{"paper":{"title":"Simple dual braids, noncrossing partitions and Mikado braids of type $D_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Barbara Baumeister, Thomas Gobet","submitted_at":"2017-03-28T14:28:13Z","abstract_excerpt":"We show that the simple elements of the dual Garside structure of an Artin group of type $D_n$ are Mikado braids, giving a positive answer to a conjecture of Digne and the second author. To this end, we use an embedding of the Artin group of type $D_n$ in a suitable quotient of an Artin group of type $B_n$ noticed by Allcock, of which we give a simple algebraic proof here. This allows one to give a characterization of the Mikado braids of type $D_n$ in terms of those of type $B_n$ and also to describe them topologically. Using this topological representation and Athanasiadis and Reiner's model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09599","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"}