  We consider Buch's rule for K-theory of the Grassmannian, in the Schur
multiplicity-free cases classified by Stembridge. Using a result of Knutson,
one sees that Buch's coefficients are related to Moebius inversion. We give a
direct combinatorial proof of this by considering the product expansion for
Grassmannian Grothendieck polynomials. We end with an extension to the
multiplicity-free cases of Thomas and Yong.
