## Fragmentation of ordered partitions and intervals.(English)Zbl 1109.60058

Summary: Fragmentation processes of exchangeable partitions have already been studied by several authors. This paper deals with fragmentations of exchangeable compositions, i.e. partitions of $$\mathbb N$$ in which the order of the blocks matters. We will prove that such a fragmentation is bijectively associated to an interval fragmentation. Using this correspondence, we then study two examples: Ruelle’s interval fragmentation and the interval fragmentation derived from the standard additive coalescent.

### MSC:

 60J25 Continuous-time Markov processes on general state spaces 60G09 Exchangeability for stochastic processes
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