The coefficients of the Kazhdan–Lusztig polynomials are nonnegative integers that are upper semicontinuous relative to Bruhat order. Conjecturally, the same properties hold for -polynomials of local rings of Schubert varieties. This suggests a parallel between the two families of polynomials. We prove our conjectures for Grassmannians, and more generally, covexillary Schubert varieties in complete flag varieties, by deriving a combinatorial formula for . We introduce drift configurations to formulate a new and compatible combinatorial rule for . From our rules we deduce, for these cases, the coefficient-wise inequality .
Li Li. Alexander Yong. "Kazhdan–Lusztig polynomials and drift configurations." Algebra Number Theory 5 (5) 595 - 626, 2011. https://doi.org/10.2140/ant.2011.5.595