{"paper":{"title":"A family of irretractable square-free solutions of the Yang-Baxter equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GR","authors_text":"David Bachiller, Eric Jespers, Ferran Cedo, Jan Okninski","submitted_at":"2015-11-24T16:01:25Z","abstract_excerpt":"A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. All these solutions are strong twisted unions of multipermutation solutions of multipermutation level at most two. A large subfamily consists of irretractable and square-free solutions. This subfamily includes a recent example of Vendramin, who first gave a counterexample to Gateva-Ivanova's Strong Conjecture. All the solutions in this subfamily are new counterexamples to Gateva-Ivanova's Strong Conjecture and also they answer a question of Cameron and Gateva-Ivanova. It is proved that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07769","kind":"arxiv","version":2},"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"}