{"paper":{"title":"Equitable 2-partitions of the Hamming graphs with the second eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Valyuzhenich, Ivan Mogilnykh","submitted_at":"2019-03-29T02:41:01Z","abstract_excerpt":"The eigenvalues of the Hamming graph $H(n,q)$ are known to be $\\lambda_i(n,q)=(q-1)n-qi$, $0\\leq i \\leq n$. The characterization of equitable 2-partitions of the Hamming graphs $H(n,q)$ with eigenvalue $\\lambda_{1}(n,q)$ was obtained by Meyerowitz in [15]. We study the equitable 2-partitions of $H(n,q)$ with eigenvalue $\\lambda_{2}(n,q)$. We show that these partitions are reduced to equitable 2-partitions of $H(3,q)$ with eigenvalue $\\lambda_{2}(3,q)$ with exception of two constructions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12333","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"}