Random integer partitions with restricted numbers of parts

Currently, no mathematical software includes a function to do this. From combing the literature and peer help cites, though the question has been asked, it doesn't appear to have been solved.

It, at least, has not been implemented into a straightforward computing algorithm. I derive the algorithm, provide a generic code representation for it, provide a specific Python based implementation, and compare the performance to the random partitioning function of Sage (a powerful and generally very fast computer algebra environment). Figures and table are placed at the end of the paper.