Distribution of Distinguishable Objects to Bins: Generating All Distributions

In this paper we give an algorithm to generate all distributions of distinguishable objects to bins without repetition. Our algorithm generates each distribution in constant time. To the best of our knowledge, our algorithm is the first algorithm which generates each solution in O(1) time in ordinary sense. As a byproduct of our algorithm, we get a new algorithm to enumerate all multiset partitions when the number of partitions is fixed and the partitions are numbered. In this case, our algorithm generates each multiset partition in constant time (in ordinary sense). Finally, we extend our algorithm for the case when the bins have priorities associated with them. Overall space complexity of our algorithm is O(km), where there are m bins and the objects fall into k different classes.