Foulkes' plethysm inequality conjecture

Let $a_\lambda(d[n])$ denote the plethysm coefficient indexed by a partition $\lambda\vdash nd$. Foulkes' conjecture. If $d>n$, then

$$a_\lambda(d[n])\geq a_\lambda(n[d])$$

for all $\lambda\vdash nd$.

This is a fundamental comparison problem for plethysm coefficients. The source gives no resolution.