{"paper":{"title":"Intrinsic reflections in Coxeter systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bernhard M\\\"uhlherr, Koji Nuida","submitted_at":"2016-07-04T07:36:16Z","abstract_excerpt":"Let $(W,S)$ be a Coxeter system and let $s \\in S$. We call $s$ a right-angled generator of $(W,S)$ if $st = ts$ or $st$ has infinite order for each $t \\in S$. We call $s$ an intrinsic reflection of $W$ if $s \\in R^W$ for all Coxeter generating sets $R$ of $W$. We give necessary and sufficient conditions for a right-angled generator $s \\in S$ of $(W,S)$ to be an intrinsic reflection of $W$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00757","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"}