  In 2007 Lam and Pylyavskyy found a combinatorial formula for the dual stable
Grothendieck polynomials, which are the dual basis of the stable Grothendieck
polynomials with respect to the Hall inner product. In 2016 Galashin, Grinberg,
and Liu introduced refined dual stable Grothendieck polynomials by putting
additional sequence of parameters in the combinatorial formula of Lam and
Pylyavskyy. Grinberg conjectured a Jacobi--Trudi type formula for refined dual
stable Grothendieck polynomials. In this paper this conjecture is proved by
using bijections of Lam and Pylyavskyy.
