{"paper":{"title":"Density estimates for $k$-impassable lattices of balls and general convex bodies in ${\\Bbb R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"E. Makai, H. Martini, Jr.","submitted_at":"2016-12-05T11:03:54Z","abstract_excerpt":"G. Fejes T\\'oth posed the following problem: Determine the infimum of the densities of the lattices of closed balls in $\\bR^n$ such that each affine $k$-subspace $(0 \\le k \\le n-1)$ of $\\bR^n$ intersects some ball of the lattice. We give a lower estimate for any $n,k$ like above. If, in the problem posed by G. Fejes T\\'oth, we replace the ball $B^n$ by a (centrally symmetric) convex body $K\\subset \\bR^n$, we may ask for the infimum of all above infima of densities of lattices of translates of $K$ with the above property, when $K$ ranges over all (centrally symmetric) convex bodies in $\\bR^n$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01307","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"}