{"paper":{"title":"Complex Lines with Restricted Angles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"Aidan Roy","submitted_at":"2013-06-05T04:19:52Z","abstract_excerpt":"This thesis is a study of large sets of unit vectors in $\\cx^n$ such that the absolute value of their standard inner products takes on only a small number of values.\n  We begin with bounds: what is the maximal size of a set of lines with only a given set of angles? We rederive a series of upper bounds originally due to Delsarte, Goethals and Seidel, but in a novel way using only zonal polynomials and linear algebra. In the process we get some new results about complex $t$-designs and also some new characterizations of tightness.\n  Next we consider constructions. We describe some generic constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0978","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"}