An explicit formula expressing the coefficients of the tilde R-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.
F. Caselli (2006). Non-negativity properties of R-polynomials. EUROPEAN JOURNAL OF COMBINATORICS, 27, 1005-1021 [10.1016/j.ejc.2005.03.005].
Non-negativity properties of R-polynomials
CASELLI, FABRIZIO
2006
Abstract
An explicit formula expressing the coefficients of the tilde R-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
