  We consider Kingman's partition structures which are regenerative with
respect to a general operation of random deletion of some part. Prototypes of
this class are the Ewens partition structures which Kingman characterised by
regeneration after deletion of a part chosen by size-biased sampling. We
associate each regenerative partition structure with a corresponding
regenerative composition structure, which (as we showed in a previous paper)
can be associated in turn with a regenerative random subset of the positive
halfline, that is the closed range of a subordinator. A general regenerative
partition structure is thus represented in terms of the Laplace exponent of an
associated subordinator. We also analyse deletion properties characteristic of
the two-parameter family of partition structures.
