{"paper":{"title":"Coherent configurations over copies of association schemes of prime order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mitsugu Hirasaka, Reza Sharafdini","submitted_at":"2013-09-15T05:32:24Z","abstract_excerpt":"Let $G$ be a group acting faithfully and transitively on $\\Omega_i$ for $i=1,2$. A famous theorem by Burnside implies the following fact: If $|\\Omega_1|=|\\Omega_2|$ is a prime and the rank of one of the actions is greater than two, then the actions are equivalent, or equivalently $|(\\alpha,\\beta)^G|=|\\Omega_1|=|\\Omega_2|$ for some $(\\alpha,\\beta)\\in \\Omega_1\\times \\Omega_2$.\n  In this paper we consider a combinatorial analogue to this fact through the theory of coherent configurations, and give some arithmetic sufficient conditions for a coherent configuration with two homogeneous components o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3725","kind":"arxiv","version":3},"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"}