Coincidences among skew stable and dual stable Grothendieck polynomials

Abstract

The question of when two skew Young diagrams produce the same skew Schur function has been well studied. We investigate the same question in the case of stable Grothendieck polynomials, which are the $K$-theoretic analogues of the Schur functions. We prove a necessary condition for two skew shapes to give rise to the same dual stable Grothendieck polynomial. We also provide a necessary and sufficient condition in the case where the two skew shapes are ribbons.