Proof of a conjectured Mobius inversion formula for Grothendieck polynomials

Schubert polynomials G(w) are polynomial representatives for cohomology classes of Schubert varieties in a complete flag variety, while Grothendieck polynomials G(w) are analogous representatives for the K-theory classes of the structure sheaves of Schubert varieties. In the special case that G(w) is a multiplicity-free sum of monomials, K. Meszaros, L. Setiabrata, and A. St. Dizier conjectured that G(w) can be easily computed from G(w) via Mobius 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.