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Fast Algorithms for Generating Integer Partitions

We present two new algorithms for generating integer partitions in the standard representation. They generate partitions in lexicographic and antilexicographic order, respectively. We prove that both algorithm generate partitions with constant average delay, exclusive of the output. The performance of all known integer partition algorithms is measured and compared, separately for the standard and multiplicity representation. An empirical test shows that both new algorithms are several times faster than any of previously known algorithms for generating unrestricted integer partitions in the standard representation. Moreover, they are faster than any known algorithm for generating integer partition in the multiplicity representation (exclusive of the output). 1This research is partially supported by NSERC