{"paper":{"title":"A proof of Lov\\'asz's theorem on maximal lattice-free sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.OC","authors_text":"Gennadiy Averkov","submitted_at":"2011-10-05T15:03:03Z","abstract_excerpt":"Let $K$ be a maximal lattice-free set in $\\mathbb{R}^d$, that is, $K$ is convex and closed subset of $\\mathbb{R}^d$, the interior of $K$ does not cointain points of $\\mathbb{Z}^d$ and $K$ is inclusion-maximal with respect to the above properties. A result of Lov\\'asz assert that if $K$ is $d$-dimensional, then $K$ is a polyhedron with at most $2^d$ facets, and the recession cone of $K$ is spanned by vectors from $\\mathbb{Z}^d$. A first complete proof of mentioned Lov\\'asz's result has been published in a paper of Basu, Conforti, Cornu\\'ejols and Zambelli (where the authors use Dirichlet's appr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1014","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"}