## Regenerative partition structures

Venue: | Electron. J. Combin. 11 Research Paper |

Citations: | 14 - 7 self |

### BibTeX

@ARTICLE{Gnedin_regenerativepartition,

author = {Er Gnedin and Jim Pitman},

title = {Regenerative partition structures},

journal = {Electron. J. Combin. 11 Research Paper},

year = {},

pages = {2120107}

}

### OpenURL

### Abstract

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.