On Plethysm conjectures of Stanley and Foulkes

Independently Siemons and Wagner [I.J. Siemons, O. Wagner, private communication, 1986] and Stanley [R.P. Stanley, Positivity problems and conjectures in algebraic combinatorics, in: Mathematics: Frontiers and Perspectives, Amer. Math. Soc., 2000, pp. 295–319] conjecture that if a partition λ dominates its conjugate partition λ′ then an FSn-homomorphism is injective. We demonstrate a method of adding columns to the partition λ that preserves the injectivity of ψλ.