Schubert polynomials \(\mathfrak {S}_w\) are polynomial representatives for cohomology classes of Schubert varieties in a complete flag variety, while Grothendieck polynomials \(\mathfrak {G}_w\) are analogous representatives for the K-theory classes of the structure sheaves of Schubert varieties. In the special case that \(\mathfrak {S}_w\) is a multiplicity-free sum of monomials, K. Mészáros, L. Setiabrata, and A. St. Dizier conjectured that \(\mathfrak {G}_w\) can be easily computed from \(\mathfrak {S}_w\) via Möbius inversion on a certain poset. We prove this conjecture. Our approach is to realize monomials as Chow classes on a product of projective spaces and invoke a result of M. Brion on flat degenerations of such classes.
