{"paper":{"title":"On finitely generated closures in the theory of cutting planes","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":"2011-10-18T13:13:50Z","abstract_excerpt":"Let $P$ be a rational polyhedron in $\\mathbb{R}^d$ and let $\\mathcal{L}$ be a class of $d$-dimensional maximal lattice-free rational polyhedra in $\\mathbb{R}^d$. For $L \\in \\mathcal{L}$ by $R_L(P)$ we denote the convex hull of points belonging to $P$ but not to the interior of $L$. Andersen, Louveaux and Weismantel showed that if the so-called max-facet-width of all $L \\in \\mathcal{L}$ is bounded from above by a constant independent of $L$, then $\\bigcap_{L\\in \\mathcal{L}} R_L(P)$ is a rational polyhedron. We give a short proof of a generalization of this result. We also give a characterizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3967","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"}