  We give necessary conditions for the positivity of Littlewood-Richardson
coefficients and SXP coefficients. We deduce necessary conditions for the
positivity of the plethystic coefficients. Explicitly, our main result states
that if $S^\lambda(V)$ appears as a summand in the decomposition into
irreducibles of $S^\mu(S^\nu(V))$, then $\nu$'s diagram is contained in
$\lambda$'s diagram.
