{"paper":{"title":"Congruence classes of triangles in $\\mathbb{F}_p^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Le Anh Vinh, Pham Van Thang","submitted_at":"2016-10-24T13:40:48Z","abstract_excerpt":"In this short note, we give a lower bound on the number of congruence classes of triangles in a small set of points in $\\mathbb{F}_p^2$. More precisely, for $\\mathcal{A}\\subset \\mathbb{F}_p^2$ with $|\\mathcal{A}|\\le p^{2/3}$, we prove that the number of congruence classes of triangles determined by points in $\\mathcal{A}\\times \\mathcal{A}$ is at least $|\\mathcal{A}|^{7/2}$. This note is not intended for journal publication."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07408","kind":"arxiv","version":3},"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"}