{"paper":{"title":"On Kazhdan--Lusztig basis elements having no reversal factorization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Spahiu, Jiayuan Wang, Mark Skandera, Tommy Parisi","submitted_at":"2026-05-20T20:48:39Z","abstract_excerpt":"For $w$ in the symmetric group $S_n$, let $\\widetilde C_w$ be the corresponding modified, signless Kazhdan--Lusztig basis element of the type-$A$ Hecke algebra $H_n(q)$. An extension [Ann. Comb. 25, no. 3 (2021) pp. 757--787] of a result of Deodhar [Geom. Dedicata 36, (1990) pp. 95--119] implies that any factorization of the form \\begin{equation*}\n  \\widetilde C_w = \\frac1{f(q)} \\widetilde C_{v^{(1)}} \\cdots \\widetilde C_{v^{(r)}},\n  \\end{equation*} with $v^{(1)},\\dotsc,v^{(r)}$ maximal elements of parabolic subgroups of $S_n$ and $f(q) \\in \\mathbb N[q]$ depending on these, provides cancellati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21733","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/2605.21733/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"}