Here's an observation that might lead to a quick way to determine unique bucket combinations.
The set of bucket sizes above is the union of two sets: the set of all unique arrangements of (1 1 1 3), and the set of all unique arrangements of (1 1 2 2). The sum of the numbers is equal to the number of catagories.
This can be generalized to cover different numbers of buckets and different numbers of categories.
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