A Lam–Postnikov–Pylyavskyy inequality for hybrid Grothendieck polynomials

We prove a multivariate Lam–Postnikov–Pylyavskyy(LPP)-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 LPP inequality and a conjecture by Thomas–Yong to the (equivariant) Schubert and Grothendieck polynomial setting.