The number of m-Dimensional Partitions of Eleven and Twelve

By Shalosh B. EKHAD

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(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)

Feb. 16, 2012

Last update of this webpage (but not of article): March 21, 2012.

We have come a long way since 1967! Then Oliver Atkin, Paul Bratley, Ian Macdonald, and John McKay, derived explicit expressions in m, for the number of m-dimensional partitions of n, for n up to 10. Here we "easily" do it for n=11 and n=12, and with better code, and bigger computers, one might be able to go up to n=20. But will we ever be able to know the expression for n=300? I doubt it! So, after all, we have not come such a long way.

Added March 21, 2012: I strongly recommend Suresh Govindarajan's beautiful and deep article, that goes as far as n=25, and contains lots of insightful mathematics of independent interest!

Maple Package

This article is accompanied by Maple package mDimPars .

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