{"paper":{"title":"Partial Difference Sets in $C_{2^n} \\times C_{2^n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ken W. Smith, Martin E. Malandro","submitted_at":"2018-11-27T19:50:49Z","abstract_excerpt":"We give an algorithm for enumerating the regular nontrivial partial difference sets (PDS) in the group $G_n = C_{2^n}\\times C_{2^n}$. We use our algorithm to obtain all of these PDS in $G_n$ for $2\\leq n\\leq 9$, and we obtain partial results for $n=10$ and $n=11$. Most of these PDS are new. For $n\\le 4$ we also identify group-inequivalent PDS. Our approach involves constructing tree diagrams and canonical colorings of these diagrams. Both the total number and the number of group-inequivalent PDS in $G_n$ appear to grow super-exponentially in $n$. For $n=9$, a typical canonical coloring represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11223","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"}