{"paper":{"title":"Difference between families of weakly and strongly maximal integral lattice-free polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MG","math.OC"],"primary_cat":"math.CO","authors_text":"Gennadiy Averkov","submitted_at":"2018-07-17T10:40:08Z","abstract_excerpt":"A $d$-dimensional closed convex set $K$ in $\\mathbb{R}^d$ is said to be lattice-free if the interior of $K$ is disjoint with $\\mathbb{Z}^d$. We consider the following two families of lattice-free polytopes: the family $\\mathcal{L}^d$ of integral lattice-free polytopes in $\\mathbb{R}^d$ that are not properly contained in another integral lattice-free polytope and its subfamily $\\mathcal{M}^d$ consisting of integral lattice-free polytopes in $\\mathbb{R}^d$ which are not properly contained in another lattice-free set. It is known that $\\mathcal{M}^d = \\mathcal{L}^d$ holds for $d \\le 3$ and, for e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06327","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"}