A superplethystic formula for superrestriction coefficients

The Schur superalgebra $S(m,n;d)$ contains $S_{m}\times S_{n}$ as a multiplicative subgroup. We consider the problem of determining the restriction coefficients when an irreducible supermodule of $S(m,n;d)$ is restricted to $S_{m}\times S_{n}$. We introduce the notion of superplethysm and provide a superplethystic variant of Littlewood's formula for these restriction coefficients. As an application, we provide several unimodality results for bipartite superpartitions.