Unified framework for tableau models of Grothendieck polynomials

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.