Partitioning integers in n dimensions

Abstract

In one dimension, it is possible to partition an integer N into 2^N−1 ordered sets of non-zero integers. Likewise we can partition an integer N into exactly K non-negative integers in

[equation: see PDF]

ways. In the present paper, for particular cases in 2 and 3 dimensions, we obtain exact values (many by counting) of partitions into matrices of non-negative integers. Some implications and formulae are obtained or conjectured.

Received November 1968. 
 


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Atlas Computer Laboratory, Chilton, Didcot, Berkshire

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Now at Rutherford Laboratory, Chilton, Didcot, Berkshire