{"paper":{"title":"Deep lattice points in zonotopes, lonely runners, and lonely rabbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.MG","authors_text":"Matthias Beck, Matthias Schymura","submitted_at":"2023-01-28T12:46:39Z","abstract_excerpt":"Let $K \\subseteq \\mathbb{R}^d$ be a convex body and let $\\mathbf{w} \\in \\operatorname{int}(K)$ be an interior point of $K$. The coefficient of asymmetry $\\operatorname{ca}(K,\\mathbf{w}) := \\min\\{ \\lambda \\geq 1 : \\mathbf{w} - K \\subseteq \\lambda (K - \\mathbf{w}) \\}$ has been studied extensively in the realm of Hensley's conjecture on the maximal volume of a $d$-dimensional lattice polytope that contains a fixed positive number of interior lattice points. We study the coefficient of asymmetry for lattice zonotopes, i.e., Minkowski sums of line segments with integer endpoints. Our main result gi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.12182","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.12182/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}