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Abstract for Allan Adler, Magic N-Cubes Form a Free Monoid

In this paper we prove a conjecture stated in an earlier paper [A-L].
The conjecture
states that with respect to a rather natural operation, the set of 
$N$-dimensional magic cubes forms a free monoid for every integer $N>1$.
A consequence of this conjecture is a certain identity of formal Dirichlet
series. These series and the associated power series are shown to diverge.
Generalizations of the underlying ideas are presented. We also prove
variants of the main results for magic cubes with remarkable power sum
properties.

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