Powerset without subset with more than k elements

50 Views Asked by At

I am looking for something very similar to the powerset concept but i don't know how to search for it. This is what I found:

Wikipedia defines the powerset as follow:

In mathematics, the power set (or powerset) of any set S is the set of all subsets of S, including the empty set and S itself.

And provides this example: the powerset of {x, y, z} is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}

I am looking for an algorithm that given the number of elements n of a set and the max number of elements in the subsets k can return the powerset of a given set except the empty set and except all the subsets with more than k elements.

Does that set have a name? I mean, how do you call such a set (or the algorithm that produces it)?