Formulas for the expansion of the plethysms s2[S(a,b)] and S2[S(nk)] Original Research Article

Building on the ideas of Carbonara, Remmel, and Yang who, recently, gave explicit formulas for the Schur function expansion of the plethysms s2[Sμ] and s12[Sμ] where μ is a hook shape, we derive explicit formulas for the Schur function expansion of the plethysms s2[Sμ] and s12 [Sμ] where μ has two rows or two columns. These formulas generalize classical formulas of Littlewood for the Schur function expansions of s2[S(n)] and s12[S(n)]. We also derive explicit formulas for s2[Sλ] and s12 [Sλ] where λ = (nk) for some k and n.