On plethysm conjectures of Stanley and Foulkes: the 2 × n case

الأصل · EN

We prove Stanley's plethysm conjecture for the 2 × n case, which composed with the work of Black and List provides another proof of Foulkes conjecture for the 2 × n case. We also show that the way Stanley formulated his conjecture, it is false in general, and suggest an alternative formulation.