{"paper":{"title":"A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Alex Iosevich, David Covert, Derrick Hart, Ignacio Uriarte-Tuero, Steven Senger","submitted_at":"2010-09-21T03:44:47Z","abstract_excerpt":"We show that if $E \\subset \\mathbb{F}_q^d$, the $d$-dimensional vector space over the finite field with $q$ elements, and $|E| \\geq \\rho q^d$, where $ q^{-\\frac{1}{2}}\\ll \\rho \\leq 1$, then $E$ contains an isometric copy of at least $c \\rho^{d-1} q^{d+1 \\choose 2}$ distinct $(d+1)$-point configurations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3991","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"}