  Jantzen-Seitz partitions are those $p$-regular partitions of~$n$ which label
$p$-modular irreducible representations of the symmetric group $S_n$ which
remain irreducible when restricted to $S_{n-1}$; they have recently also been
found to be important for certain exactly solvable models in statistical
mechanics. In this article we study their combinatorial properties via a
detailed analysis of their residue symbols; in particular the $p$-cores of
Jantzen-Seitz partitions are determined.
