2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71682We 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.5 pages, 3 figuresCombinatorics05E10text