  The problem of computing products of Schubert classes in the cohomology ring
can be formulated as the problem of expanding skew Schur polynomials into the
basis of ordinary Schur polynomials. In contrast, the problem of computing the
structure constants of the Grothendieck ring of a Grassmannian variety with
respect to its basis of Schubert structure sheaves is not equivalent to
expanding skew stable Grothendieck polynomials into the basis of ordinary
stable Grothendiecks. Instead, we show that the appropriate K-theoretic analogy
is through the expansion of skew reverse plane partitions into the basis of
polynomials which are Hopf-dual to stable Grothendieck polynomials. We
combinatorially prove this expansion is determined by Yamanouchi set-valued
tableaux. A by-product of our results is a dual approach proof for Buch's
K-theoretic Littlewood-Richardson rule for the product of stable Grothendieck
polynomials.
