{"paper":{"title":"Coloring link diagrams by Alexander quandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Yongju Bae","submitted_at":"2011-05-18T17:19:20Z","abstract_excerpt":"In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial $\\Delta_{L}(t)$ is vanishing, then $L$ admits a non-trivial coloring by any non-trivial Alexander quandle $Q$, and that if $\\Delta_{L}(t)=1$, then $L$ admits only the trivial coloring by any Alexander quandle $Q$, also show that if $\\Delta_{L}(t)\\not=0, 1$, then $L$ admits a non-trivial coloring by the Alexander quandle $\\Lambda/(\\Delta_{L}(t))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3695","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"}