The "Grothendieck to Lascoux" conjecture

TL;DR

This paper proposes a conjectural combinatorial rule that expands Grothendieck polynomials into Lascoux polynomials, generalizing previous formulas for Schubert and stable Grothendieck polynomials.

Contribution

It introduces a new conjectural rule linking Grothendieck and Lascoux polynomials, extending known formulas for related polynomial families.

Findings

Formulation of a conjectural combinatorial rule

Generalization of formulas for Schubert and stable Grothendieck polynomials

Refinement of existing polynomial expansion formulas

Abstract

This report formulates a conjectural combinatorial rule that positively expands Grothendieck polynomials into Lascoux polynomials. It generalizes one such formula expanding Schubert polynomials into key polynomials, and refines another one expanding stable Grothendieck polynomials.