{"paper":{"title":"Improved bounds on the diameter of lattice polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OC"],"primary_cat":"math.MG","authors_text":"Antoine Deza, Lionel Pournin","submitted_at":"2016-10-02T19:21:38Z","abstract_excerpt":"We show that the largest possible diameter $\\delta(d,k)$ of a $d$-dimensional polytope whose vertices have integer coordinates ranging between $0$ and $k$ is at most $kd-\\lceil2d/3\\rceil$ when $k\\geq3$. In addition, we show that $\\delta(4,3)=8$. This substantiates the conjecture whereby $\\delta(d,k)$ is at most $\\lfloor(k+1)d/2\\rfloor$ and is achieved by a Minkowski sum of lattice vectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00341","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"}