{"paper":{"title":"Packing and covering with balls on Busemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.MG","authors_text":"Bertrand Estellon, Guyslain Naves, Victor Chepoi","submitted_at":"2015-08-04T14:04:22Z","abstract_excerpt":"In this note we prove that for any compact subset $S$ of a Busemann surface $({\\mathcal S},d)$ (in particular, for any simple polygon with geodesic metric) and any positive number $\\delta$, the minimum number of closed balls of radius $\\delta$ with centers at $\\mathcal S$ and covering the set $S$ is at most 19 times the maximum number of disjoint closed balls of radius $\\delta$ centered at points of $S$: $\\nu(S) \\le \\rho(S) \\le 19\\nu(S)$, where $\\rho(S)$ and $\\nu(S)$ are the covering and the packing numbers of $S$ by ${\\delta}$-balls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00778","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"}