{"paper":{"title":"On parabolic Kazhdan-Lusztig R-polynomials for the symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Grace L.D. Zhang, Neil J.Y. Fan, Peter L. Guo","submitted_at":"2015-01-18T09:24:09Z","abstract_excerpt":"Parabolic $R$-polynomials were introduced by Deodhar as parabolic analogues of ordinary $R$-polynomials defined by Kazhdan and Lusztig. In this paper, we are concerned with the computation of parabolic $R$-polynomials for the symmetric group. Let $S_n$ be the symmetric group on $\\{1,2,\\ldots,n\\}$, and let $S=\\{s_i\\,|\\, 1\\leq i\\leq n-1\\}$ be the generating set of $S_n$, where for $1\\leq i\\leq n-1$, $s_i$ is the adjacent transposition. For a subset $J\\subseteq S$, let $(S_n)_J$ be the parabolic subgroup generated by $J$, and let $(S_n)^{J}$ be the set of minimal coset representatives for $S_n/(S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04275","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"}