{"paper":{"title":"New necessary conditions for (negative) Latin square type partial difference sets in abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zeying Wang","submitted_at":"2019-05-09T16:13:00Z","abstract_excerpt":"Partial difference sets (for short, PDSs) with parameters ($n^2$, $r(n-\\epsilon)$, $\\epsilon n+r^2-3\\epsilon r$, $r^2-\\epsilon r$) are called Latin square type (respectively negative Latin square type) PDSs if $\\epsilon=1$ (respectively $\\epsilon=-1$). In this paper, we will give restrictions on the parameter $r$ of a (negative) Latin square type partial difference set in an abelian group of non-prime power order. As far as we know no previous general restrictions on $r$ were known. Our restrictions are particularly useful when $a$ is much larger than $b$. As an application, we show that if th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03730","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"}