{"paper":{"title":"A Class of Kazhdan-Lusztig R-Polynomials and q-Fibonacci Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael X.X. Zhong, Neil J.Y. Fan, Peter L. Guo, William Y.C. Chen","submitted_at":"2013-12-08T03:39:09Z","abstract_excerpt":"Let $S_n$ denote the symmetric group on $\\{1,2,\\ldots,n\\}$. For two permutations $u, v\\in S_n$ such that $u\\leq v$ in the Bruhat order, let $R_{u,v}(q)$ and $\\R_{u,v}(q)$ denote the Kazhdan-Lusztig $R$-polynomial and $\\R$-polynomial, respectively. Let $v_n=34\\cdots n\\, 12$, and let $\\sigma$ be a permutation such that $\\sigma\\leq v_n$. We obtain a formula for the $\\R$-polynomials $\\R_{\\sigma,v_n}(q)$ in terms of the $q$-Fibonacci numbers depending on a parameter determined by the reduced expression of $\\sigma$. When $\\sigma$ is the identity $e$, this reduces to a formula obtained by Pagliacci. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2170","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"}