  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
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 algorithms
from the literature.
