An orthodontia formula for Grothendieck polynomials

TL;DR

This paper introduces a new combinatorial operator formula for Grothendieck polynomials, extending Magyar's Demazure operator approach for Schubert polynomials, and applies it to establish a divisibility condition for monomials.

Contribution

It provides a novel combinatorial operator formula for Grothendieck polynomials, differing from previous geometric and representation theoretic methods.

Findings

New operator formula for Grothendieck polynomials

Purely combinatorial proofs contrasting previous approaches

Divisibility condition for monomials in Grothendieck polynomials

Abstract

We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools used by Magyar. We apply our formula to prove a necessary divisibility condition for a monomial to appear in a given Grothendieck polynomial.