{"paper":{"title":"Finding well approximating lattices for a finite set of points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. Hajdu, L. Hajdu, R. Tijdeman","submitted_at":"2016-04-20T14:59:50Z","abstract_excerpt":"In this paper we address the problem of finding well approximating lattices for a given finite set $A$ of points in ${\\mathbb R}^n$. More precisely, we search for $\\v{o},\\v{d_1}, \\dots,\\v{d_n}\\in \\mathbb{R}^n$ such that $\\v{a}-\\v{o}$ is close to $\\Lambda=\\v{d_1}\\mathbb{Z}+\\dots+\\v{d_n}\\mathbb{Z}$ for every $\\v{a}\\in A$. First we deal with the one-dimensional case, where we show that in a sense the results are almost the best possible. These results easily extend to the multi-dimensional case where the directions of the axes are given, too. Thereafter we treat the general multi-dimensional case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05989","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"}