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Abstract
An explicit formula expressing the coefficients of the R̃-polynomials as a linear combinations of those of the corresponding R-polynomials is given. Several systems of inequalities satisfied by the coefficients of the R-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) non-negativity properties.
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