{"paper":{"title":"Upper bounds for $s$-distance sets and equiangular lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Alexey Glazyrin, Wei-Hsuan Yu","submitted_at":"2016-11-29T04:06:20Z","abstract_excerpt":"The set of points in a metric space is called an $s$-distance set if pairwise distances between these points admit only $s$ distinct values. Two-distance spherical sets with the set of scalar products $\\{\\alpha, -\\alpha\\}$, $\\alpha\\in[0,1)$, are called equiangular. The problem of determining the maximum size of $s$-distance sets in various spaces has a long history in mathematics. We suggest a new method of bounding the size of an $s$-distance set in compact two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-dista"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09479","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"}