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Some computations for m-dimensional partitions

Published online by Cambridge University Press:  24 October 2008

A. O. L. Atkin
Affiliation:
The Atlas Computer Laboratory, Chilton, Didcot; University of Edinburgh; Magdalen College, Oxford; University of Edinburgh
P. Bratley
Affiliation:
The Atlas Computer Laboratory, Chilton, Didcot; University of Edinburgh; Magdalen College, Oxford; University of Edinburgh
I. G. Macdonald
Affiliation:
The Atlas Computer Laboratory, Chilton, Didcot; University of Edinburgh; Magdalen College, Oxford; University of Edinburgh
J. K. S. McKay
Affiliation:
The Atlas Computer Laboratory, Chilton, Didcot; University of Edinburgh; Magdalen College, Oxford; University of Edinburgh

Extract

1. It was known to Euler that p(n), the number of unrestricted partitions of n into non-increasing integral parts, is generated by

with the usual convention that p(0) = 1.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)MacMahon, P. A.Combinatory analysis, vol. 2 (Cambridge, 1916; reprinted Chelsea, New York, 1960).Google Scholar
(2)Chaundy, T. W.Partition-generating functions. Quart. J. Math. (Oxford) 2 (1931), 234240.CrossRefGoogle Scholar
(3)Nanda, V. S.Partition theory and thermodynamics of multi-dimensional oscillator assemblies. Proc. Cambridge Philos. Soc. 47 (1951), 591601.CrossRefGoogle Scholar
(4)Nanda, V. S.Tables of solid partitions. Proc. Nat. Inst. Sci. India, part A 19 (1953), 313314.Google Scholar
(5)Wright, E. M.The generating function of solid partitions. Proc. Roy. Soc. Edinburgh. A 67 (19651967), 185195.Google Scholar
(6)Bratley, P. & McKay, J. K. S.A multi-dimensional partition generator. Algorithm 313, Comm. ACM 10 (1967).Google Scholar