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Bipartite partitions

Published online by Cambridge University Press:  24 October 2008

V. S. Nanda
V. S. Nanda
Affiliation:
Delhi UniversityDelhi, India
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Extract

Asymptotic theory of partitions of unipartite numbers has been extensively investigated after the classic work of Hardy and Ramanujan on the subject. The more complicated problem of bipartite partitions has been only recently broached. Auluck(1) has deduced asymptotic formulae for p(m, n), the number of partitions of the bipartite number (m, n), both for m fixed and n → ∞, and for both m and n tending to infinity in such a way that m/n = 0(1) and n/m = 0(1). It will be shown here that the formula obtained for the first case is actually valid for m = 0(n¼). This proves the conjecture made earlier by the author (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 273 - 277
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Auluck, F. C.Proc. Camb. Phil. Soc. 49 (1953), 72.CrossRefGoogle Scholar
(2)Hardy, G. H.Ramanujan (Cambridge, 1940).Google Scholar
(3)Nanda, V. S. Statistical mechanics and partition theory of numbers (Dissertation, Delhi, 1951).Google Scholar