Residues, Grothendieck Polynomials, and K-Theoretic Thom Polynomials

Abstract Grothendieck polynomials were introduced by Lascoux and Schützenberger play an important role in K-theoretic Schubert calculus. In this paper, we give a new definition of double stable based on iterated residue operation. We illustrate the power our calculating expansion Thom ${\mathcal {A}}_{2}$ singularities. present two versions: one displays its stabilization property, while other expected finiteness property.