{"paper":{"title":"Persistent Subdivisions of Coxeter Permutahedra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jes\\'us A. De Loera, Melissa Sherman-Bennett, Timothy Blanton","submitted_at":"2026-06-27T01:41:35Z","abstract_excerpt":"We investigate the realizations of Coxeter permutahedra which are also Coxeter matroid polytopes; these are polytopes of the form $\\mathrm{conv}(W \\cdot \\mathbf{a})$ where $W$ is a finite Coxeter group acting on $\\mathbb{R}^n$ and $\\mathbf{a}$ is generic. Our main focus is how the geometric properties of $\\mathrm{conv}(W \\cdot \\mathbf{a})$ change as $\\mathbf{a}$ changes, with particular attention to persistent simplices, triangulations, and subdivisions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28680","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28680/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}