Non-negativity properties of R-polynomials

@article{Caselli2006NonnegativityPO,
  title={Non-negativity properties of R-polynomials},
  author={Fabrizio Caselli},
  journal={Eur. J. Comb.},
  year={2006},
  volume={27},
  pages={1005-1021}
}
An explicit formula expressing the coefficients of thẽ R-polynomials as a linear combinations of those of the corresponding R-polynomials is given. Several sys tems of inequalitie s satisfied by the coefficients of theR-polynomials are shown and applied to obtain a lower bound for the coefficient of q2 in Kazhdan–Lusztig polynomials. Finally we present a basis of the space of polynomials of a given degree with respect to which both Kazhdan–Lusztig and R-polynomials have some nice (conjectural… CONTINUE READING