{"paper":{"title":"Affine vector space partitions and spreads of quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francesco Pavese, Somi Gupta","submitted_at":"2024-02-12T18:47:57Z","abstract_excerpt":"An affine spread is a set of subspaces of $\\mathrm{AG}(n, q)$ of the same dimension that partitions the points of $\\mathrm{AG}(n, q)$. Equivalently, an {\\em affine spread} is a set of projective subspaces of $\\mathrm{PG}(n, q)$ of the same dimension which partitions the points of $\\mathrm{PG}(n, q) \\setminus H_{\\infty}$; here $H_{\\infty}$ denotes the hyperplane at infinity of the projective closure of $\\mathrm{AG}(n, q)$. Let $\\mathcal{Q}$ be a non degenerate quadric of $H_\\infty$ and let $\\Pi$ be a generator of $\\mathcal{Q}$, where $\\Pi$ is a $t$-dimensional projective subspace. An affine spr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07882","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/2402.07882/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"}