{"paper":{"title":"(t,s)-racks and their link invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Jessica Ceniceros, Sam Nelson","submitted_at":"2010-11-24T18:54:11Z","abstract_excerpt":"A (t,s)-rack is a rack structure defined on a module over the ring $\\ddot\\Lambda=\\mathbb{Z}[t^{\\pm 1},s]/(s^2-(1-t)s)$. We identify necessary and sufficient conditions for two $(t,s)$-racks to be isomorphic. We define enhancements of the rack counting invariant using the structure of (t,s)-racks and give some computations and examples. As an application, we use these enhanced invariants to obtain obstructions to knot ordering."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5455","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"}