Corpus ID: 119588404

A Class of Kazhdan-Lusztig R-Polynomials and q-Fibonacci Numbers

  title={A Class of Kazhdan-Lusztig R-Polynomials and q-Fibonacci Numbers},
  author={W. Chen and Neil J. Y. Fan and P. L. Guo and Michael X. X. Zhong},
  journal={arXiv: Combinatorics},
  • W. Chen, Neil J. Y. Fan, +1 author Michael X. X. Zhong
  • Published 2013
  • Mathematics
  • arXiv: Combinatorics
  • 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… CONTINUE READING


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