  Composing two representations of the general linear groups gives rise to
Littlewood's (outer) plethysm. On the level of characters, this poses the
question of finding the Schur expansion of the plethysm of two Schur functions.
A combinatorial interpretation for the Schur expansion coefficients of the
plethysm of two Schur functions is, in general, still an open problem. We
identify a proof technique of combinatorial representation theory, which we
call the "$s$-perp trick", and point out several examples in the literature
where this idea is used. We use the $s$-perp trick to give algorithms for
computing monomial and Schur expansions of symmetric functions. In several
special cases, these algorithms are more efficient than those currently
implemented in {\sc SageMath}.
