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

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.