Find all possible partitions of n elements with k-sized subsets, where two elements share same set only once
I have n elements that need to be partitioned into x sets, each set has to hold exactly k=4 elements. I need to find all possible partitions with the constraint that each pair of elements only shares the same set once. So if I start with [1 2 3 4] [5 6 7 8] [...], all consecutive partitions cannot hold e.g. [1 2 X X] or [X X 1 3]. sets...