The "Grothendieck to Lascoux" conjecture

2021/02/24 by Reiner, Victor, Yong, Alexander
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.12399

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.

Related

• Grothendieck to Lascoux expansions
• Lascoux expansion of the product of a Lascoux and a stable Grothendieck
• Connection between Schubert polynomials and top Lascoux polynomials
• Changing Bases with Pipe Dream Combinatorics
• Set-valued tableaux rule for Lascoux polynomials