{"paper":{"title":"On the equivalence of linear sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bence Csajb\\'ok, Corrado Zanella","submitted_at":"2015-01-14T18:39:28Z","abstract_excerpt":"Let $L$ be a linear set of pseudoregulus type in a line $\\ell$ in $\\Sigma^*=\\mathrm{PG}(t-1,q^t)$, $t=5$ or $t>6$. We provide examples of $q$-order canonical subgeometries $\\Sigma_1,\\, \\Sigma_2 \\subset \\Sigma^*$ such that there is a $(t-3)$-space $\\Gamma \\subset \\Sigma^*\\setminus (\\Sigma_1 \\cup \\Sigma_2 \\cup \\ell)$ with the property that for $i=1,2$, $L$ is the projection of $\\Sigma_i$ from center $\\Gamma$ and there exists no collineation $\\phi$ of $\\Sigma^*$ such that $\\Gamma^{\\phi}=\\Gamma$ and $\\Sigma_1^{\\phi}=\\Sigma_2$.\n  Condition (ii) given in Theorem 3 in Lavrauw and Van de Voorde (Des. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03441","kind":"arxiv","version":2},"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"}