{"paper":{"title":"Inversion arrangements and Bruhat intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Axel Hultman","submitted_at":"2010-10-04T09:26:38Z","abstract_excerpt":"Let $W$ be a finite reflection group. For a given $w \\in W$, the following assertion may or may not be satisfied:\n  (*) The principal Bruhat order ideal of $w$ contains as many elements as there are regions in the inversion hyperplane arrangement of $w$.\n  We present a type independent combinatorial criterion which characterises the elements $w\\in W$ that satisfy (*). A couple of immediate consequences are derived:\n  (1) The criterion only involves the order ideal of $w$ as an abstract poset. In this sense, (*) is a poset-theoretic property.\n  (2) For $W$ of type $A$, another characterisation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0515","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"}