I'm looking for an algorithm to generate/enumerate all possibilities for partitioning a set of size $n$ to $k$ non-empty subsets, each with size at most $b$.
More specifically, given a set $V$ where $|V|=n$, how to enumerate all possibilities to choose subsets $X_1, ..., X_k \subseteq V$ such that
1) $1 \leq |X_i| \leq b$,
2) $\forall_{i \neq j} X_i,X_j :$ $X_i \cap X_j = \emptyset$,
3) $\bigcup_{i \in \{1,...,k\}} X_i = V$,
Two partitioning are different if they do not have exactly same subsets. The order of subsets doesn't matter.
Can anyone suggest an approach to enumerate such partitioning?
