The stable Grothendieck Lam–Postnikov–Pylyavskyy inequality

Let $\lambda$ and $\mu$ be partitions, and let $\widetilde G_\lambda(\mathbf x)$ denote the stable Grothendieck polynomial. Write $\lambda\vee\mu$ and $\lambda\wedge\mu$ for the join and meet of the two partitions, and interpret $\leq_{\widetilde G}$ as the stable Grothendieck positivity order. Stable Grothendieck LPP inequality.

$$\widetilde G_\lambda(\mathbf x)\widetilde G_\mu(\mathbf x) \leq_{\widetilde G} \widetilde G_{\lambda\vee\mu}(\mathbf x)\widetilde G_{\lambda\wedge\mu}(\mathbf x).$$

This is the Grassmannian specialization of the vexillary Grothendieck inequality and was previously predicted by Thomas and Yong. It remains open.