  Exchangeable sequences of random probability measures (partitions of mass)
and their corresponding exchangeable bridges play an important role in a
variety of areas in probability, statistics and related areas, including
Bayesian statistics, physics, finance and machine learning. An area of
theoretical as well as practical interest, is the study of coagulation and
fragmentation operators on partitions of mass. In this regard, an interesting
but formidable question is the identification of operators and distributional
families on mass partitions that exhibit interesting duality relations. In this
paper we identify duality relations for a large sub-class of mixed
Poisson-Kingman models generated by a stable subordinator. Our results are
natural generalizations of the duality relations developed in Pitman, Bertoin
and Goldschmidt, and Dong, Goldschmidt and Martin for the two-parameter Poisson
Dirichlet family. These results are deduced from results for corresponding
bridges.
