  Suppose $s$ and $t$ are coprime natural numbers. A theorem of Olsson says
that the $t$-core of an $s$-core partition is again an $s$-core. We generalise
this theorem, showing that the $s$-weight of the $t$-core of a partition
$\lambda$ is at most the $s$-weight of $\lambda$. Then we consider the set
$\mathcal C_{s:t}$ of partitions for which equality holds, which we call
$[s{:}t]$-cores; this set has interesting structure, and we expect that it will
be the subject of future study. We show that the set of $[s{:}t]$-cores is a
union of finitely many orbits for an action of a Coxeter group of type $\tilde
A_{s-1}\times\tilde A_{t-1}$ on the set of partitions. We also consider the
problem of constructing an $[s{:}t]$-core with specified $s$-core and $t$-core.
