{"paper":{"title":"New Upper Bounds for Equiangular Lines by Pillar Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Emily J. King, Xiaoxian Tang","submitted_at":"2016-06-10T10:23:56Z","abstract_excerpt":"We derive a procedure for computing an upper bound on the number of equiangular lines in various Euclidean vector spaces by generalizing the classical pillar decomposition developed by (Lemmens and Seidel, 1973); namely, we use linear algebra and combinatorial arguments to bound the number of vectors within an equiangular set which have inner products of certain signs with a negative clique. After projection and rescaling, such sets are also certain spherical two-distance sets, and semidefinite programming techniques may be used to bound the size. Applying our method, we prove new relative bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03259","kind":"arxiv","version":4},"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"}