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.
Non-negativity properties of R-polynomials / F. Caselli. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - STAMPA. - 27:(2006), pp. 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.
