  For any partition of $\{1, 2, ..., n\}$ we define its {\it increments} $X_i,
1 \le i \le n$ by $X_i = 1$ if $i$ is the smallest element in the partition
block that contains it, $X_i = 0$ otherwise. We prove that for partially
exchangeable random partitions (where the probability of a partition depends
only on its block sizes in order of appearance), the law of the increments
uniquely determines the law of the partition. One consequence is that the
Chinese Restaurant Process CRP($\theta$) (the partition with distribution given
by the Ewens sampling formula with parameter $\theta$) is the only exchangeable
random partition with independent increments.
