The GrunbaumKalaiSarkaria conjecture

Let $\Delta$ be a simplicial complex of dimension $d$. Assume that $\Delta$ admits a PL embedding into $\mathbb{R}^{2d}$. GrunbaumKalaiSarkaria conjecture. Then

$$f_d(\Delta)\leq (d+2)f_{d-1}(\Delta).$$

This conjecture seeks sharp face-number bounds for complexes PL-embedded in the highest dimension where nontrivial obstructions to embedding occur. The source discusses it as an application of the weak Lefschetz property, but does not state a resolution here.