Kazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations

@article{Billey2000KazhdanLusztigPF,
  title={Kazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations},
  author={Sara C. Billey and Gregory S. Warrington},
  journal={Journal of Algebraic Combinatorics},
  year={2000},
  volume={13},
  pages={111-136}
}
AbstractIn (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials Px,w in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where $$W = \mathfrak{S}_n $$ (the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic on all subexpressions of any fixed reduced expression for w. As a… 
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