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The number of m-Dimensional Partitions of Eleven and Twelve
By Shalosh B. EKHAD

.pdf
.ps
.tex

(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 .
## Automatically Generated webbook

The
input file
yields

the output file .

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