An algebraic proof of determinant formulas of Grothendieck polynomials

TL;DR

This paper provides an algebraic proof for the determinant formulas of factorial Grothendieck polynomials, confirming their validity through an alternative approach.

Contribution

It introduces an algebraic proof for existing determinant formulas of factorial Grothendieck polynomials, expanding the theoretical understanding.

Findings

Validated determinant formulas algebraically

Confirmed previous combinatorial results

Enhanced theoretical framework for Grothendieck polynomials

Abstract

We give an algebraic proof of the determinant formulas for factorial Grothendieck polynomials obtained by Hudson--Ikeda--Matsumura--Naruse and by Hudson--Matsumura.