{"paper":{"title":"On Lattice-Free Orbit Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.MG","authors_text":"Achill Sch\\\"urmann, Katrin Herr, Thomas Rehn","submitted_at":"2014-01-15T15:53:29Z","abstract_excerpt":"Given a permutation group acting on coordinates of $\\mathbb{R}^n$, we consider lattice-free polytopes that are the convex hull of an orbit of one integral vector. The vertices of such polytopes are called \\emph{core points} and they play a key role in a recent approach to exploit symmetry in integer convex optimization problems. Here, naturally the question arises, for which groups the number of core points is finite up to translations by vectors fixed by the group. In this paper we consider transitive permutation groups and prove this type of finiteness for the $2$-homogeneous ones. We provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3638","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"}