{"paper":{"title":"On sequences of projections of the cubic lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Antonio Campello, Jo\\~ao Strapasson","submitted_at":"2011-10-13T16:20:14Z","abstract_excerpt":"In this paper we study sequences of lattices which are, up to similarity, projections of $\\mathbb{Z}^{n+1}$ onto a hyperplane $\\bm{v}^{\\perp}$, with $\\bm{v} \\in \\mathbb{Z}^{n+1}$ and converge to a target lattice $\\Lambda$ which is equivalent to an integer lattice. We show a sufficient condition to construct sequences converging at rate $O(1/ |\\bm{v}|^{2/n})$ and exhibit explicit constructions for some important families of lattices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2995","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"}