A generalisation of core partitions

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 λ is at most the s-weight of λ  . Then we consider the set Cs:tCs:t of partitions for which equality holds, which we call [s:t][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][s:t]-cores is a union of finitely many orbits for an action of a Coxeter group of type A˜s−1×A˜t−1 on the set of partitions. We also consider the problem of constructing an [s:t][s:t]-core with specified s-core and t-core.