Random integer partitions with restricted numbers of parts

Abstract

Note: I have derived a faster and more versatile algorithm that solves this problem, and does not use Sage. It will be posted soon as a preprint on PeerJ, and the code for it is available here: https://github.com/klocey/partitions/blob/master/Python/partitions.py. A preprint of a manuscript revealing a conceptually simple and comparatively fast algorithm for generating uniform 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. Despite being accurate and comparitively very fast, the function herein that implements the algorithm can be made faster. Finally, and the reason I tagged macroecology, maxent, and economics, I reveal how random integer partitioning algorithms such as this can and have already been used to address current and meaningful problems in the natural and social sciences. Also, the pseudo-code needs work. Additionally, the following provided some of the reason for posting this on figshare: http://emckiernan.wordpress.com/2012/09/21/why-i-chose-figshare-for-my-homeless-manuscript/