{"paper":{"title":"A geometric characterization of known maximum scattered linear sets of $\\mathrm{PG}(1,q^n)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Giovanni Giuseppe Grimaldi, Giovanni Longobardi, Rocco Trombetti, Somi Gupta","submitted_at":"2024-05-02T15:15:24Z","abstract_excerpt":"An $\\mathbb{F}_q$- linear set $L=L_U$ of $\\Lambda=\\mathrm{PG}(V, \\mathbb{F}_{q^n}) \\cong \\mathrm{PG}(r-1,q^n)$ is a set of points defined by non-zero vectors of an $\\mathbb{F}_q$-subspace $U$ of $V$. The integer $\\dim_{\\mathbb{F}_q} U$ is called the rank of $L$. In [G. Lunardon, O. Polverino: Translation ovoids of orthogonal polar spaces. Forum Math. 16 (2004)], it was proven that any $\\mathbb{F}_q$-linear set $L$ of $\\Lambda$ of rank $u$ such that $\\langle L \\rangle=\\Lambda$ is either a canonical subgeometry of $\\Lambda$ or there are a $(u-r-1)$-dimensional subspace $\\Gamma$ of $\\mathrm{PG}(u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.01374","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.01374/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}