{"paper":{"title":"A word property for twisted involutions in Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Axel Hultman, Mikael Hansson","submitted_at":"2017-04-26T19:54:14Z","abstract_excerpt":"Given an involutive automorphism $\\theta$ of a Coxeter system $(W,S)$, let $\\mathfrak{I}(\\theta) \\subseteq W$ denote the set of twisted involutions. We provide a minimal set of moves that can be added to the braid moves, in order to connect all reduced $\\underline{S}$-expressions (also known as admissible sequences, reduced $I_\\theta$-expressions, or involution words) for any given $w \\in \\mathfrak{I}(\\theta)$. This can be viewed as an analogue of the well-known word property for Coxeter groups. It improves upon a result of Hamaker, Marberg, and Pawlowski, and generalises similar statements va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08329","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"}