A Lam--Postnikov--Pylyavskyy inequality for hybrid Grothendieck polynomials

Abstract

We prove a multivariate Lam--Postnikov--Pylyavskyy type inequality for hybrid Grothendieck polynomials, unifying and refining results for stable and dual stable Grothendieck polynomials established by Chan--Chen--Pak--Soskin. We also conjecture extensions of the Lam--Postnikov--Pylyavskyy inequality and a conjecture by Thomas--Yong to the (equivariant) Schubert and Grothendieck polynomial setting.

28 pages