  The Chern-Schwartz-MacPherson (CSM) and motivic Chern (mC) classes of
Schubert cells in a Grassmannian are one parameter deformations of the
fundamental classes of the Schubert varieties in cohomology and K-theory
respectively. Like the fundamental classes, the deformed classes form a basis
for the cohomology and K-theory ring of the Grassmannian. The purpose of this
paper is to initiate the study of the structure constants associated to the
basis CSM and mC classes in terms of the combinatorics of polynomials. First,
we prove formulas for the structure constants of projective spaces that involve
binomial coefficients. Then, using residue calculus on wieght functions, we
describe the structure constants of projective spaces and certain related
structure constants of 2-plane Grassmannians as coefficients of explicit
polynomials in one variable. Finally, we propose an approach for obtaining more
general results in this direction, and make conjectures generalizing the
aformentioned results for projective spaces.
