Fast Algorithm for Generating Ascending Compositions

In this paper we give a fast algorithm to generate all partitions of a positive integer n. Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. It is known the fact that the ascending composition generation algorithm is substantially more efficient than its descending composition counterpart. Using tree structures for storing the partitions of integers, we develop a new ascending composition generation algorithm which is substantially more efficient than the algorithm from the literature.