I'm interested in efficiently generating (or iterating over) sets of all monomials of a degree $n$ over $r$ variables,, up to relabeling variables; this can be identified with the set of partitions of $n$ into at most $r$ parts.

More generally, I need to efficiently generate (or iterate over) the set of all sets of $k$ distinct monomials of degree $n$ over $r$ variables, up to relabeling variables. I can think of a few ways to solve both problems, but nothing that isn't extremely computationally intensive. Are there good known algorithms for these computations?