{"paper":{"title":"Covering lattice points by subspaces and counting point-hyperplane incidences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Josef Cibulka, Martin Balko, Pavel Valtr","submitted_at":"2017-03-14T22:15:50Z","abstract_excerpt":"Let $d$ and $k$ be integers with $1 \\leq k \\leq d-1$. Let $\\Lambda$ be a $d$-dimensional lattice and let $K$ be a $d$-dimensional compact convex body symmetric about the origin. We provide estimates for the minimum number of $k$-dimensional linear subspaces needed to cover all points in $\\Lambda \\cap K$. In particular, our results imply that the minimum number of $k$-dimensional linear subspaces needed to cover the $d$-dimensional $n \\times \\cdots \\times n$ grid is at least $\\Omega(n^{d(d-k)/(d-1)-\\varepsilon})$ and at most $O(n^{d(d-k)/(d-1)})$, where $\\varepsilon>0$ is an arbitrarily small c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04767","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"}