ha83,He85,Bu95}, where it is proved that the image of any line is a normal rational curve in some subspace.\n  In this note a more detailed geometric description is achieved.\n  Consequences are found related to mixed partitions of the projective spaces; in particular, it is prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4309","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"}