Ramos's conjecture for the Grünbaum–Hadwiger–Ramos function

Let $\Delta(j,k)$ be the minimal dimension $d$ of a Euclidean space $\mathbb{R}^d$ such that every collection of $j$ masses in $\mathbb{R}^d$ admits a $k$-arrangement equiparting all the masses. Ramos's conjecture.

$$\Delta(j,k)=\left\lceil \frac{2^k-1}{k}j\right\rceil$$

for every $j\geq 1$ and $k\geq 1$. The formula would determine the minimal dimension in the Grünbaum–Hadwiger–Ramos mass-partition problem. It is motivated by the lower bound derived from Avis's ideas and Ramos's work; the source presents the equality as a conjecture, with its general status unresolved.