On Plethysm Conjectures of Stanley and Foulkes: The $2 \times n$ Case

  • Pavlo Pylyavskyy


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