{"paper":{"title":"The small Kakeya sets in $T^{*}_{2}(\\mathcal{C})$, $\\mathcal{C}$ a conic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maarten De Boeck","submitted_at":"2016-01-14T10:12:45Z","abstract_excerpt":"A Kakeya set in the linear representation $T^{*}_{2}(\\mathcal{C})$, $\\mathcal{C}$ a non-singular conic, is the point set covered by a set of $q+1$ lines, one through each point of $\\mathcal{C}$. In this article we classify the small Kakeya sets in $T^{*}_{2}(\\mathcal{C})$. The smallest Kakeya sets have size $\\left\\lfloor\\frac{3q^{2}+2q}{4}\\right\\rfloor$, and all Kakeya sets with weight less than $\\left\\lfloor\\frac{3(q^{2}-1)}{4}\\right\\rfloor+q$ are classified: there are approximately $\\sqrt{\\frac{q}{2}}$ types."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03539","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"}