Jacobi–Trudi formulas for flagged refined dual stable Grothendieck polynomials

Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. The polynomials defined as a generating function for reverse plane partitions of given shape. They interpolate between Schur by Lam Pylyavskyy 2007. Flagged more version where lower upper bounds entries each row or column. In this paper Jacobi--Trudi-type formulas flagged proved using plethystic substitution. This resolves conjecture Grinberg generalizes result Iwao Amanov--Yeliussizov.