Unified framework for tableau models of Grothendieck polynomials

TL;DR

This paper introduces a unified combinatorial framework that proves dualities for Grothendieck polynomials and their refined versions, extending known results to new cases.

Contribution

It provides the first combinatorial proof of duality for refined Grothendieck polynomials using a unified tableau-based approach.

Findings

Established duality for refined Grothendieck polynomials

Unified combinatorial framework for various tableau models

Extended duality results to new refined cases

Abstract

We give combinatorial proofs of two types of duality for Grothendieck polynomials by constructing a unified combinatorial framework incorporating set-valued tableaux, musltiset-valued tableaux, reverse plane partitions and valued-set tableaux. Importantly, our proofs extend to proofs of these dualities for the refined Grothendieck polynomials. The second of these dualities was formerly unknown for the refined case.