{"paper":{"title":"Solid angles associated to Minkowski reduced bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Danny Nguyen","submitted_at":"2012-06-20T06:07:19Z","abstract_excerpt":"Given a lattice $\\Lambda \\subset \\mathbb{R}^n$, we consider its Minkowski reduced basis and the solid angle $\\Omega$ spanned by the basis vectors. Such a basis satisfies strong near-orthogonality conditions, which allow us to bound from above and below the measure of $\\Omega$. Sharp upper and lower bounds are derived for all rank $3$ and rank $4$ lattices so that $\\Omega$ always measures in between. Extreme cases happen when $\\Lambda$ is similar to the rectangular ($\\mathcal{R}$) or alternating ($\\mathcal{A}$) lattice. This result settles a question raised earlier by Fukshansky and Robins in c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4390","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"}