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The Computer Journal 1970 13(3):278-283; doi:10.1093/comjnl/13.3.278
© 1970 by British Computer Society
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Partitioning integers in n dimensions

A. G. Bell * §

Rutherford Laboratory, Chilton, Didcot, UK

In one dimension, it is possible to partition an integer N into 2N–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.

* Atlas Computer Laboratory, Chilton, Didcot, Berkshire

§ Now at Rutherford Laboratory, Chilton, Didcot, Berkshire


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