{"paper":{"title":"Representability of Lyndon-Maddux relation algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Jeremy F. Alm","submitted_at":"2017-03-18T16:08:18Z","abstract_excerpt":"In Alm-Hirsch-Maddux (2016), relation algebras $\\mathfrak{L}(q,n)$ were defined that generalize Roger Lyndon's relation algebras from projective lines, so that $\\mathfrak{L}(q,0)$ is a Lyndon algebra. In that paper, it was shown that if $q>2304n^2+1$, $\\mathfrak{L}(q,n)$ is representable, and if $q<2n$, $\\mathfrak{L}(q,n)$ is not representable. In the present paper, we reduced this gap by proving that if $q\\geq n(\\log n)^{1+\\varepsilon}$, $\\mathfrak{L}(q,n)$ is representable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06314","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"}