{"paper":{"title":"Incidences between planes over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Le Anh Vinh, Nguyen Duy Phuong, Thang Pham","submitted_at":"2015-10-12T23:03:35Z","abstract_excerpt":"We use methods from spectral graph theory to obtain bounds on the number of incidences between $k$-planes and $h$-planes in $\\mathbb{F}_q^d$ which generalize a recent result given by Bennett, Iosevich, and Pakianathan (2014). More precisely, we prove that the number of incidences between a set $\\mathcal{P}$ of $k$-planes and a set $\\mathcal{H}$ of $h$-planes with $h\\ge 2k+1$, which is denoted by $I(\\mathcal{P},\\mathcal{H})$, satisfies \\[\\left\\vert I(\\mathcal{P},\\mathcal{H})-\\frac{|\\mathcal{P}||\\mathcal{H}|}{q^{(d-h)(k+1)}}\\right\\vert \\lesssim q^{\\frac{(d-h)h+k(2h-d-k+1)}{2}}\\sqrt{|\\mathcal{P}|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03481","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"}