{"paper":{"title":"Uniqueness of Butson Hadamard matrices of small degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hirasaka Mitsugu, Kyoung-Tark Kim, Yoshihiro Mizoguchi","submitted_at":"2014-02-27T07:07:21Z","abstract_excerpt":"For positive integers $m$ and $n$, we denote by $\\mathrm{BH}(m,n)$ the set of all $H\\in M_{n\\times n}(\\mathbb{C})$ such that $HH^\\ast=nI_n$ and each entry of $H$ is an $m$-th root of unity where $H^\\ast$ is the adjoint matrix of $H$ and $I_n$ is the identity matrix.\n  For $H_1,H_2\\in \\mathrm{BH}(m,n)$ we say that $H_1$ is \\textit{equivalent} to $H_2$ if $H_1=PH_2 Q$ for some monomial matrices $P, Q$ whose nonzero entries are $m$-th roots of unity.\n  In this paper we classify $\\mathrm{BH}(17,17)$ up to equivalence by computer search."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6807","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"}