I want to apply statistical analysis, in particular work with various measurements on the absolute frequency of blocks of a fixed cardinality in a finite partition. I've found a convoluted and ugly looking way to describe this using degree sequences of graphs, though I'm wondering if there is some nicer standard definition for extracting this information like one does with the cycle type of a permutation. As I'd rather not be making up a bunch of definitions/notation if I don't have to.
To be precise I'm trying to get a multiset or a sequence of the cardinalities of each set in a finite partition. However if possible I don't want to make up my own notation. E.g. using the partition:
$$\{\{a,b,c\},\{2,8,9\},\{\pi,\tau\},\{\alpha,\beta\},\{\delta,\gamma\},\{i\},\{j\}\}$$
This would correspond with the multiset $\{3,3,2,2,2,1,1\}$ or the sequence $(3,3,2,2,2,1,1)$.