{"paper":{"title":"Cubulation of Bruhat graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.RT","authors_text":"Alex Bishop, Anne Thomas, Elizabeth Mili\\'cevi\\'c","submitted_at":"2025-04-03T21:51:30Z","abstract_excerpt":"For $(W,S)$ an arbitrary Coxeter system and any $y \\in W$, we investigate the condition that the Bruhat graph for the interval $[1,y]$ can be cubulated, meaning roughly that this graph can be spanned by a product of subintervals of $\\mathbb{Z}$. Results of Carrell-Peterson and Elias-Williamson imply that if $[1,y]$ can be cubulated, then the Kazhdan-Lusztig polynomial $P_{x,y} = 1$ for all $x \\leq y$. We consider the converse to this result. For $(W,S)$ finite and $w_0$ the longest element in $W$, so that $P_{x,w_0} = 1$ for all $x \\in W$, we use normal form forests to construct cubulations of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.03046","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"}