{"paper":{"title":"Distinct spreads in vector spaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Lund, Le Anh Vinh, Thang Pham","submitted_at":"2016-11-17T16:32:26Z","abstract_excerpt":"In this short note, we study the distribution of spreads in a point set $\\mathcal{P} \\subseteq \\mathbb{F}_q^d$, which are analogous to angles in Euclidean space. More precisely, we prove that, for any $\\varepsilon > 0$, if $|\\mathcal{P}| \\geq (1+\\varepsilon) q^{\\lceil d/2 \\rceil}$, then $\\mathcal{P}$ generates a positive proportion of all spreads. We show that these results are tight, in the sense that there exist sets $\\mathcal{P} \\subset \\mathbb{F}_q^d$ of size $|\\mathcal{P}| = q^{\\lceil d/2 \\rceil}$ that determine at most one spread."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05768","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"}