Coincidences among skew dual stable Grothendieck polynomials

TL;DR

This paper explores when two skew shapes produce identical dual stable Grothendieck polynomials, providing necessary conditions and a complete characterization for ribbons, advancing understanding in K-theoretic symmetric functions.

Contribution

It establishes necessary conditions for equality of dual stable Grothendieck polynomials and fully characterizes this for ribbon shapes, extending classical results to K-theoretic analogues.

Findings

Necessary condition for equality of dual stable Grothendieck polynomials

Complete characterization for ribbons

Extension of classical skew shape results to K-theoretic case

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.