{"paper":{"title":"The maximum number of points in the cross-polytope that form a packing set of a scaled cross-polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Ji Hoon Chun","submitted_at":"2019-08-15T17:47:21Z","abstract_excerpt":"The problem of finding the largest number of points in the unit cross-polytope such that the $l_{1}$-distance between any two distinct points is at least $2r$ is investigated for $r\\in\\left(1-\\frac{1}{n},1\\right]$ in dimensions $\\geq2$ and for $r\\in\\left(\\frac{1}{2},1\\right]$ in dimension $3$. For the $n$-dimensional cross-polytope, $2n$ points can be placed when $r\\in\\left(1-\\frac{1}{n},1\\right]$. For the three-dimensional cross-polytope, $10$ and $12$ points can be placed if and only if $r\\in\\left(\\frac{3}{5},\\frac{2}{3}\\right]$ and $r\\in\\left(\\frac{4}{7},\\frac{3}{5}\\right]$ respectively, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05650","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/1908.05650/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"}