{"paper":{"title":"From Tarski's plank problem to simultaneous approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.MG","authors_text":"Andrey B. Kupavskii, J\\'anos Pach","submitted_at":"2015-11-25T16:45:39Z","abstract_excerpt":"A {\\em slab} (or plank) of width $w$ is a part of the $d$-dimensional space that lies between two parallel hyperplanes at distance $w$ from each other. It is conjectured that any slabs $S_1, S_2,\\ldots$ whose total width is divergent have suitable translates that altogether cover $\\mathbb{R}^d$. We show that this statement is true if the widths of the slabs, $w_1, w_2,\\ldots$, satisfy the slightly stronger condition $\\limsup_{n\\rightarrow\\infty}\\frac{w_1+w_2+\\ldots+w_n}{\\log(1/w_n)}>0$. This can be regarded as a converse of Bang's theorem, better known as Tarski's plank problem.\n  We apply our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08111","kind":"arxiv","version":2},"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"}