{"paper":{"title":"On the Smith normal form of a skew-symmetric D-optimal design of order $n\\equiv 2\\pmod{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary Greaves, Sho Suda","submitted_at":"2018-01-23T12:48:47Z","abstract_excerpt":"We show that the Smith normal form of a skew-symmetric D-optimal design of order $n\\equiv 2\\pmod{4}$ is determined by its order. Furthermore, we show that the Smith normal form of such a design can be written explicitly in terms of the order $n$, thereby proving a recent conjecture of Armario. We apply our result to show that certain D-optimal designs of order $n\\equiv 2\\pmod{4}$ are not equivalent to any skew-symmetric D-optimal design. We also provide a correction to a result in the literature on the Smith normal form of D-optimal designs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07516","kind":"arxiv","version":2},"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"}