# Flagged Grothendieck polynomials

## TL;DR

This paper introduces a determinant formula for flagged Grothendieck polynomials, generalizing previous work, and extends the concept to flagged skew Grothendieck polynomials, establishing their equivalence.

## Contribution

The paper provides a Jacobi-Trudi type determinant expression for flagged Grothendieck polynomials and introduces flagged skew Grothendieck polynomials, proving their equivalence.

## Key findings

- Derived a determinant formula for flagged Grothendieck polynomials
- Extended the framework to flagged skew Grothendieck polynomials
- Proved the equivalence of two expressions for flagged skew Grothendieck polynomials

## Abstract

We show that the flagged Grothendieck polynomials defined as the generating functions of flagged set-valued tableaux of Knutson-Miller-Yong can be expressed by a Jacobi-Trudi type determinant formula generalizing the work of Hudson-Matsumura. We also introduce the flagged skew Grothendieck polynomials in these two expressions and show that they coincide.